international conference on differential equations...

International Conference on Differential Equations andControl Problems: Modeling, Analysis and

Computations(ICDECP19)

June 17-19, 2019

ABSTRACT BOOKLETEditted by

Dr. Muslim MalikAssistant Professor, School of Basic Sciences

&Compiled by

A Team of Research ScholarSchool of Basic sciences, India Institute of Technology Mandi

Organised by:

School of Basic SciencesIndian Institute of Technology Mandi, Mandi, H.P.

June 12, 2019

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Contents

Plenary Talks 1PDE: Classical and Modern (Prof. A. K. Nandkumaran) . . . . . . . . . . . . . . . . . . . . . . 1Set Differential Equations: An Overview and Recent Developments (Gnana Bhaskar Tenali) . . 1Mathematical modeling and numerical simulation of particles in fluids of complex geometries (S.

Sundar , Nityananda Roy, Thomas Goetz) . . . . . . . . . . . . . . . . . . . . . . . . . . 1NUMERICAL METHODS TO CAPTURE δ SHOCKS ARISING IN THE SYSTEMS OF PRES-

SURELESS GAS DYNAMICS (G.D. Veerappa Gowda) . . . . . . . . . . . . . . . . . . 2Chaotic behaviour in Differential and Difference Equations with their Fractal Nature (Mohammad

Sajid) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2A New Higher Order Nonliear PDE Model for Effective Image Denoising and its Fourier Spectral

Accurate Solution (B.V. Rathish Kumar) . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Application of Operator Theory in Controllability Analysis (Raju K. George) . . . . . . . . . . 3Parameter Uniform Numerical Schemes for a class of Singularly Perturbed Problems (Kapil Ku-

mar Sharma) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Can parallel bearing surfaces support load- A Tribological Study (Prawal Sinha) . . . . . . . . 6AN OVERVIEW ON INVERSE PROBLEMS ARISING IN FLUID DYNAMICS (JAIME H.

ORTEGA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Differential quadrature in the study of vibrations of non-uniform FG circular plates under hydro-

static peripheral loading and thermal environment (Roshan Lal) . . . . . . . . . . . . . . . 7

Invited Speakers 9A Domain Decomposition Method for Singularly Perturbed Parabolic Reaction-Diffusion Prob-

lems (S.C.S. Rao1 and S. Kumar2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9A Finite element approach to a moving boundary problem with variable thermal conductivity

(Rajeev and Rishabh Daal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Approximation Method for Generalized Fractional Derivatives with Application (Rajesh Pandey) 10Entropy Stable Schemes For Relativistic Hydrodynamics Equations (Harish Kumar) . . . . . . 10

Nonlinear dynamics of Some Complex Ecological Sytems (R. P. Gupta) . . . . . . . . . . . . . 10A high-order quasi-variable meshes two-level implicit compact scheme for solving three-dimensional

nonlinear non-stationary advection-diffusion equation (Navnit Jha) . . . . . . . . . . . . . 11Delayed Mathematical Models of HIV (Saroj Kumar Sahani) . . . . . . . . . . . . . . . . . . . 11

Numerical Solution to Blood Model Navier-Stokes Equations in the Entrance Region of Concen-tric Annuli with Rotating Inner Wall (Srinivasa Rao Nadiminti1; N. Gayathri Devi1 andA.Kandasamy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

On the nondegenerate soliton solutions of Manakov system (M. Senthilvelan) . . . . . . . . . . 12Noise-Induced extinction in an ecological model (Partha Sarathi Mandal) . . . . . . . . . . . . 13Numerical Investigation of Natural Convection of Casson Fluids in a Square Porous Cavity under

the Effects of Thermal Radiation. (Sapna Sharma) . . . . . . . . . . . . . . . . . . . . . 13A PARAMETER-UNIFORM IMPLICIT SCHEME FOR TWO-PARAMETERS SINGULARLY

PERTURBED PARABOLIC PROBLEMS (Devendra Kumar) . . . . . . . . . . . . . . . 14

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Modeling Lithiation Induced Stresses in High-Capacity Electrode Particles with ConcentrationDependent Properties (Poornesh Kumar Koorata) . . . . . . . . . . . . . . . . . . . . . . 14

Understanding molecular transport in a non-conserving systems: The role of interactions (ArvindKumar Gupta) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

SH-wave propagation in monoclinic medium with linearly varying inhomogeneity ( Sumit KumarVishwakarma, Tapas Ranjan Panigrahi, Rupinderjit Kaur.) . . . . . . . . . . . . . . . . . 15

Stabilization and chaos control in multispecies system (Anuraj Singh) . . . . . . . . . . . . . . 16A fourth-order orthogonal spline collocation method to fourth-order boundary value problems (

Anil) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Asymptotic Analysis of Steady Stokes Equations in an Oscillating Domain ( Bidhan Chandra

Sardar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Periodic solutions of vector disease model with harvesting term (Shilpee Srivastava) . . . . . . . 17Mixed Virtual Element Methods for fourth order nonlinear parabolic problems (P. Dhanumjaya,

K. Balaje) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Generation of Uniform Magnetic Flux using different Coil and Plate Arrangement (Md Tarikul

Islam, Md Ataur Rahman Khan, Md. Moniruzzaman Bhuyan, Mohammad Anwar Hossain,Md. Mehedi Hasan Bhuiyan.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Optimization methods and algorithms for non-parallel support vector machines (M. Tanveer) . . 18Elliptic problems with critical growth sign changing nonlinearities. (Sarika) . . . . . . . . . . . 19Modeling and Simulation of dc-dc Converter Based Power Electronics Learning : a review (In-

dresh Yadav) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Solution of two-parameter singularly perturbed one dimensional parabolic equations using non-

polynomial spline ( Shahna, Talat Sultana and Arshad Khan) . . . . . . . . . . . . . . . . 19Creeping flow of a sphere in non-concentric spherical container using slip condition ( M. Krishna

Prasad) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Two-warehouse inventory model with quantity discount policy ( Himanshu Rathore) . . . . . . 20A Comparative Study of Natural Nanouid Convection for Different Initial and Boundary Condi-

tions ( Jyoti Sharma) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Application of finite fractional Hankel-type transformation in Dirichlets problem (V. R. Lakshmi

Gorty) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Existence Results for Fractional Impulsive Delay Differential Equations (Renu Chaudhary ) . . 22OPTIMAL CONTROL IN STOCHASTIC LANDAU-LIPSCHITZ-GILBERT EQUATION (Ananta

K. Majee) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Survey of Nature Inspired Optimization Algorithms in Fuzzy Control Systems (Gaurav Saxena,

Gomathi Bhavani, Shilpee S. Saxena) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23A study of approximate controllability for abstract nonlocal neutral integro-differential equations

with finite delay (Kamaljeet) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Complex plankton dynamics induced by adaptation and defense (Nilesh Kumar Thakur and

Archana Ojha) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23CONVERGENCE ANALYSIS OF TIKHONOV REGULARIZATION FOR NON-LINEAR STA-

TISTICAL INVERSE LEARNING PROBLEMS (ABHISHAKE, GILLES BLANCHARDAND PETER MATHE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

CONTROLLABILITY OF A CLASS OF FRACTIONAL IMPULSIVE DIFFERENTIAL EQUA-TIONS IN A BANACH SPACE (Abdur Raheem) . . . . . . . . . . . . . . . . . . . . . . 24

APPROXIMATE CONTROLLABILITY OF SECOND ORDER SEMILINEAR CONTROL SYS-TEM WITH NONLOCAL CONDITIONS (Urvashi Arora and N. Sukavanam) . . . . . . 25

BOUNDEDNESS AND COMPACTNESS OF WEIGHTED DIFFERENTIATION COMPOSI-TION OPERATORS BETWEEN SOME WEIGHTED SPACES (Zaherr Abbas) . . . . . . 25

Optimization criteria for performance of heat engines working under different constraints ( RenukaRai and Ramandeep Singh Johal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

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Wind turbine blade section optimization using a quantitative study (M. Balachandar) . . . . . . 26Mathematical modeling in health science (Jagdev Singh) . . . . . . . . . . . . . . . . . . . . . 26Fractional exothermic reactions models having constant heat source in porous media with differ-

ent kind of memories (Devendra Kumar ) . . . . . . . . . . . . . . . . . . . . . . . . . . 26Piezothermoelastic continuum subjected to point mechanical load (Anita Devi Thakur) . . . . . 27Dynamical Analysis of Michaelis-Menten Enzyme Reactions (B S Lakshmi and S S Phulsagar) . 27Truss Topology Optimization With Static And Dynamic Constraints Using AISC-ASD ( Ghan-

shyam G. Tejani) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Inuence of Temperature Jump and Concentration Slip on inclined MHD Bioconvection past a ver-

tical porous plate in the presence of Nanoparticles and Gyrotactic Microorganism (RakeshChoudhary and Shalini Jain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Numerical Solution of Linear and Higher order Delay Differential Equations using Coded Differ-ential Transform Method (Giriraj Methi And Anil Kumar) . . . . . . . . . . . . . . . . . . 29

Studies of Hyperloop Vehicle for Transportation: A Review (V. K. Srivastav; Aditya Priyanka;Abhishek Kumar; Shudhanshu Kumar; Anand Raj.) . . . . . . . . . . . . . . . . . . . . . 29

Effect of active case nding on dengue control: Implications from a mathematical model (PankajKumar Tiwari) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Change in Stability Behavior of Spatiotemporal Phytoplankton Dynamics with Different Typesof Functional Response (Randhir Singh Baghel) . . . . . . . . . . . . . . . . . . . . . . . 30

Modelling of duct based photovoltaic thermal (PVT) air collector (Rohit Tripathi1; G. N. Tiwari;Deepak Sharma) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Mathematical model of unstable self-limiting thermo chemical temperature oscillations in Aus-tralian Cycades (Akash Bhavsar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

On the existence and uniqueness of solutions to discontinuous dynamic equation on time scales (Sanket Tikare) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Generalized energy inequality for weak solutions to Damped Navier-Stokes equations (RajibHaloi and Subha Pal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Dynamical study of a delayed SEIRS model with saturated incidence and impulsive vaccination:Effect of household wastes ( Kunwer Singh Mathur) . . . . . . . . . . . . . . . . . . . . . 32

Thermal Convection in Oldroydian Nanouid Layer Saturating a Porous medium with Rigid-freeand Rigid-rigid Boundaries ( Abhilasha) . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Inclined MHD Williamson Fluid Flow with Slip Boundary and Heat and Mass Transfer due toPorous and Melting Stretching Surface with Non-Linear Radiation and Heat Source ( AmitParmar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

(Sandip Rakshit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34An overview to investigate role of rheology on thermal convection in ferrofluids (Veena Sharma) 34(Sheetal Dharmatti ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Paper Presentation 35Numerical Solution of Lane-Emden type Equations Using Multilayer Perceptron Neural Network

Method (Akanksha Verma, Manoj Kumar) . . . . . . . . . . . . . . . . . . . . . . . . . . 35Computational Simulation for Time-Fractional Diffusion Equation with Neumann Boundary Con-

ditions (A.S.V. Ravi Kanth, Neetu Garg) . . . . . . . . . . . . . . . . . . . . . . . . . . . 35On Solution of Fractional Order Advection-Diffusion Equation in Porous Media (Prashant Pandey) 36An exact l1 penalty function method for multi-dimensional first-order PDE constrained control

optimization problem (Preeti) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Numerical solution of Lane-Emden type equations using Adomian decomposition method with

unequal step-size partitions (UMESH, Manoj Kumar) . . . . . . . . . . . . . . . . . . . . 37Solution of Riemann problem for non-ideal magnetogasdynamic flow (Pooja Gupta) . . . . . . 37

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Wave interaction with a tunnel in a sea with bottom undulation (MANISHA, Dr. RAMANABABUKALIGATLA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Subgrid multiscale stabilized finite element analysis for various transport equations (ManishaChowdhury, B.V. Rathish Kumar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Numerical solution for two dimensional space-time fractional reaction diffusion equation (SachinKumar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Mathematical Modeling of Surface wave transference in a piezo-composite media using WKBtechnique (Sonal Nirwal, Sanjeev A. Sahu) . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Modelling of Aeration Efficiency At Gabion Weir (KM. Luxmi, Nand Kumar Tiwari, SubodhRanjan Vajesnayee) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Modelling of scour around spur dykes (Amit kumar, Subodh ranjan vajesnayee, and Nand kumarTiwari) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Modelling the delay dynamics of malware propagation (Sangeeta Kumari) . . . . . . . . . . . . 40Analysis of a density dependent model with discrete delays (Anuraj Singh, Ankit Parwaliya and

Ajay kumar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Approximate analytical solution for shock wave in rotational axisymmetric perfect gas: Isother-

mal flow (G. Nath, Sumeeta Singh) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41MULTIBODY MODELLING OF A RAIL VEHICLE USING MR SUSPENSION SYSTEM

(Deepak Goyal, Sultan Singh, Anil Kumar) . . . . . . . . . . . . . . . . . . . . . . . . . . 41Size-dependent vibration of microplate resonators based on the modified couple stress theory and

three-phase-lag heat conduction model (Harendra Kumar and Santwana Mukhopadhyay) . 42Stability Analysis of a Delay Induced Dynamical Model on Oncolytic Virotherapy (Hitesh K.

Singh and Dwijendra N. Pandey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42On Existence of Solution of First Order Retarded Differential equations with piecewise constant

delays (Aradhana Bandekar, Y. S. Valaulikar ) . . . . . . . . . . . . . . . . . . . . . . . . 43Evolution of weak shock wave in two-dimensional steady supersonic flow in dusty gas (Rahul

Kumar Chaturvedi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Existence and regularity of solutions of fractional differential equations involving Hilfer frac-

tional derivative of order 1 < α < 2 and type 0 ≤ β ≤ 1 (Anjali Jaiswal, D. Bahuguna) . . 43On First Integral Method and Lie Symmetry of meta-mKdV equation (Mahima Poonia, K. Singh) 44On Monotone Method for a First Order Neutral Differential Equation (Mamta Kumari, Y. S.

Valaulikar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Space time fractional nonlinear partial differential system: Exact solution and conservation laws

(Baljinder Kour, Sachin Kumar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Solution of Partially Singularly Perturbed System of Initial and Boundary Value Problems Using

Non-Uniform Haar Wavelet (Akmal Raza, Arshad Khan) . . . . . . . . . . . . . . . . . . 45Existence, Uniqueness and Regularity of Mild Solutions of Fractional Order Navier-Stokes Equa-

tions with Finite Delay (Md Mansur Alam, Shruti Dubey) . . . . . . . . . . . . . . . . . . 45A new approach of operational matrices for hyperbolic partial differential equations (Somveer

Singh, Mani Mehra) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Analytical Solution of 1-D Advection-Dispersion Equation with an Additional Source/Sink term

in the Semi-infinite Aquifer using Dispersion Theory (RohitKumar, Manish Chaudhary andMritunjay Kumar Singh) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Exponentiable objects in Q-TOP (Harshita Tiwari) . . . . . . . . . . . . . . . . . . . . . . . . 46Lp Spectra of Strongly Carleman Pseudo Differential Operators associated with integral transform

(Pragya Shukla ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Metrical fixed point theorems via locally finitely T-transitive binary relations under certain control

functions (Aftab Alam, Mohammad Arif and Mohammad Imdad) . . . . . . . . . . . . . . 47Some Results on Summation-Integral-type Operators and Their Properties (Rishikesh Yadav, Ra-

makanta Meher, Vishnu Narayan Mishra) . . . . . . . . . . . . . . . . . . . . . . . . . . 47

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Kantorovich type generalization of modided Szasz-Mirakjan Operators (Ankita R Devdhara,Vishnu Narayan Mishra) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

θ∗-WEAK CONTRACTIONS AND DISCONTINUITY AT THE FIXED POINT (ATIYA PER-VEEN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

A New Type of Paranorm Intuitionistic Fuzzy Zweier I-convergent Double Sequence Spaces(Hira Fatima) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Relation-theoretic multi-valued θ-contraction]Relation-theoretic fixed point results for Multi-valued(θ,R)-contractions with an Application (Mohammad Imdad , Md Hasanuzzaman and WaleedM. Alfaqih) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Optimal control analysis of an e-epidemic model including firewall effect (Prerna Singh, RanjitKumar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Solution of Differential Algebraic Equations using Coded Differential Transform Method (AnilKumar and Giriraj Methi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Dynamic modeling and control of divided wall distillation multicomponent separation (ManaliKokare, C. S. Mathpati, Ajit Kumar, S. S. Jogwar) . . . . . . . . . . . . . . . . . . . . . . 50

ASYMPTOTIC ANALYSIS OF BOUNDARY OPTIMAL CONTROLPROBLEM ON A GEN-ERAL BRANCHED STRUCTURE (S. AIYAPPAN,A. K. NANDAKUMARAN , AND ABUSUFIAN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Approximate controllability of multi-term time-fractional differential inclusions with nonlocalconditions (Ashish Kumar, Dwijendra N. Pandey) . . . . . . . . . . . . . . . . . . . . . . 51

Approximate Controllability of Semilinear Fractional Evolution Systems with multiple Delays inControl (Abdul Haq, N. Sukavanam) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

CONTROLLABILITY OF NONLOCAL FRACTIONAL ORDER INTEGRO-DIFFERENTIALSYSTEMS WITH TIME VARYING DELAY (Ajay Kumar, N. Sukavanam) . . . . . . . . 52

Development of Higher-order Implicit-Explicit Robert-Asselin Type Time Filters (Praveen K.Maurya, Manoj K. Rajpoot) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Modelling hydraulic characteristics of Gabion weir by soft computing techniques (SiddharthSonkar1, N.K.Tiwari2, and Subodh Ranjan Vajesnayee3) . . . . . . . . . . . . . . . . . . . 53

Effect of radiative heat transfer on the growth and decay of acceleration waves in non-ideal mag-netogasdynamics (Shobhit Kumar Srivastava) . . . . . . . . . . . . . . . . . . . . . . . . 53

Wind turbine blade section optimization using a quantitative study (M.Balachandar, B.U RajaRamakrishnaa and N.Ramanan) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Hybrid impulsive effects on quasi-synchronization of neural networks with parameter mismatchand mixed time-varying delays (Rakesh Kumar) . . . . . . . . . . . . . . . . . . . . . . . 54

Novel divergence measure for refined single valued neutrosophic sets and its utility in decisionmaking (Adeeba Umar, R. N. Saraswat) . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Analysis of Surface Seismic Waves in Piezomagnetic Layered Structure (Suman Goyal, SanjeevAnand Sahu ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Velocity Profile of Shear Horizontal (SH) surface waves in Bi-layered FGPM/Porous Piezoelec-tric Plate (Shreeta Kumari, Sanjeev A. Sahu1, Kamlesh K. Pankaj) . . . . . . . . . . . . . 55

Thermal analysis of convective-radiative pin fin with MATLABs inbuilt tool Pdepe consideringtemperature dependent properties (Sarvjeet Singh, Rohit K. Singla) . . . . . . . . . . . . . 56

Effect of Solar Flare on climate change by Solar Flare Wave Model and Its Application (SumitBainjwan, Vishal Dhakane ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Modelling Aeration Efficiency of Hydraulic Jump at Under Sluice Gate (Nirali Vashishth, SubodhRanjan Vajasneyee, and N K Tiwari) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Interference of Closely Placed Bridge Piers On Local Scour (Anuj Kataria1 and Baldev Setia2) . 57The influence of vegetation type and cover on rain garden hydrological performance ( Anuj

kumar1, Krishna Kumar Singh2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

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Non-linear Deformation of Thin Elastic Model Membrane Driven by Electrostatic Forces (AmarShrivastava and Paritosh Mahata) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Integral Equation technique for solution of diffraction of obliquely incident water waves by rect-angular asymmetric trench (1Amandeep Kaur, 1S. C. Martha, 2A. Chakrabarti) . . . . . . . 59

Life Cycle Analysis (LCA) of Low Volume Rural Hill Roads (Akhilesh Nautiyala, Sunil Sharmab) 59Flow Characteristics at the Confluence of WJC and SYL Canals (Pradeep kumar1 and Baldev

Setia2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60TREND ANALYSIS OF HYDROLOGICAL PARAMETERS OF TWO AGRARIAN DISTRICTS

OF HARYANA, INDIA (Mridula Sharma1, Arun Goel) . . . . . . . . . . . . . . . . . . . 60GEOMETRIC PROPERTIES OF THE EXTENDED τ GAUSS HYPERGEOMETRIC FUNC-

TION (R. ROY AND R. K. JANA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Theoretical Investigation of Networks of Interacting Exclusion Processes (Tripti Midha, Arvind

Kumar Gupta) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

CNA 63On solvability of some nonlinear functional-integral equations with applications (Amar Deep and

Deepmal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Effect of Solar Flare on climate change by Solar Flare Wave Model and Its Application (Sumit

Bainjwan, Vishal Dhakane ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Entropy Generation in the Flow of Sisko Nanofluids over a Stretching Sheet (Ankita Bisht and

Rajesh Sharma) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Adomian Decomposition Method for the solution of a Parial Differential Equations of Fractional

Order ( Pratibha Verma and Manoj Kumar) . . . . . . . . . . . . . . . . . . . . . . . . . 64A new efficient numerical scheme for variable order fractional sub-diffusion equation ( Sarita

Nandal, Dwijendra Narain Pandey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Transverse Hydromagnetic and Media Permeability Effect on Mixed Convective Flow in a Chan-

nel Filled by Porous Medium with asymmetric wall heating condition ( Km. Renu, AshokKumar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Numerical study of entropy generation in porous medium vertical channel subjected to mixedconvection ( Paresh Vyas, Kusum Yadav) . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Curvelet optimized method for solving partial differential equations on general manifolds ( DeepikaSharma, Kavita Goyal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Solution of inverse fractional Fisher’s equation by differential quadrature method ( G. Arora,Pratiksha) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Uncertainty propagation using Wiener-Bspline wavelet expansion (Navjot Kaur and Kavita Goyal) 67Entropy Generation Analysis For A Micropolar Fluid Flow Due To A Moving Surface (Paresh

Vyas, Manvi Adha) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Mathematical analysis of surface wave propagation in Functionally Graded Material using WKB

approximation (Sonali Mondal, Sanjeev A. Sahu) . . . . . . . . . . . . . . . . . . . . . . 68Data bounded WENO reconstructions of high order schemes (Ritesh Kumar Dubey, Sabana Parvin) 68Solution of singular fractional Lane-Emden type equations by an analytical technique (Anoop

Kumar, Seema) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69NUMERICAL APPROACH FOR A COUPLED SYSTEM OF SINGULARLY PERTURBED

CONVECTION-DIFFUSION PROBLEM WITH NON-SMOOTH DATA (Aarthika K, V.Shanthi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

THRESHOLDING FUNCTIONS INVOLVED IN THE WAVELET BASED DENOISING METHOD(Princess Raina and Zaheer Abbas ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

One-dimensional solute migration model with first-order production term in semi-infinite porousmedia (Affreen Akhter, Mritunjay Kumar Singh ) . . . . . . . . . . . . . . . . . . . . . . . 70

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STUDY OF FRACTIONAL THERMOELASTIC PROBLEM WITH MOVING HEAT SOURCE(Jaya Bikram, G.D. Kedar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Numerical Solution of Fractional Order Non-Conservative Advection-Diffusion Equation (AnupSingh and S. Das) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Finite element analysis of semilinear time-fractional diffusion equation (Dileep Kumar∗a, Sud-hakar Chaudharyb, V.V.K Srinivas Kumar∗) . . . . . . . . . . . . . . . . . . . . . . . . . 71

Effect of Aspect Ratio on Natural Convective flow in a Rectangular Enclosure Occupied byAnisotropic Porous Medium (Ashok Kumar, Ajay Kumar∗1, Km. Renu and M. S. Rawat) . . 72

NUMERICAL SOLUTION OF DAMPED FORCED OSCILLATOR PROBLEMS BY OPER-ATIONAL MATRIX OF INTEGRATION (Dr. Mithilesh Singh1, Seema Sharma2, SunilRawan3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Flow of a Hydromagnetic Fluid through a porous medium between permeable beds with dampingeffects. (Ravi Kumar and B.G. Prasad) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Finite element solution of a problem on coupled thermoelasticity for functionally graded ma-terial by two different approaches for time domain (Om Namha Shivay∗ and SantwanaMukhopadhyay) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Simulation of Heat transfer of Ferro fluid in Cylindrical Micro-Channel (Ramesh kumar1∗, HarryGarg2, S.K Dhiman1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Computational Analysis of Bed of a Mobile Channel (Atul Ailawadhi1 Baldev Setia2,) . . . . . . 74Numerical study on MHD flow of nanofluid due to a rotating disk with heat generation and partial

slip effect (V. K. Chaurasiya, Ramayan Singh and Rajat Tripathi) . . . . . . . . . . . . . . 75Fibonacci collocation method to solve nonlinear space-time fractional order advection-reaction-

diffusion equation (Kushal Dhar Dwivedi) . . . . . . . . . . . . . . . . . . . . . . . . . . 75Abhishek Verma,N K Singh 1 1Department of Mechanical Enginee (Abhishek Verma,N K Singh ) 76Numerical study of inclined stretchable partially heated enclosure filled with nanofluid (Pentyala

Srinivasa Rao, Anil Kumar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

CP 77Dynamic modeling and control of divided wall distillation multicomponent separation (Manali

Kokare, C. S. Mathpati, Ajit Kumar, S. S. Jogwar) . . . . . . . . . . . . . . . . . . . . . . 77

DE 79Existence of mild solutions for neutral fractional functional integro-differential equations with

non instantaneous impulses of order α ∈ (1, 2) (Pallavi Bedi, Anoop Kumar) . . . . . . . . 79CHARACTERIZATION OF POLARIZED SHEAR WAVES IN POROUS-PIEZOELECTRIC

MEDIUM OVER A HETEROGENEOUS ELASTIC SUBSTRATE CONTAINING POINTSOURCE (SUBHASHIS KARMAKAR*, SANJEEV A. SAHU) . . . . . . . . . . . . . . . . 80

Smooth stable manifold for delay equations with arbitrary growth rates (Lokesh Singh*, Dhiren-dra Bahuguna) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Approximation of fixed points and the solution of delay differential equation via new iterativescheme (Javid Ali, Faeem Ali) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Classification of Some Functional Differential Equations with Constant Coefficients to SolvableLie Algebras (Jervin Zen Lobo, Y.S Valaulikar) . . . . . . . . . . . . . . . . . . . . . . . 81

MD 83Speech analysis based emotion-aware healthcare system (Akshita Abrol, Praveen K. Lehana) . . 83Analysing the efficiency of hexagonal microfluidic fuel cell (Jyoti Lalotra, Praveen K. Lehana) . 83Varying Trends of Smart Bandaging (Priti Rajput, Praveen K. Lehana) . . . . . . . . . . . . . . 84Varying Trends of Smart Bandaging (Verasis Kour, Praveen K. Lehana) . . . . . . . . . . . . . 84Impact of rigid surface on dispersion and damping characteristic of Love-type wave propagating

in an initially stressed piezoelectric layer (Shishir Gupta, Rachaita Dutta, Soumik Das) . . 85

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Discharge characteristic of multi-cycle triangular labyrinth weir (Subhankar Das, Parthajit Roy) 85Geometrical changes in journal bearing due to piezoelectric actuators (Aayush Trivedia, Wolfgang

Seemannb, and Mohammad Talhac) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Studies of Hyperloop Vehicle for Transportation: A Review (V.K. Srivastav1, Aditya Priyanka1,

Abhishek Kumar1, Shudhanshu Kumar1, Anand Raj1) . . . . . . . . . . . . . . . . . . . . 86Studies of Hyperloop Vehicle for Transportation: A Review (V.K. Srivastav1, Aditya Priyanka1,

Abhishek Kumar1, Shudhanshu Kumar1, Anand Raj1) . . . . . . . . . . . . . . . . . . . . 86Bivariate Bernstein-Schurer-Stancu type GBS operators based on (p, q)-integers (Mohd. Ahasan

and M. Mursaleen) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Uncertain eigenvalue analysis of finite element modelled functionally gradient arches (Moham-

mad Amir#, Mohammad Talha∗) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Studies of Hyperloop Vehicle for Transportation: A Review (V.K. Srivastav1, Aditya Priyanka1,

Abhishek Kumar1, Shudhanshu Kumar1, Anand Raj1) . . . . . . . . . . . . . . . . . . . . 87Second-order statistics of the elastic buckling of skewed functionally gradient plates with material

uncertainties (Mohammed Shakir1∗ and Mohammad Talha 2) . . . . . . . . . . . . . . . . 88Estimation of mean rainfalls using Geostatistical techniques in Kabul River Basin, Afghanistan

(Shamsullah Sultani1 1∗, Arun Goel 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88COMPUTATIONAL AND EXPERIMENTAL STUDIES OF FLY ASH BRICK (V. K. Srivastav1

R. K. Singh1, R. Kumar1, A Kumar1, A. K. Chhotu1, A. R. Paul2) . . . . . . . . . . . . . . 893D Stress Analysis of Reinforced Concrete Sleeper (Tejas M. Gondhalekar1 and S. K. Panigrahi2) 89Triple-diffusive convection with more realistic two temperature model for nanofluids (Urvashi

Gupta) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Design of wind turbine for the application of desalination process (S.Ramachandran1 ,S.Vasanth1∗,S.Devarajan1) 90Enhancing software reliability through the generalized inflection S-shaped failure rate with testing

effort in growth model (Vishal Pradhan1, Ajay Kumar1 and Joydip Dhar1) . . . . . . . . . 91Experimental and numerical study of blood ow characteristics in human coronary artery with

plaque (Wasim Saliha,Pradeep Kumarb, Parmod Kumarc, Mohammad Talha ∗) . . . . . . . 91Numerical simulation for radial stress and displacement of jet engine Exhaust pipe (Y.K.Singh1

and S. K. Panigrahi2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

MM 93Cross-diffusion induced Turing and non-Turing patterns in Rosenzweig-MacArthur model (Nayana

Mukherjee) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93POPULATION DYNAMIC CONSEQUENCES OF FEARFUL PREY IN A SPATIOTEMPO-

RAL PREDATOR-PREY SYSTEM (Ranjit Kumar Upadhyay, Swati Mishra ) . . . . . . . 93A Mathematical model for Human Papillomavirus and its impact on cervical cancer in India (R

Praveen Kumar, K Murugesana) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Predator-prey system: Herd behavior and anti-predator traits contribute in enriching the evolution

of stronger prey defence (Rajat Kaushik, Sandip Banerjee) . . . . . . . . . . . . . . . . . 94Effect of porosities with and without fractures on propagation of SH wave: case wise study

(Shishir Gupta, Soumik Das, Rachaita Dutta ) . . . . . . . . . . . . . . . . . . . . . . . . 95Dynamical behaviour of predator-prey systems with variation of Allee function in predator’s

growth: Structural sensitivity analysis (Deeptajyoti Sen) . . . . . . . . . . . . . . . . . . . 95MODELLING OF SEDIMENT EXCLUDER (Dibyendu Das1, N.K.Tiwari2,Subodh Ranjan vajesnayee3

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96FEM Analysis of Adhesively Bonded Composite Patches (V.Divakar1 and S. K. PanigrahiR2) . . 96Solving a variational inclusion problem with its corresponding resolvent equation problem in-

volving XOR-Operation (1Rais Ahmad,2Javid Iqbal,2Shakeel Ahmed,1Saddam Husain) . . 97Modeling and Simulation of Nylon Liner Shaped Charge Jets (Yadav Ombir Singh∗, Nimje S.V

and Choudha P.K.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

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Modeling the impact of sanitation and awareness on the spread of infectious diseases (RajanishKumar Raia, A.K. Misraa∗, Yasuhiro takeuchib) . . . . . . . . . . . . . . . . . . . . . . . 98

Modelling of scour around Cylindrical Piers (M Vignesh1, Subodh Ranjan Vajesnayee2, and N KTiwari3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

NA 99Continuous wavelet transform of Schwartz tempered distributions in S ′(Rn) (Jay Singh Maurya) 99Continuous fractional wave packet system in Sobolev type space (Manab Kundu and Akhilesh

Prasad) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Cech proximity relation and Rough Set Theory (Pankaj Kumar Singh, Surabhi Tiwari) . . . . . 100A Comparative Study of Monitor function in Mesh Reconstruction (Prabhat Mishra and Ritesh

Kumar Dubey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Studies of Hyperloop Vehicle for Transportation: A Review (V.K. Srivastav1, Aditya Priyanka1,

Abhishek Kumar1, Shudhanshu Kumar1, Anand Raj1) . . . . . . . . . . . . . . . . . . . . 101MESHLESS METHOD FOR THE NUMERICAL SOLUTION OF SPACE AND TIME FRAC-

TIONAL WAVE EQUATION (Hitesh Bansu ,Sushil Kumar) . . . . . . . . . . . . . . . . 101Semi-Analytical Solution of Fractional Convection-Dispersion Equation by using Conformable

Derivative Approach and Homotopy Analysis Method (Manish Chaudhary∗, Rohit Kumarand Mritunjay Kumar Singh) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Convergence Analysis of New Hybrid Scheme for Singularly Perturbed Parabolic Problems withInterior Layers (Mr. Narendra Singh Yadav1 Dr. Kaushik Mukherjee) . . . . . . . . . . . . 102

Fractional calculus for k-Mittag-Leffler function of two variables with the kernel F3 (Owais Khan) 102Approximation By Modified Lupas Operators Based On (p, q)Integers (M. Mursaleena, Zaheer

Abbasb and Mohd Qasimb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103HURWITZ-LERCH ZETA FUNCTION AND SOLUTION OF FRACTIONAL KINETIC EQUA-

TION (Raghib Nadeem) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Computation of fractional integrals and derivatives for the product of Mathieu-type series and

generalized Mittag-Leffler function (Mohd Saif ) . . . . . . . . . . . . . . . . . . . . . . . 103Turing patterns in a Prey-Predator Model with Hassell-Varley Functional Response (Vikas Kumar

and Nitu Kumari) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Invited Talks 105

Author Index 107

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Plenary Talks

PDE: Classical and ModernProf. A. K. Nandkumaran

Department of Mathematics, Indian Institute of Science, Bangalore- 560012, India.Email: [email protected]

In this talk, we briefly present the developments of Partial Differential Equations (PDE) as a modellingfor classical problems. We, then realize the importance of analysis in the study of PDEs. We see how theweak solutions appears naturally and some of the developments. We touch upon various equations arisingin the literature, conservation laws, calculus of variations to optimal control problems. We also see thenotions like weak solutions, Sobolev spaces, viscosity solutions etc.

Set Differential Equations: An Overview and Recent DevelopmentsGnana Bhaskar Tenali

Department of Mathematical Sciences Florida Institute of Technology Florida, USA.Email: [email protected]

The study of Set Differential Equations (SDEs) is fast evolving as an independent discipline. In thistalk, we give an outline of fundamental and recent results on the existence and uniqueness of solutions ofSDEs in Banach spaces and in Frechet spaces. We also discuss the stability theory for the solutions ofSDEs, using the standard methods as well as methods based on geometry of convex bodies and the theoryof mixed volumes.

Mathematical modeling and numerical simulation of particles in fluids of complexgeometries

S. Sundar , Nityananda Roy, Thomas GoetzHEAD, Department of Mathematics

Indian Institute of Technology Madras (IIT Madras)Chennai 600 036, India.Email: [email protected]

We are inquisitive to study on the topic regarding the behavior of soft and hard particles in complex flowsystem. In case of soft particles like droplet and bubble we applied population balance equation coupledwith hydrodynamics and for hard particles we applied Newtons and Eulers equations of motion. For softparticles our motive is to develop mathematical model as well as numerical methods to predict the numberdensity, volume fraction of particles in complex flow system. In case of hard particles we are trying toconstruct a model of particles sedimentation considering that the particles attraction force works betweenthe particle and the obstacle wall. Our purpose is to constitute a model about the behavior of non sphericalparticles in complex flow system.

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NUMERICAL METHODS TO CAPTURE δ SHOCKS ARISING IN THESYSTEMS OF PRESSURELESS GAS DYNAMICS

G.D. Veerappa GowdaTIFR Centre for Applicable Mathematics PB No:6503, Yelahanka New Town,Bengaluru-560065.

Email: [email protected]

In this study, a class of Godunov-type solvers is formulated for a weakly hyperbolic pressureless gasdynamics system. In one dimension the system is written as

ρt + (ρu)x = 0,

(ρu)t + (ρu2)x = 0. (0.0.1)

An Engquist-Osher type solver is constructed utilizing the homogeneity property. Again on introducing anew variable v = ρu in the second equation of (0.0.1), one can treat flux function ρu2 = v2/ρ as a convexfunction in v with discontinuous coefficient 1

ρ. Now by using the idea of the discontinuous flux, a Godunov-

type interface flux is constructed forv2

ρwhich is again utilized in the first equation to determine its interface

flux. The results obtained from this conservative Godunov type solver generate steady shocks with almostof double the strength as compared to other Godunov type solvers. Since the considered systems satisfy thegeneralized Rankine-Hugoniot conditions, a non-conservative version of the above schemes are proposedand tested on various numerical examples. In particular, non-conservative Godunov-type solver developedhere outclass other well-known solvers in capturing stationary shock waves. These Godunov-type solversare also extended to a two-dimensional pressureless system. Computational results clearly show a non-conservative Godunov-type solver captures steady shocks considerably better than third order DG schemein two dimensions. It is also shown for augmented Burgers systems non-conservative version captures evenmoving delta-shocks with exceptional strengths.

Chaotic behaviour in Differential and Difference Equations with their FractalNature

Mohammad SajidCollege of Engineering, Qassim University, Saudi Arabia


The real problems and issues on the frontiers of modern scientific, technological, economical, and socialresearches are nonlinear in nature. It seems that it is a nonlinear world. Most nonlinear systems are notpossible to solve analytically or much harder to analyze. During the last three decades of the 20th century,the excessive studies of nonlinear dynamics shows that chaos occurs widely. Before this period, the chaoswas generally regarded as a nuisance and designed out of the model. Many researches show that chaoticphenomena are completely deterministic and characteristic for typical nonlinear systems. Numerous re-searches are resolved by using chaos theory in the last few decades. Chaos exists everywhere in the worldsince most of the problems are nonlinear in nature. Chaos is developing in a new way that influences theworld around us, and consequently also influences our ways of approaching, analyzing and solving prob-lems. As we are aware that the technological advances require a deep understanding of physical processesin engineering and science. A variety of such physical process can be modelled as differential equations anddifference equations. The main purpose of this presentation is to explore chaotic behaviour in differentialand difference equations with their fractal nature; and brings attention of mathematicians and engineers forthose who are interested in chaotic behaviour and want to introduce something new and advanced method-ology. Fortunately, chaos is one of them. To achieve our target here, we provide some techniques to studychaos in mathematical modeling arising from differential and difference equations. In many cases, chaos

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can be effectively visualized by using fractals. The demonstration of some mathematical models associatedto chaos with their applications is explored here.

Keywords: Chaos, Difference Equations, Differential Equations, Fractals.

A New Higher Order Nonliear PDE Model for Effective Image Denoising and itsFourier Spectral Accurate Solution

B.V. Rathish KumarDepartment of Mathematics, IIT kanpur, India.


In this talk we will introduce a new higher order nonlinear PDE model for image denoising and demon-strate its ability to denoise without any staircase effect as routinely noticed with lower order PDE models.We use convexity splitting based fourier spectral scheme for the computation of the denoised version ofa given noisy image. Fourier spectral method is both accurate and faster than other standard approaches.Performance of the model and the method will be discussed based on the bench mark test images and therelated computational metrics.

Application of Operator Theory in Controllability AnalysisRaju K. George

Department of Mathematics,Indian Institute of Space Science and Technology,

Thiruvananthapuram - 695 547, Kerala, India.E-mail: [email protected]

Controllability is one of the fundamental properties of a controlled dynamical systems which ensuresthe ability of a dynamical system to steer the state of the system from any initial state to a desired finalstate in a given time interval. R.E. Kalman [3] introduced the notion of controllability in 1960’s and es-tablished the complete characterization of controllability for linear systems in finite dimensional spaces.Subsequently many researchers extended the controllability notion for nonlinear systems, especially forsemilinear systems, ( see [2]), of the form:

dx

dt= A(t)x+B(t)u+ f(t, x(t)), 0 ≤ t0 < t ≤ t1 <∞, (0.0.2)

x(t0) = x0

where, for each t ∈ [t0, t1], the state vector x(t) ∈ Rn, the control vector u(t) ∈ Rm, A(t), B(t) are matrixvalued functions and the function f : I × Rn → Rn is a nonlinear function. Many of the powerful tools ofnonlinear analysis like fixed point theory, monotone operator theory, set-valued function theory, Lie Groupapproach etc. are employed to establish controllability of such systems, refer to [3].

In this talk, we discuss the notion of controllability for both linear and nonlinear systems in finite dimen-sional and infinite dimensional settings. We show how the theory of monotone operators and fixed pointtheory are used to establish controllability results.

Bibliography

[1 ] R.W. Brockett, Finite Dimensional Linear Systems, SIAM, Philadelphia (2015).

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[2 ] R. K. George, Approximate Controllability of Non-autonomous Semilinear Systems. NonlinearAnalysis, Theory, Methods and Application, Vol.24, pp.1377-93,( 1995).

[3 ] J. Klamka, Controllability and Minimum Energy of Control, Springer, (2019).

Parameter Uniform Numerical Schemes for a class of Singularly PerturbedProblems

Kapil Kumar SharmaDepartment of Mathematics, South Asian University, New Delhi, India.

Email: [email protected](Jointly with)

Pankaj Mishra Research Scholar, SAU, New Delhi, India.Amiya K Pani, Indian Institute of Technology, Mumbai, India.

Graeme Fairweather, Mathematical Reviews, American Mathematical Society, USA.

The singularly perturbed differential equations are ubiquitous in mathematical modeling of several reallife phenomena and provide a realistic simulation of the phenomena. The singularly perturbed differentialequation is characterized by a parameter, which is multiplied in a highest order derivative term. The solutionof this class of differential equations exhibits layer behavior in narrow regions. These narrow regions areknown as layer region and rest part of the domain is known as outer region. In this talk, there is an attemptto introduce the audience with singularly perturbed problems and challenges in the development of thenumerical methods to solve this class of problems. Further, the parameter uniform numerical schemesbased on orthogonal spline collocation are presented.

Can parallel bearing surfaces support load- A Tribological StudyPrawal Sinha

Department of Mathematics and Statistics Indian Institution of Technology Kanpur, India.E-mail: [email protected]

Tribological studies are as old as the wheel. For hydrodynamic lubrication it is imperative that the bear-ing surfaces be inclined. However over the last 70 years studies have suggested that even parallel surfacescan support some load. Several researchers have experimentally investigated the thermal influence on theload carrying capacity of parallel slider bearings. The results of all these researchers show the existence of alifting force (load capacity) even when parallel bearings are in operation. However, the precise causes whichare responsible for this phenomenon are not precisely understood. Rodkiewicz and Sinha [1] provided anorderly analysis which elaborates on the mechanisms that may be responsible for the fluid generated liftingforce. It is indicated that the consideration of the fore region pressure together with the density variationmay lead to a useful load support with a reduced friction, even for parallel sliding bearing. In recent yearsresearchers have focused attention on thermohydrodynamic analysis of rough surfaces. Recently Sinha andGetachew [2] numerically analyzed the combined effect of thermal and surface roughness on the perfor-mance of an infinitely long slider bearing using stochastic approach. In their study two types of roughness:longitudinal roughness and transverse roughness were considered. The analysis indicated that for parallelsliders some load capacity may be generated due to the combined effect for both types of roughness. Allof the works that has appeared in literature do not seem to conform to the experimental results obtained forparallel sliders. It seems natural that as a consequence of heating, there would be a thermal expansion inasperities and probably a distortion of the slider surface. Thus in this study the effect of thermal distortionof the slider and asperities on different characteristics of an infinitely tilted pad rough slider bearing is ana-lyzed using stochastic approach.

References

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[1 ] Rodkiewicz, C.M., Sinha, Prawal.: On the Lubrication Theory: A Mechanism Responsible forGeneration of the Parallel Bearing Load Capacity, Trans. ASME, J. Lub. Tech. 115, 584-590 (1993)

[2 ] Sinha, Prawal and Getachew A. (2009), THD analysis for slider bearing with roughness: specialreference to load generation in parallel sliders, Acta Mechanica, 207, Issue 1, pp 11.

AN OVERVIEW ON INVERSE PROBLEMS ARISING IN FLUID DYNAMICSJAIME H. ORTEGA

Department of mathematical Engineering and Center for Mathematical Modeling, UMI 2807-CNRS UCHILEUNIVERSIDAD DE Chile Santiago- Chile.

Email : [email protected]

Inverse problems became an interesting topic of study in several areas of knowledge. The main idea isto recover some parameters of characteristic of the media which can not be obtained directly. Some areas ofapplication are optic, radar medical imaging, signal processing, nondestructive testing, astronomy, amongothers.

In this talk we will present some ideas on the called inverse geometrical problems, in which we areinterested in to recover some geometrical properties of the media by means of boundary measurements,arising in fluid dynamics. In the last years, there is an extensive literature in this topic. We will presentsome ideas on the identifiability and stability results, we will present also some numerical experiments.

Differential quadrature in the study of vibrations of non-uniform FG circularplates under hydrostatic peripheral loading and thermal environment

Roshan LalDepartment of Mathematics, IIT Roorkee, India

[email protected]

In the present study, the effect of exponential thickness variation and hydrostatic peripheral loadinghave been analyzed on axisymmetric vibrations of functionally graded circular plate subjected to non-lineartemperature rise along the thickness on the basis of Kirchoffs plate theory. The plate is graded in thicknessdirection and controlled by a power law index. The mechanical properties of the such a plate material areassumed to be temperature-dependent. Keeping the uniform thermal environment over the top and bottomsurfaces, the equations for thermo-elastic equilibrium and axisymmetric motion for such a plate model havebeen derived by Hamiltons principle. Employing generalized differential quadrature method, the frequencyequation for clamped boundary condition has been obtained, which has been solved numerically using theMATLAB. The lowest three roots so obtained have been retained as the frequencies for the first three modesof vibration. The influence of various parameters such as thickness parameter, power law index, in-planeforce parameter and temperature difference has been analyzed on the vibration characteristics of the plate.By allowing the frequency to approach zero, the critical buckling loads with varying values of other param-eters have been computed. A study with linear as well as uniform temperature rise has also been performed.The validity of the present technique is confirmed by comparing the results with the published work.

Keyword : Differential quadrature, vibration, functionally graded circular plates, exponential thick-ness variation, temperature-dependent material, Non-linear temperature distribution.

5

Invited Speakers

A Domain Decomposition Method for Singularly Perturbed ParabolicReaction-Diffusion Problems

S.C.S. Rao1 and S. Kumar2

1Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India.2Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, India.

Emails: [email protected], [email protected]

In this work we consider a singularly perturbed parabolic reaction-diffusion problem that exhibitsparabolic boundary layers. To solve this problem numerically, we develop a domain decomposition methodof Schwarz waveform relaxation type. We also provide error analysis of method. The numerical approxi-mations generated from the method are proved to be uniformly convergent, having first order in time andalmost fourth order in space. Moreover, faster convergence of the algorithm is established for small per-turbation parameter. The method is then extended to a coupled system of singularly perturbed parabolicreaction-diffusion problems. Numerical results are given in support of theoretical findings.

A Finite element approach to a moving boundary problem with variable thermalconductivity

Rajeev and Rishabh DaalDepartment of Mathematical Sciences,

Indian Institute of Technology (Banaras Hindu University)Email: [email protected]

Moving boundary problems are nonlinear problems and involves a moving interface/ boundary whichmakes it difficult to get its exact solution. In this article, we consider a mathematical model of a mov-ing boundary problem that includes variable thermal conductivity and a constant temperature at the leftboundary of the domain. The temperature distribution and moving boundary involved in the model arecalculated with the aid of similarity variables and Galerkin finite element method. To show the accuracyof the calculated solution, the comparisons between our solution and an analytical solution (for a particularcase) are demonstrated through tables. In this study, it is seen that the proposed approach is simple andsufficiently correct to estimate the solution of various moving boundary problems governing the process ofphase change.

Keywords: Phase change problem, variable thermal conductivity, similarity variable, Galerkin residualapproach.

AMS subject classifications : 35R37, 80A22, 80M10.

7

Approximation Method for Generalized Fractional Derivatives with ApplicationRajesh Pandey

Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi-221005, India.Email: [email protected]

We discuss generalized fractional derivatives and approximation methods for these fractional deriva-tives. In special case, generalized fractional derivative reduces to Riemann-Liouville and Caputo factionalderivatives. For application of the approximation schemes, fractional advection diffusion equation is con-sidered.

Entropy Stable Schemes For Relativistic Hydrodynamics EquationsHarish Kumar

Department of Mathematics, IIT Delhi, [email protected]

In this work, we propose high order finite difference schemes for the equations of relativistic hydrody-namics, which are entropy stable. The crucial components of these schemes are a computationally efficiententropy conservative flux and suitable high order entropy dissipative operators.

We first design a higher order entropy conservative flux. For the construction of appropriate entropydissipative operators, we derive entropy scaled right eigenvectors. This is then used with ENO based signpreserving reconstruction of scaled entropy variables, which results in higher order entropy stable schemes.Several numerical results are presented up to fourth order to demonstrate entropy stability and performanceof these schemes.

Nonlinear dynamics of Some Complex Ecological SytemsR. P. Gupta

Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, [email protected]

The purpose of this presentation is to offer a detailed nonlinear dynamical behavior of some ecologicalsystem. The proposed systems consider different types of functional response and nonlinear harvestingfunctions. Positivity and boundedness of the solutions of the systems are guaranteed. The uniform persis-tence of the systems are discussed. The stability and bifurcation analysis of various steady states of thesesystems are analyzed in detail. The local existence and stability of limit cycle emerging through Hopf-bifurcation are given. The emergence of homoclinic loop has been shown through simulation when thelimit cycle arising though Hopf-bifurcation collides with a saddle point. Using numerical examples it isshown that these systems admit periodic, quasi-periodic and chaotic solutions. Many forms of complexitiessuch as chaotic bands (including periodic windows, period-doubling bifurcations, period-halving bifurca-tions and attractor crisis) and chaotic attractors have been observed. Sensitivity analysis is carried out andit is observed that the solutions are highly dependent to the initial conditions. It is pointed out that even ifthe systems are simple it may exhibit chaotic dynamics.

8

A high-order quasi-variable meshes two-level implicit compact scheme for solvingthree-dimensional nonlinear non-stationary advection-diffusion equation

Navnit JhaFaculty of Mathematics and Computer Science, South Asian University, Chanakyapuri,New Delhi, India-110 021

[email protected]

A two-level implicit compact-scheme on quasi-variable meshes is reported for solving three-dimensionalsecond-order mildly nonlinear parabolic partial differential equations. The new nineteen-point compactscheme exhibit fourth-order accuracy in space and second-order in time on a variable spacing mesh networkas well as on uniformly spaced mesh points. We have also developed an operator- splitting technique to im-plement the alternating direction implicit method for computing the advection-diffusion equation. Thomasalgorithm computes each tri-diagonal matrix that arises from alternating direction implicit steps in min-imal computing time. The operator-splitting method is unconditionally stable. The improved accuracy isachieved at a lower cost of computation and stor- age, because the spatial mesh parameters tune the mesheslocation according to the behaviour of solution values. The new method successfully applied to the Navier-Stokes equation, advection-diffusion equation and Burger’s equation for the computational illustrations thatcorroborate the order, accuracies, and robustness of the new high-order implicit compact scheme. The mainhighlight of the present work lies in obtaining a fourth-order scheme on a quasi-variable mesh network, andtheir superiority over the corresponding uniform meshes high-order compact scheme.

Keywords:Quasi-variable mesh network; Compact scheme; ADI scheme; Advection-diffusion equa-tion; Navier-Stokes equation; Burger’s equation; Stability.Mathematics Subject Classification : 35G61; 65M06; 65M12; 65N06; 35Q35.

Delayed Mathematical Models of HIVSaroj Kumar Sahani

Department of Mathematics, South Asian University, Akbar Bhawan Chankyauri, New [email protected]

n this lecture, we consider a delayed HIV model with apoptosis of cells that resembles a lot of character-istics HIV infection. The delayed variable considered here are immunological and intracellular delay whichhave been introduce to make the model more logical and practical. The underlying model has been studiedtheoretically using linear stability analysis. To ascertain the global dynamics of the model, a Lyapunovfunctional approach has been performed. The stability switch criteria taking the delay as the bifurcatingparameter, leading to Hopf bifurcation has been studied. We have explored the possibility of the transitionof the system from order to chaos using the numerical simulations. The analytical results obtained havebeen verified by numerical simulations with the parametric values available in literatures. The results thuscan be used to describe the extensive dynamics exhibited by the model introduced in this article. The effectsof apoptosis on viral load has been explored with the help of numerical simulations.

9

Numerical Solution to Blood Model Navier-Stokes Equations in the EntranceRegion of Concentric Annuli with Rotating Inner Wall

Srinivasa Rao Nadiminti1; N. Gayathri Devi1 and A.Kandasamy

Division of Mathematics, Department of Science and Humanities, Vignan’s Foundation for Science, Technology andResearch (VFSTR) Vadlamudi, Guntur, Andhrapradesh - 522213, India

Department of Mathematical and Computational Sciences National Institute of Technology Karnataka, SurathkalMangalore, Karnataka-575025, India.

[email protected]

Blood model Navier-Stokes equation in the entrance region of concentric annuli has been studied nu-merically. We assumed that the inner cylinder is rotating with a constant angular velocity and the outercylinder is stationary. A finite difference analysis method is used to obtain the velocity profiles in thevarious directions and pressure variations along the radial direction. Under the Prandtl’s boundary layer as-sumptions, the continuity and momentum equations are solved iteratively using a finite difference analysismethod. Computational results are obtained for various non-Newtonian flow parameters and geometricalconsiderations. Comparison of the present results with the results available in literature for various particu-lar cases like Newtonian fluid has been done and found to be in good agreement.

Keywords:Concentric Annuli; Entrance Region Flow; Casson Fluid; Rotating Wall; Finite DifferenceMethod.

On the nondegenerate soliton solutions of Manakov systemM. Senthilvelan

Department of Nonlinear Dynamics School of Physics Bharathidasan University Tiruchirappalli - 620 [email protected]

In this talk, we demonstrate that the celebrated Manakov system can admit a more general type of non-degenerate fundamental solitons corresponding to different wave numbers, undergo collisions without anyenergy redistribution. We show that the previously known soliton solutions which allow energy redistribu-tion among the modes turns out to be a special case corresponding to solitary waves with identical wavenumbers in both the modes and travelling with the same velocity. We also discuss how these nondegeneratesoliton solutions exhibit various symmetric and asymmetric wave pro

les in detail. Finally, we present the collision scenario in detail for all the cases.

Keywords:Degenerate soliton, Nondegenerate soliton, Manakov equation, Hirota bilinear method

10

Noise-Induced extinction in an ecological modelPartha Sarathi Mandal

Department of Mathematics, NIT [email protected]

In this talk, we study a stochastically forced predator-prey model with strong Allee effect in prey popu-lation. In the deterministic case, we show that the model exhibits the stable interior equilibrium point orlimit cycle corresponding to the co-existence of both species. We investigate a probabilistic mechanism ofthe noise-induced extinction in a zone of stable interior equilibrium point. Computational methods based onthe stochastic sensitivity function technique are applied for the analysis of the dispersion of random statesnear stable interior equilibrium point. This method allows to construct an elliptic domain and estimate thethreshold value of the noise inten- sity for a transition from the coexistence to the extinction.

Keywords: Allee effect; Noise-induced transition; Stochastic sensitivity function.

Numerical Investigation of Natural Convection of Casson Fluids in a Square PorousCavity under the Effects of Thermal Radiation.

Sapna SharmaThapar Institute of Engineering and Technology,Patiala

[email protected]

In nature most of the fluids exhibit non-Newtonian behavior such as oils, emulsions, blood etc. Vis-coplastic fluids are class of non-Newtonian fluids which possess some yield stress. These fluids deform orflow only when value of applied stress is more than yield stress. To understand the behavior of such fluidsvarious rheological model are developed. One such model is Casson fluid which was studied by Cassonin 1959 to understand the characteristics of pigments of printing ink. In the present study, free convectionin a square porous cavity filled with casson fluid under the influence of thermal radiation is investigated.The governing equations of the flow problem are converted into finite element equations and solved byusing Penalty Finite Element method. The square porous cavity has been partially heated from below bya heating source and symmetrically cooled from both side walls. The effects of yield stress of the fluid onheat and fluid transport inside the cavity is studied for different values of temperature difference, across thehot and cold surfaces. Also, the effects of different lengths of heated zone is investigated for three differentvalues of heated zone. All important results have been expressed in terms of Casson fluid parameter, Darcynumber, Rayleigh number, Prandtl number, Radiation parameter. It is observed that with rise in Cassonfluid parameter rate of heat transfer and fluid flow rate enhances.

Keywords:Casson fluid; Radiation; Penalty Finite Element method; square porous cavity

11

A PARAMETER-UNIFORM IMPLICIT SCHEME FOR TWO-PARAMETERSSINGULARLY PERTURBED PARABOLIC PROBLEMS

Devendra Kumar

Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan-333031, India.Email: [email protected]

A parameter-uniform implicit scheme for two-parameter singularly perturbed boundary value problemsis constructed. Sharp bounds on the solution derivatives are derived. The solution is also decomposedinto the sum of regular and singular components and the bounds on the derivatives of these componentswhich are used in the convergence analysis are also drawn. The numerical method comprises the backwardEulers scheme based on the Rothes technique in the temporal direction and the Crank-Nicolson scheme on apredefined Shishkin mesh in the spatial direction. Through rigorous analysis, the theoretical results for twodifferent cases: Case I. ε1/ε22 → 0 as ε2 → 0, and Case II. ε22/ε1 → 0 as ε1 → 0 which show that the methodis convergent irrespective to the size of the parameters ε1, ε2 are provided. The order of accuracy in the firstand second cases are shown O((∆t)2 + N−1(lnN)2) respectively. Two test problems are encountered toverify the computational results with theoretical results.

Modeling Lithiation Induced Stresses in High-Capacity Electrode Particles withConcentration Dependent Properties

Poornesh Kumar Koorata

Applied Solid Mechanics Lab, Department of Mechanical Engineering, NITK Surathkal, Mangalore [email protected]

The lithium ion intercalation in high-capacity electrode particle is modeled in terms of concentrationux over particle’s radius that is governed by differential expression for concentration dependent diffusion.The itercalation effect is modeled in terms of governing equations for stresses. The combined equationof elasticity and ion concentration diffusion is solved for stress distribution to better understand the par-ticle’s response to intercalation. In this article the set of PDEs are solved for a spherical particle usingCrank-Nicolson scheme. The interesting portion of the article is dedicated for predicting the responseunder realistic circumstances with concentration dependent variation in elastic modulus which is linearlyvaried from 100 GPa to 30GPa from zero to fully lithiated condition, respectively. The results are obtainedin terms of radial and circumferential stresses and effective and hydrostatic stresses normalized over yieldlimit of high-capacity particle.

12

Understanding molecular transport in a non-conserving systems: The role ofinteractions

Arvind Kumar GuptaDepartment of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India-140001.

[email protected]

Many non-equilibrium biological processes such as intracellular transport, cellular organization, cellu-lar motility, etc are supported by the enzymatic molecules called molecular motors/motor proteins. Thesemotors carry vesicles (≥ 50 nm) and typically move with 5nm steps along microtubules. For performingthe mechanical work, they convert the chemical energy derived from the hydrolysis of ATP. Experimentssuggest that they behave in a cooperative manner and interact locally among them. The interaction energy(E) is either attractive (E > 0) or repulsive (E < 0). Similar kind of interactions is also visualized invehicular traffic. Driven diffusive systems provide a fruitful framework for studying the statistical prop-erties of such non equilibrium realistic processes. In the presence of driven external field, they reach anon equilibrium steady state (NESS) characterized with non-vanishing particle current. Totally asymmetricsimple exclusion process (TASEP) is the minimal model for describing the unidirectional motion of parti-cles along a lattice, where each particle occupies and covers only a single site of the lattice. We explainthe collective behavior of interacting particles using a variant of TASEP that consolidates the interactionsin the thermodynamically consistent procedure. These interacting molecular motors or interacting vehiclesmove along linear filaments (tracks) and can reversibly associate/dissociate from them. It is shown that evenfor weak interactions, theoretical predictions from simple mean-field approach deviate significantly fromMonte Carlo simulation results. To overcome this issue, we proposed a new theoretical method namelycorrelated cluster mean-field theory that takes into account some correlations. The effect of interactions onstationary phase diagrams, particle currents and densities are explicitly evaluated. The theoretical resultsare further tested with extensive computer simulations.

Keywords: Exclusion processes; Monte Carlo simulation; Mean-field approximation; Correlations; In-teraction.

Mathematics Subject Classification :82C70; 82C80; 82C22.

SH-wave propagation in monoclinic medium with linearly varying inhomogeneitySumit Kumar Vishwakarma, Tapas Ranjan Panigrahi, Rupinderjit Kaur.

Department of Mathematics, BITS-Pilani, Hyderabad Campus, Hyderabad-500078, [email protected]

The present work studies SH-wave propagation in a monoclinic layer lying over a monoclinic half space.The elastic constants of the layer and the half space have been assumer to varies linearly with depth. Usingsuitable boundary conditions, the dispersion equation has been deduced in closed form. The results arecompared with the isotropic case for the validation of the study. The effect of inhomogeneity parameterassociated with the elastic constants have been studied numerically and presented graphically. It has beenfound that inhomogeneity associated with medium has a great bearing on the phase velocity of the SH-wave.

Keywords: SH wave, monoclinic medium, inhomogeneity, dispersion equation, phase velocity.

Mathematics Subject Classification : 83C10; 74J15

13

Stabilization and chaos control in multispecies systemAnuraj Singh

ABV-Indian Institute of Information Technology and Management Gwalior, M.P., [email protected]

In this work different mechanisms are used to stabilize and chaos control in the models. To appreciatethe challenge of chaos control, there are two categories in control algorithm: feedback and non-feedback.By approximate linearization approach, a feedback control law is obtained which stabilizes the closed loopsystem. On the other hand, by suitable change of coordinates in the state space, a feedback control law isobtained. This feedback control renders the complex nonlinear system to be linear controllable system suchthat the positive equilibrium point of the closed-loop system is globally asymptotically stable. Anotherapproach is for chaotic system in which the control is applied to the system so as the controlled systemadmits a stable attractor which may be an equilibrium point or a limit cycle. The bounded feedback is usedto achieve the stabilization of unstable fixed point of the uncontrolled chaotic system. Delayed feedbackcontrol is used to control the chaos to periodic orbits. Numerical results substantiate the analytical findings.

A fourth-order orthogonal spline collocation method to fourth-order boundaryvalue problems

AnilDepartment of Mathematics, Birla Institute of Technology and Science, Goa.

[email protected]

In this article, we study the orthogonal spline collocation methods (OSCM) for fourth-order linear andnonlinear boundary value problems. Cubic monomial basis functions and piecewise Hermite cubic basisfunctions are used to approximate the solution u for both linear and nonlinear boundary value problems,respectively. Earlier, several numerical experiments were performed to fourth-order linear and nonlin-ear boundary value problems using finite difference methods, finite element methods, B-spline technique,Sinc-Galerkin method and decomposition method. All the methods lead to the order of convergence onlyoptimal or sub-optimal at the nodal points with more computational cost. In this paper, we use orthogonalcubic spline collocation methods and obtained optimal order of convergence for Also, super-convergentresult is achieved for norm. We use MATLAB version of Almost block diagonal (ABD) solver to mini-mize the computational cost. It requires only order of n operations. We discuss dynamics of the stationarySwiftHohenberg equation for different values of α.

Keywords: Orthogonal cubic spline collocation methods (OCSCM), Fourth-order linear and nonlinearboundary value problem, Cubic monomial basis functions, Piecewise Hermite cubic basis functions andAlmost block diagonal (ABD) matrix, MATLAB version of ABD solver.

14

Asymptotic Analysis of Steady Stokes Equations in an Oscillating DomainBidhan Chandra Sardar

Dr. Bidhan Chandra Sardar IIT [email protected]

In this talk, we consider the steady Stokes system in a n-dimensional domain with a rapidly oscillating(n -1) dimensional boundary prescribed with Neumann boundary condition and periodicity along the lateralsides is considered. Our aim is to study the limiting analysis (as ε → 0) of the steady Stokes problemand identify the limit problem in a fixed domain. Finally, show the weak convergences of velocities areimproved to strong convergence by introducing corrector terms.

Keywords: Differential equations, Nano uids, Natural convection, Rayleigh number, Metallic and non-metallic nanoparticles.

Periodic solutions of vector disease model with harvesting termShilpee Srivastava

Department of Mathematics Birla Institute of Technology and Sciences Pilani, Dubai campus Dubai, 345055, [email protected]

System of delay differential equations plays a vital role in the field of science and are now widelyused for prediction and analysis in various areas of life sciences for example immunology, populationdynamics, physiology, neural networks and epidemiology and atmospheric sciences, e.g. NPZ models.Time delays occur in these models due to duration of certain hidden process like stages of a life cycle,duration of infectious period, the immune period and so on. Introduction of time delays in models increasethe complexity of these models and therefore it is essential to study the qualitative behavior of such modelsusing stability or bifurcation analysis. To understand some of the outcomes here the qualitative behaviour ofvector disease model with constant delay has been analysed. In this paper, we have studied the existence ofpositive peiodic solution of vector disease model proposed by Kenneth L. Cooke with effect of harvestingterm.

y′(t) = −c(t)y(t) + b(t)y(t− τ(t))(1− y(t))− I(t, y(t))

An example has been given to illustrate the outcome. Also by simulation, assuming parameters a functionof time we have shown how delay term affect the periodicity of the solution.

Keywords: Periodic Solution, Positive Solution, vector disease model, harvesting term.

Mathematics Subject Classification : 34K13, 34K15, 39A10, 39A12.

15

Mixed Virtual Element Methods for fourth order nonlinear parabolic problemsP. Dhanumjaya, K. Balaje

Department of Mathematics, BITS-Pilani K K Birla Goa Campus, Zuarinagar, GOA-403 726, [email protected]

Virtual element method (VEM) is a recent numerical technique which is a generalisation of the finiteelement method on polygons. The difference between the various finite element methods and the virtualelement method is that it admits non-polynomial basis functions which are not required to be computed inpractice. Instead, the degrees of freedom are chosen so that the stiffness matrix is computed exactly withoutexplicitly knowing the basis functions. This enables us to work with more general meshes that the finiteelement method cannot handle in general. In this paper, we discuss mixed virtual element method (VEM)for a class of fourth order nonlinear parabolic problems. We prove some theoretical results including apriori bounds, optimal error estimates for the semi-discrete and completely discrete schemes. Finally, weperform some numerical experiments to validate the theoretical results.

Keywords: Fourth order nonlinear parabolic problems, mixed virtual element method, a priori bounds,semidiscrete Galerkin method, completely discrete Galerkin method, optimal error estimates and numericalexperiments.

Generation of Uniform Magnetic Flux using different Coil and Plate ArrangementMd Tarikul Islam, Md Ataur Rahman Khan, Md. Moniruzzaman Bhuyan, Mohammad Anwar Hossain,

Md. Mehedi Hasan Bhuiyan.Department of Electrical and Electronic Engineering, Southern University Bangladesh, Chittagong, Bangladesh

[email protected]

In this paper we have studied the generation of uniform magnetic flux Coil-Plate arrangement. Here wehave shown by simulation that if we use cupper plate and cupper coil, the magnetic flux increases with theincrease of coil number. But at one point the magnetic flux start to decrease with the increase of coil num-ber because the magnetic flux reaches at its saturation point. We observe that if we gradually increase thecoil number up to six coil the magnetic flux reaches its peak value. If we further increase the coil numberabove six the magnetic flux decreases. On the other hand we also observe the phenomena for gold plate andcoil but the magnetic flux is comparatively low. Our proposed coil-plate arrangement may have potentialapplication in Magnetic Resonance Imaging (MRI).

Keywords: Coil; Conductive Plate; Simulation; Magnetic Flux.

Optimization methods and algorithms for non-parallel support vector machinesM. Tanveer

Department of Mathematics, IIT [email protected]

In this talk, I will discuss twin support vector machines (TWSVM), a binary SVM classifier that deter-mines two nonparallel planes by solving two related SVM-type problems, each of which is smaller than in aconventional SVM. The twin SVM formulation is in the spirit of proximal SVMs via generalized eigenval-ues. Further, few recent variants of TWSVM will be discussed to show their performances and applicationsto real-world problems.

16

Elliptic problems with critical growth sign changing nonlinearities.Sarika

Bennett University, Greater [email protected],

The talk is concerned about the existence and multiplicity results of elliptic equations involving poly-nomial/exponential type nonlinearities with sign changing weight functions. The bering map analysis andNehari method play an important role to obtain the existence and multiplicity of weak solutions for suchtype of elliptic equations. I will explain this analysis and also would like to discuss the extension of thistechnique to non-local elliptic equations involving p-fractional Laplace operator.

Modeling and Simulation of dc-dc Converter Based Power Electronics Learning : areview

Indresh Yadav

Solution of two-parameter singularly perturbed one dimensional parabolicequations using non-polynomial spline

Shahna, Talat Sultana and Arshad Khan

Department of Mathematics, Jamia Millia Islamia, New Delhi-25, India.Department of Mathematics, Lakshmibai College, University of Delhi, New Delhi-52, India.

[email protected]

In this paper, a class of second order singularly perturbed interior layer problems is examined. Non-polynomial mixed spline is used in this paper to develop the tridiagonal scheme. Error analysis is also car-ried out. The method is shown to converge point-wise to the true solution with second as well as fourth order.Linear and nonlinear second order singularly perturbed boundary value problems have been solved by thepresented method. Numerical illustrations are given to demonstrate the efficiency of proposed method..

Keywords: Heat engines, Optimization, Non-equilibrium thermodynamics.

Mathematics Subject Classification : 80A05, 82-08.

17

Creeping flow of a sphere in non-concentric spherical container using slip conditionM. Krishna Prasad

Department of Mathematics, National Institute of Technology, Raipur-492010, Chhatisgarh, [email protected]

Creeping axisymmetric ow caused by a sphere in viscous uid within non-concentric spherical containeris investigated using slip condition on the surface of the sphere. The boundary conditions on the sphericalcon- tainer are Cunningham’s (Mehta-Morse) and Kvashnin’s models. Previously Faltas and Saad ( Math.Meth. Appl. Sci. 2011, 34, 1594-1605) considered the same problem using Happel and Kuwabara models.In the limit of small Reynolds number, a general solution is constructed from the superposition of the solu-tions in the two spherical coordinate systems based on the inner sphere and spherical container. Numericalresults for the hydrodynamic drag force exerted on the inner sphere are obtained with good convergencefor various values of the relative distance between the centers of the sphere and spherical container, slipcoefficient of the sphere, and the volume fraction. The hydro-dynamic drag results are in good agreementwith the existing solutions in the literature.

Keywords: Creeping flow; slip sphere; hydrodynamic drag force; spherical container.

Mathematics Subject Classification : 76A05; 76D07; 76S05.

Two-warehouse inventory model with quantity discount policyHimanshu Rathore

Manipal University Jaipur, Jaipur, Rajasthan, [email protected]

In present study a two-warehouse inventory model is established for deteriorating items. Controllabledeterioration rate under the effect of preservation technologies. The market environment is such that the de-mand is received according to linear function of advertising frequency and selling price. Quantity discountpolicy is presented to keep bond of customer solid. The selling price, total cycle length and preservationcost parameters are taken as decision variables. The study is numerically verified with suitable graphicalrepresentation.

Keywords: advertisement frequency, preservation, quantity discount, two-warehouse.

Mathematics Subject Classification : 49-XX.

18

A Comparative Study of Natural Nanouid Convection for Different Initial andBoundary Conditions

Jyoti Sharma

U.I.E.T., Panjab University, Chandigarh-160014, [email protected]

In present study a two-warehouse inventory model is established for deteriorating items. Controllabledeterioration rate under the effect of preservation technologies. The market environment is such that the de-mand is received according to linear function of advertising frequency and selling price. Quantity discountpolicy is presented to keep bond of customer solid. The selling price, total cycle length and preservationcost parameters are taken as decision variables. The study is numerically verified with suitable graphicalrepresentation.The paper presents partial differential equations based on conservation laws of mass, mo-mentum and energy which are analyzed to study the onset of convection in a nanouid layer for differentinitial and boundary conditions. The equations are solved to get steady state solution and perturbations areadded to the original variables. The obtained partial differential equations are converted into ODE by seek-ing solution which is exponentially varying in time and space. Further these ordinary differential equationsare solved to get expression for thermal Rayleigh number which is studied ana lytically and numerically.A detailed comparative analysis of the problem is undertaken for various initial and boundary conditionswhich leads to different equations and hence affect the convective nature of the system broadly. The impactof various nanouid parameters on the instability of the system are explored using metallic and non-metallicnanoparticles.

Keywords: Differential equations, Nano uids, Natural convection, Rayleigh number, Metallic and non-metallic nanoparticles.

Application of finite fractional Hankel-type transformation in Dirichlets problemV. R. Lakshmi Gorty

SVKMs NMIMS University, [email protected]

In this paper, finite fractional Hankel-type transformation has been defined depending on three real pa-rameters. Operational calculus properties are shown in an application problem at the end of the paper. Theclassical concept on a more generalized version of finite fractional Hankel transforms is studied and appliedto Dirichlets problem at the end of the study showing application in engineering field.

19

Existence Results for Fractional Impulsive Delay Differential EquationsRenu Chaudhary

GD Goenka University, Gurugram, [email protected]

In this paper, we apply the monotone iterative technique coupled with the method of lower and uppersolutions to obtain the existence of extremal mild solutions for delay fractional integrodifferential equationswith non-instantaneous impulses in an ordered Banach X

cDνy(t) = Ay(t) + F (t, yt,∫ t

0a(t, s, ys)ds), t ∈ ∪mn=0(kn, tn+1], m ∈ N,

y(t) = Gn(t, yt), t ∈ ∪mn=1(tn, kn],y(t) = θ(t), t ∈ (−∞, 0],

(0.0.3)

where cDν is the Caputo fractional derivative of order ν, 0 < ν < 1. A is a closed densely defined lin-ear operator which generates a strongly continuous semigroup S(t)t>0 of bounded linear operators onBanach space X . 0 = t0 = k0 < t1 < k1 < t2 < · · · < tm < km < tm+1 = b are impulsive points.The function yt : (−∞, 0] → X express the time history of the function y from −∞ to the present timet and determined by yt(φ) = y(t + φ) for φ ∈ (−∞, 0] which belongs to some abstract phase space B.The nonlinear functions a : ∆ × B → X , F : [0, b] × B × X → X and Gn : (tn, kn] × B → X with∆ = (t, s) : 0 6 s 6 t 6 b, satisfies certain assumptions to be mentioned later. The impulses startssuddenly at the points tn and their effect remains on the interval [tn, kn]. More precisely, at the points tn,the function y experience an abrupt impulse and follow different rules in the two subintervals (tn, kn] and[kn, tn+1]. The function y is continuous at the points kn, n = 0, 1, 2, . . . ,m, m ∈ N. At last, an applicationis discussed to show the applicability of the obtained results.

Keywords: Non-instantaneous impulses, Monotone iterative technique, Measure of noncompactness,Semigroup theory.

Mathematics Subject Classification : 34A08, 34G20, 34K30, 34K45, 47D06.

OPTIMAL CONTROL IN STOCHASTIC LANDAU-LIPSCHITZ-GILBERTEQUATION

Ananta K. MajeeIIT Delhi

[email protected]

In this presentation, we study an optimal control problem for the stochastic LandauLipschitz-Gilbertequation on a bounded domain in Rd (d = 1; 2; 3). We first establish existence of a relaxed optimal controlfor relaxed version of the problem. As the control acts linearly in the equation, we then establish existenceof an optimal control for the underlying problem. Moreover, convergence of a structure preserving finiteelement approximation for d = 1 and physically relevant computational studies will be discussed. Further-more, we study an optimal control problem of N interacting ferromagnetic particles which are immersedinto a heat bath through the application of a distributed exterior field minimizing a quadratic cost functional.With the dynamic programming principle, we show the existence of a unique strong solution of the optimalcontrol problem. With a Hopf-Cole transformation the related nonlinear Hamilton-Jacobi-Bellman equa-tion is recast into a linear PDE on the manifold M = (S2)N, whose classical solution is represented witha Feynman-Kac formula. We propose to use this probabilistic representation to numerically study optimalswitching dynamics with Monte Carlo simulations.

20

Survey of Nature Inspired Optimization Algorithms in Fuzzy Control SystemsGaurav Saxena, Gomathi Bhavani, Shilpee S. Saxena

Birla Institute of Technology and Sciences Pilani, Dubai campus Dubai, 345055, [email protected]

Several Non-deterministic Polynomial-time (NP) hard problems are nowadays solved with metaheuris-tic, nature inspired optimization algorithms. However, the problem of parameter adaptation continues toplague these methods. To remedy this, many approaches using Fuzzy logic have been suggested. Fuzzylogic controllers play a significant role in control system design and their major objective is to tackle uncer-tainty and imprecision which could be data or process driven. For exact modelling of process parametersand control, it is vital that the fuzzy controller parameters have to be chosen and tuned in a way that theycapture the process dynamics quite accurately. In this paper, we endeavor to present advances in nature in-spired computing with reference to their contribution to control systems application. Various nature inspiredtechniques have been explored and surveyed with applications to optimization of parameters in control sys-tems. The scope of fuzzy logic systems in solving the parameter optimization problem and thereupon po-tentially improving the performance of some nature inspired optimization methods also has been presented.We also review many nature inspired metaheuristic algorithms for optimization of fuzzy control parameters.

Keywords: Ant Colony Optimization Algorithms, Fuzzy logic controller, Meta- heuristics, Nature In-spired Optimization Algorithms, Particle Swarm Optimization

A study of approximate controllability for abstract nonlocal neutralintegro-differential equations with finite delay

Kamaljeet

Complex plankton dynamics induced by adaptation and defenseNilesh Kumar Thakur and Archana Ojha

Department of Mathematics, National Institute of Technology Raipur, India.Emails: [email protected], [email protected]

In this paper, we have investigated a model for phytoplanktonzooplankton interaction and incorporatedthe adaptation (dormancy of the predators such as resting eggs) in zooplankton. The dormant stages areusually better equipment to withstand harsh environmental conditions than active ones. It has also beenobserved that the phytoplankton produces toxin in order to provide a self-defense from predators. We havestudied how (i) adaptations allow an organism to be successful in a particular harsh environment, (ii) toxinspread surrounding the water surface provide defense. Analytically we have studied the local stability of themodel system. To understand the effect of adaptation and defense on plankton dynamics we have plotted thetime series and spatiotemporal pattern. Our numerical investigation reveal that the adaptation can suppressthe fluctuation in population densities, and system shows a transient complex spatiotemporal pattern whichis either a mixture of spatially periodic steady states or travelling/standing waves by increasing the time andspace.

Keywords: Adaptation dormancy plankton spatiotemporal pattern.

AMS subject classifications : 92D25, 34K20, 37M05

21

CONVERGENCE ANALYSIS OF TIKHONOV REGULARIZATION FORNON-LINEAR STATISTICAL INVERSE LEARNING PROBLEMS

ABHISHAKE, GILLES BLANCHARD AND PETER MATHEInstitute of Mathematics, University of Potsdam, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany

[email protected]

We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quan-tity through a non-linear operator at some random design points. We consider the widely used Tikhonovregularization (or method of regularization, MOR) approach to reconstruct the estimator of the quantityfor the non-linear ill-posed inverse problem. The estimator is defined as the minimizer of a Tikhonovfunctional, which is the sum of a data misfit term and a quadratic penalty term. We develop a theoreticalanalysis for the minimizer of the Tikhonov regularization scheme using the ansatz of reproducing kernelHilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classesof admissible solutions, defined through appropriate source conditions.

Keywords:Statistical inverse problem; Tikhonov regularization; Reproducing kernel Hilbert space;General source condition; Minimax convergence rates.Mathematics Subject Classification : 65J20; Secondary: 62G08, 62G20, 65J15, 65J22.

CONTROLLABILITY OF A CLASS OF FRACTIONAL IMPULSIVEDIFFERENTIAL EQUATIONS IN A BANACH SPACE

Abdur RaheemAMU, Aligarh

[email protected]

In the present paper, we considered the following class of controlled fractional impulsive differentialequations in a Banach space X:

cDα(t) = Ax(t) +Bu(t) + f(t, x(t), x(ν(t))), t ∈ [0, T0], t 6= ti, i = 1, 2, ...q

∆x(ti) = Ii(x(ti)), i = 1, 2, ..., q

∆x′(ti) = Ji(x(ti)), i = 1, 2, ..., q

x(t) = h(t), x′(t) = g(t) t ∈ [−τ, 0]

where the state variable takes values in Banach space X and the control function u· is given in L2([0;T0] :U), the Banach space of admissible control functions with U a Banach space, cDα denotes the fractionalderivative of Caputo of order α ∈ (12],−A is the infinitesimal generator of a strongly continuous α-order cosine family Cα(t)t≥0 on a Banach space X . The maps f : [0, T0] × X2 → X and maps I

i ;Ji

defined on X satisfy some suitable conditions, and the function v : [0;T0] → [0;T0] is continuous suchthat 0 ≤ vi(t) ≤ t; ti → [0, T0] for all i = 1, 2, .., q such that t1 < t2 < ... < tq; and m, q → N, T0 >0.h, g → C1([−τ ; 0];X) i.e. h, g are continuously differentiable on [−τ ; 0]. Let I = [0, T0]. In this paperan associated integral equation is obtained by using fractional integral and the family of cosine or sine oflinear operators and then by using measure of non compactness and Monch’s fixed point theorem, we provethat considered problem is controllable on [0;T0]. We included an example to illustrate the abstract results.

Keywords:Controllability; Fractional differential equations; Impulsive conditions; Monch FIxed pointtheorem.

Mathematics Subject Classification : 93B05, 34A08, 35R12, 47H08.

22

APPROXIMATE CONTROLLABILITY OF SECOND ORDER SEMILINEARCONTROL SYSTEM WITH NONLOCAL CONDITIONS

Urvashi Arora and N. SukavanamDepartment of Mathematics Bennett University, Greater Noida, India.

Email: [email protected])

This paper is concerned with the approximate controllability of second order semilinear control systemwith nonlocal conditions in Hilbert spaces. Sufficient conditions for the approximate controllability areestablished by assuming the approximate controllability of the corresponding linear system. The results areobtained when the nonlinear term satisfies monotone condition which is a weaker condition than the Lip-schitz continuity. Some approaches made by earlier authors led to certain inequality conditions involvingvarious system constants. But, in the proposed approach, there is no need of any inequality condition toprove the approximate controllability results. Finally, an example is provided to illustrate the application ofthe obtained results.

Keywords:Approximate controllability, Semilinear systems, Monotone condition, Nonlocal Condi-tions.

Mathematics Subject Classification : 34K30; 34K35; 93C25.

BOUNDEDNESS AND COMPACTNESS OF WEIGHTED DIFFERENTIATIONCOMPOSITION OPERATORS BETWEEN SOME WEIGHTED SPACES

Zaherr AbbasDepartment of Mathematical Sciences, Baba Ghulam Shah Badshah University Rajouri

[email protected]

The paper shall begin with an introduction to function spaces, composition operators, weighted com-position operators and product of composition operators with differentiation. Afterwards, some classicaloperators will be shown to be composition (or weighted) operators, thus making the class of compositionoperators to be rich. Then we shall discuss the main aims of studying composition operators. Finally,boundedness and compactness of weighted differentiation composition operators between some weightedspaces of analytic functions will be discussed.

Optimization criteria for performance of heat engines working under differentconstraints

Renuka Rai and Ramandeep Singh JohalDepartment of Applied Sciences, University Institute of Engineering and Technology, Panjab University,

Chandigarh-160014, India.Department of Physical Sciences, IISERMohali, Mohali, India.

[email protected]

Although Carnot efficiency gives an upper bound for thermal efficiency of heat engines, it has limitationsin understanding the performance of real heat engines. In practice, heat engines are irreversible. Here thethermo- dynamic processes take place at finite rate, infinite time and may have nite sizes of source and sink.In this work, we compare the optimization criteria and the resulting bounds on efficiency of heat enginesworking under different constraints. The resulting optimization problem for maximum work extraction

23

in finite time involves solving the corresponding Euler-Lagrange equation for the control variables. Theequation is simplified assuming tight-coupling conditions. The

nite time output and efficiency are compared with the corresponding exergy analysis in the quasi-staticcase.

Keywords: Heat engines, Optimization, Non-equilibrium thermodynamics.

Mathematics Subject Classification : 80A05, 82-08.

Wind turbine blade section optimization using a quantitative studyM. Balachandar

Sri Sai Ram Institute of Technology, Chennai.

Mathematical modeling in health scienceJagdev Singh

Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India.Email: [email protected]

A mathematical model is a representation of a system by employing mathematical concepts, logic andlanguage. The procss of developing a mathematical model is named as mathematical modelling. In thistalk, we will discuss about the concept of mathematical modelling and about a giving up smoking modelpertaining to a new fractional derivative non-singular kernel in nature. We will explore the numerical resultswhich are obtained with the aid of iterative scheme. The talk will cover the existence and uniqueness of thesolution by applying the fixedpoint theorem. Further, we will discuss about the numerical results of newsmoking model associated with new fractional derivative and will compare with other derivatives.

Keywords: Mathematical modeling; Smoking model ; New fractional derivative ; Fixed-point theorem.

Fractional exothermic reactions models having constant heat source in porousmedia with different kind of memories

Devendra KumarDepartment of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India.


In this work, we study the exothermic reactions models having constant heat source in the porous mediawith different kind of memories. The patterns of heat flow profiles are very essential for heat transfer inevery kind of the thermal insulation. In this work, we focus on the driving force problem due to the factthat temperature gradient is assumed. The mathematical equation of the mathematical model is confined ina fractional energy balance equation (FEBE), which furnishes the temperature portrayal in conduction statehaving uniform heat source on steady state. An iterative algorithm is used to derive the numerical solutionof the FEBE. Some numerical results are given in the form of graphs and tables to see the effects of differentparameters and variables on temperature profiles.

Keywords: Fractional exothermic reactions models; Porous media; Heat source; Fractional derivatives;Iterative method

24

Piezothermoelastic continuum subjected to point mechanical loadAnita Devi Thakur

Vallabh Govt. College Mandi, Himachal Pradesh, India.Email: [email protected]

In this paper two-dimensional problem of piezothermoelasticity has been considered to investigate thedisturbance in homogeneous, transversely isotropic (6mm class) generalized cylindrical piezothermoelasticcontinuum subjected to continuous mechanical load acting on thermally insulated and electrically shortedsurface. The Laplace and Hankel transforms technique have been employed to express the boundary condi-tions in the transformed domain. The formal solutions are employed to obtain the system of simultaneouslinear algebraic equations. These systems of equations are solved by using Gauss elimination process forthe unknowns. These values of unknowns are used to find the expressions of displacements, temperaturechange, electric potential, stresses and electric displacement in the transformed domain. The inverse trans-form integrals are evaluated by using numerical technique. Temperature, normal stress and shear stressso obtained in the physical domain, are computed numerically from the relevant expressions and relationscode for PZT-5A material. Finally, the illustration of the results for classical and non-classical models ofthermoelasticity has been presented graphically.

Keywords: Piezoelectric; Integral transforms; Relaxation time; Pyroelectric.

Dynamical Analysis of Michaelis-Menten Enzyme ReactionsB S Lakshmi and S S Phulsagar

Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, Sagar, [email protected]

Enzymes are biological catalysts that alter the rates of reactions in cells without being changed them-selves during the course of a reaction. A biochemical reaction almost invariably has an output which is notnecessarily linear. Such nonlinear phenomena involving enzymes have been explained by several people,amongst them Michaelis and Menten are worth mentioning. A simple form of Michaelis-Menten enzymeequation is

V0 = Vmax[S]

Km + [S]

where V is the velocity of the reaction, V = V0 at t = 0, Vmax is the maximum velocity of the reaction,[S] is the concentration of the substrate S, Km is the Michaelis constant. Following the law of mass action,there are many mathematical models with a Michaelis Menten type output. With an output of this kind onecould consider the following set of equations

dx

dτ= a− bx− xpyq, dy

dτ= xpyq − cy

y + 1

This equation when viewed as Predator-Prey equations, the term cyy+1

represent the type II functional re-sponse of Holling. Taking some particular values of the parameters a, b, p, q a detailed analysis of thesystem is taken up. The system is analysed by studying the associated differential equations, phase planeanalysis and bifurcation analysis. Some of the oscillating chemical reactions viz. Belousov-Zhabotinskyreaction has a similar form of enzyme reactions.

Keywords:Enzyme reaction, Michaelis-Menten, system of differential equations, equilibrium points,phase plane, bifurcation analysis.

Mathematics Subject Classification : 80A30, 92C45.

25

Truss Topology Optimization With Static And Dynamic Constraints UsingAISC-ASD

Ghanshyam G. TejaniSchool of Technology, GSFC University, Vadodara, Gujarat, India.

[email protected]

In this study, simultaneous size and topology optimization of planar and space trusses subjected to staticand dynamic constraints are investigated. All the benchmark trusses consider discrete cross-sectional areasfrom the American Institute of Steel Construction - Allowable Strength Design (AISC-ASD) to considerthe practical aspect of manufacturing. Moreover, the trusses are seen with multiple loading conditions andsubjected to constraints for natural frequencies, element stresses, nodal displacements, Euler buckling cri-teria, and kinematic stability conditions. Truss Topology Optimization (TTO) can be accomplished by theremoval of super uous elements and nodes from the ground structure, and results in the saving of the mass ofthe truss. In this method, the difficulties arise due to singular solution and unnecessary analysis; therefore,FEA model is reformed to resolve these difficulties. The static and dynamic responses to the TTO prob-lems are challenging due to its search space, which is implicit, non-convex, non-linear, and often leadingto divergence. This study compares performance of four meta-heuristics such as TeachingLearning-BasedOptimization (TLBO), Heat Transfer Search (HTS), Symbiotic Organisms Search (SOS), and Water waveoptimization (WWO) for solving discrete TTO problems.

Keywords: Non-linear problem Structural optimization; Metaheuristic; Planar and space trusses; AISC-ASD; Discrete sections.

Mathematics Subject Classification : 65-05:Experimental papers; 46N10: Applications in optimiza-tion; 90C30: Nonlinear programming.

Inuence of Temperature Jump and Concentration Slip on inclined MHDBioconvection past a vertical porous plate in the presence of Nanoparticles and

Gyrotactic MicroorganismRakesh Choudhary and Shalini Jain

Bhartiya Skill Development University, Jaipur India. University of Rajasthan, Jaipur, Rajasthan, [email protected]

In this paper, we examined the effects of temperature jump and concentration slip on inclined MHDbioconvection past a vertical porous plate through porous media in the presence of both nanoparticles andgyrotactic microorganism. The governing partial differential equations are reduced into ordinary differentialequation with using suitable similarity transformation. A numerical scheme, called Runge-Kutta fourth

fth order Fehlberg method (RKF45) has been used to solve above ordinary differential equations. Theeffects of pertinent parameter for variation in the velocity profile, velocity profile at far

eld, temperature profile, concentration prole and motile microorganism density prole has been obtained. We have validate the result obtained from current study with existing results.

Keywords:Gyrotactic microorganism; Temperature jump; Concentration slip; Inclined MHD; Nanopar-ticles; RKF-45.

Mathematics Subject Classification : 76-XX.

26

Numerical Solution of Linear and Higher order Delay Differential Equations usingCoded Differential Transform Method

Giriraj Methi And Anil KumarDepartment of Mathematics and Statistics, Manipal University Jaipur-303003, Rajasthan, India

Aim of the paper is to obtain numerical solutions of linear and higher order delay differential equations(DDEs) using Coded Differential Transform Method (CDTM). We have numerically solved some initialvalue delay differential equations by coded differential transform method in Mathematica version 11 andcompared the solutions with the exact solutions. We have illustrated few examples to show efficacy of ourmethod. We have obtained various terms of series solution by CDTM. Our solutions are approximatelyclose to exact solutions. The CDTM may be one of the suitable method to solve DDEs.

Keywords:Delay Differential Equations, Coded Differential transform Method, Numerical Solution,Mathematica.

Mathematics Subject Classification : 39B99; 65Q20; 65Q30

Studies of Hyperloop Vehicle for Transportation: A ReviewV. K. Srivastav; Aditya Priyanka; Abhishek Kumar; Shudhanshu Kumar; Anand Raj.

Motihari College of Engineering, Motihari, [email protected]

This paper presents a critical review of hyperloop vehicle that is useful for next generation transporta-tion. The Hyperloop concept is proposed as a quicker, cheaper alternative to high-speed rail. It is seenfrom the literature that computational simulation play an important role to simulate the air flow around thecapsule considering the effect of the axial-flow air compressor and the levitation cushion on the air flow. Inthis paper, we provide all the boundary conditions in tabular form that was used in both computational aswell as experimental papers. The present work will also compare different hyperloop models used by theresearchers.

Keywords: Hyperloop, Computational Fluid Dynamics (CFD), Tube transport system, Tube vehicle

Effect of active case nding on dengue control: Implications from a mathematicalmodel

Pankaj Kumar TiwariDepartment of Mathematics, University of Kalyani, Kalyani

[email protected]

Dengue control in India is a challenging task due to complex healthcare settings. In yesteryears, an am-plication of dengue infections in India posed the need for introspection of existing dengue control policies.Prior understanding of the impacts of control interventions is necessary for their future implementation. Inthis paper, we propose and analyze a compartmental model of dengue to assess the impact of active casending (ACF) on dengue disease transmission. Currently, primary prevention of dengue is possible only withvector control and personal protection from the bites of infected mosquitoes. Although a few experimentalstudies are performed to assess ACF in dengue disease, but this is the rst attempt to represent and studythe dynamics of disease using ACF as a control strategy. Local and global dynamics of the system are

27

studied. We use sensitivity analysis to see the effects of controllable parameters of the model on the basicreproduction number and total number of infective population. We nd that decrease in the biting rate ofmosquitoes, and increase in the rate of hospitalization and/or notication, death rate of mosquitoes and ACFfor asymptomatic and symptomatic individuals play crucial role for the reduction of disease prevalence. Wecalibrate our model to the yearly dengue cases in eight dengue endemic states of India. The results of ourstudy show that ACF of symptomatic individuals will have signicant effect on dengue case reduction butACF of asymptomatic individuals cannot be ignored. Our ndings indicate that the healthcare organizationsmust focus on ACF of symptomatic as well as asymptomatic individuals along with personal protection andmosquitoes control to achieve rapid reduction of dengue cases in India.

Change in Stability Behavior of Spatiotemporal Phytoplankton Dynamics withDifferent Types of Functional Response

Randhir Singh BaghelDepartment of Mathematics, Poornima University, Jaipur, Rajasthan,India

[email protected]

In this paper, we focus on the comparison between two types of functional responses, namely, Hollingtype-II and ratio-dependent functional response interaction on the phytoplankton dynamics with susceptibleand infected class of populations with diffusion. We observed that the system dynamical behavior affectedby the response functions and the system is more stable in the case with ratio dependent functional response.Furthermore, we explore the higher-order stability analysis of the system for both linear and no-linear sys-tem with respect to both response functions.

Keywords: Diffusion driven instability, Pattern formation, Higher-order stability analysis.

Modelling of duct based photovoltaic thermal (PVT) air collectorRohit Tripathi1; G. N. Tiwari; Deepak Sharma

chool of Electrical, Electronics and Communication Engineering, Galgotias University, G. Noida, U.P., India.Centre for Energy Studies, Indian Institute of Technology Delhi, Houz Khas, New Delhi, India

[email protected]

In present study, photovoltaic thermal collector has been proposed with duct where the semitransparentsilicon solar cell based photovoltaic module is used. The area of PV module is considered as 0.605 m2.This PV module generates 35 Peak Watts electrical power. Just below the PV module, one closed ductis placed and small portion on duct, back to PV module, and one DC fan is placed. This DC fan can beoperation with 12 volts and 0.5 A. The comparative study has been analyzed for one convectional Flat Platecollector, one photovoltaic module and proposed duct based PVT collector with air. In this study, it is foundthat the proposed system is generating more electrical power to convectional photovoltaic module and morethermal energy from convectional photovoltaic thermal system, 20% and 36%, respectively. The limitationis that the cost of proposed system is slightly high to others but it is self-sustainable system and this thermalenergy can be further used for heating purpose also, like: building heating, drying etc.

Keywords:PV Module, FPC, Energy, Exergy and Power.

Mathematics Subject Classification :

28

Mathematical model of unstable self-limiting thermo chemical temperatureoscillations in Australian Cycades

Akash BhavsarSchool of Technology, GSFC University, Vadodara, Gujarat, India.

[email protected]

In this study, mathematical models have been developed to explain unstable, self-limiting thermo chem-ical temperature oscillations, which are observed in Australian cycads macrozamia lucida and M macleayiduring the pollination period. These cones develop daily midday thermogenic temperature rises as high as12 C above ambient temperature, during their approximately two week pollination period. The cone tem-perature response model is developed to accurately predict the cone temperatures over multiple days, basedon simulations of experimental results from 28 thermogenic events from 3 different cones, each simulatedfor either 9 or 10 sequential days. Determined the optimum values of parameters that are responsible forunstable, self-limiting thermo chemical temperature oscillations. Determined the simple possible modelthat can explain the temperature responses obtained in the field study and lab experiments, for complexsystems like this more than one solution is possible to simulate the system.

Keywords: Mathematical modeling; Thermal system optimization; Inverse thermo-chemical system;Bio chemical system; System parameters identification.

Mathematics Subject Classification : 65-05:Experimental papers; 46N10:Applications in optimiza-tion; 90C05:linear programming

On the existence and uniqueness of solutions to discontinuous dynamic equation ontime scalesSanket Tikare

Department of Mathematics, Ramniranjan Jhunjhunwala College, Ghatkopar (W), Mumbai (MS), India - 400 [email protected]

In this paper, we study the existence and uniqueness of solutions to the dynamic equation x∆(t) =f(t, x(t)

), t ∈ T, where x : T → R, f : T × R → R and T = [a, b]T is a finite time scale interval with

minT = a and maxT = b. Here we do not assume any sort of continuity about f . The Arzela–Ascolilemma and Banach’s fixed point theorem are used to investigate the existence of solutions. We obtain themaximum interval for the existence of solution under certain growth conditions. We prove uniqueness ofsolution under certain conditions.

Keywords: Existence and uniqueness; Dynamic equations; Time scales; Caratheodory function; Fixedpoint theorem.

Mathematics Subject Classification :26E70; 34A36; 34N05.

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Generalized energy inequality for weak solutions to Damped Navier-Stokesequations

Rajib Haloi and Subha Pal

Department of Mathematical Sciences, Tezpur University, Assam, [email protected]

Existence of weak solutions to the damped NavierStokes equation with no slip boundary condition in abounded domain in R3 are proved and generalized energy inequality for the solutions are discussed.

Keywords: Navier Stokes equation, Semi-discretization method, No slip boundary condition.

Mathematics Subject Classification :76D05, 35Q30,76D03.

Dynamical study of a delayed SEIRS model with saturated incidence and impulsivevaccination: Effect of household wastes

Kunwer Singh Mathur

Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, Sagar, [email protected]

With the increasing of urban population, the accumulation of household waste and its disposal has be-come an increasingly arduous issue. The household wastes cause spreading several kinds of deadly diseasesand hence aroused the attention from all sectors of society. In this paper, a delayed SEIRS model with asaturated incidence rate is proposed to study the dynamics of diseases spread by household wastes. Tocontrol the spread of diseases, vaccinations into susceptible population and disinfection of bacteria fromenvironment are done at every fixed moment of time in an impulsive manner. It is obtained that the modelhas a disease-free unique positive T-periodic solution, which is globally asymptotically stable under certainconditions. Further, the comparison theorem of impulsive differential equations is used to prove the per-manence of the system. Finally, the numerical simulation confirms and validates these theoretical findings.This study provides useful information for decision-makers to select appropriate choices in controlling ofdiseases spread by household waste and save cost.

Keywords: Household waste, impulse, delay, SEIRS model, global stability, permanence.

Mathematics Subject Classification : 92Bxx, 92B05.

30

Thermal Convection in Oldroydian Nanouid Layer Saturating a Porous mediumwith Rigid-free and Rigid-rigid Boundaries

AbhilashaDepartment of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005 INDIA.

[email protected]

The present paper investigates the effect of rheology on the onset of convection in top- heavy nanofluidheated from below saturating an isotropic and homogeneous porous medium. The rheology of the nanofluidis described by Oldroyd model (a relation between shear thining and stress thickening). The employedmodel incorporates the effects of Brownian motion and thermophoresis due to the presence of nanoparti-cles. The governing nonlinear partial differential equations of the dynamical system are reduced to non-dimensional ordinary linear differential equations by using the linear theory, normal mode technique andthe non-dimensional variables. The mathematical analysis is concerned with the solutions of the charac-teristic value problem for two cases: i) rigid-free and ii) rigid-rigid boundaries, respectively. The decidingstability parameter, the non-dimensional thermal Rayleigh number for each of these two cases is derivedusing trial functions satisfying the appropriate boundary conditions in each of these cases. The variationof thermal Rayleigh number with respect to wave number for certain fixed permissible values of other pa-rameters are computed numerically using the software MATHEMATICA-5.2. It is found that the stationaryconvection is independent of both Pramdlt number and particle density Rayleigh number. The stabilizingeffects of medium porosity, strain retardation and the destabilizing effects of stress relaxation, Lewis num-ber, concentration Rayleigh number, modified diffusivity ratio are also shown graphically. These results arecompared favorably with those obtained earlier.

Keywords: Nanofluid, Oldroyd model, Thermal Convection, Porous Medium, Thermal Rayleigh num-ber.

Mathematics Subject Classification : 76Exx, 76Sxx.

Inclined MHD Williamson Fluid Flow with Slip Boundary and Heat and MassTransfer due to Porous and Melting Stretching Surface with Non-Linear Radiation

and Heat SourceAmit Parmar

Poornima College of Engineering Rajasthan, [email protected]

In this article, we have investigated a problem for momentum, thermal energy and mass transfer behaviorof inclined Williamson fluid due to melting stretching surface in the presence of non-linear thermal radiationand heat source with suction and slip boundary condition. Williamson is a real fluid. A real fluid has bothminimum viscosity and maximum viscosity depending upon the molecular shape of the fluid. By usingsuitable transformation, the governing equations are converted into non-linear coupled ODEs and solved byusing RungeKutta based shooting technique with MATLAB. The effect of various parameters on velocityand temperature profiles are discussed and display graphically. Local Nusselt number and skin frictioncoefficient are tabulated.

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Sandip Rakshit

An overview to investigate role of rheology on thermal convection in ferrofluidsVeena Sharma

Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171 005, India.Email: [email protected]

A fascinating smart fluid magnetorheological fluid (MRF) has the potential in designing hydraulic sys-tems (active shock and vibration dampers, actuators, values, automobile suspensions, seats), very fast,powerful computers of less cost as well as convenient softwares and are being used in material research,and bio-medications etc. The various rheological models of ferrofluids are synthesized and prepared by theresearchers in the present era so as to examine to control the stability and the form of convective motions(whether stationary cellular motion or oscillatory motion) both experimentally and theoretically, in the con-sidered physical system. Therefore, there is compelling need to develop new and improved MRF to lowertheir production cost through improved manufacturing processes and develop MR fluid based applicationdevices that will demonstrate the engineering feasibility of the MR fluid concept and will highlight theimplementation challenges in near future. An important application of MRF also lies in biomedicine areawhere the carrier liquid is blood which is known to have special rheological properties. In the present talkwe will discuss the survey of the gradual developments from the research and applications point of view.A special thrust in the discussion will be given to the ultra precision polishing of ceramics using MRFand diamond abrasives which have promising potential in aerospace applications (silicon nitride bearingsare used in main engines of NASAs space shuttle and thruster in Rocket engine). In addition to this, wewill also examine how the rheological behavior of ferrofluids affects the stability of convective motions inphysical systems using Galerkin finite element of weighted residues and truncated Fourier series method.

Sheetal DharmattiData assimilation type Optimal control problem for Cahn Hilliard Navier Stokes’ system.

Department of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram, In-dia.Email: [email protected]

This work is concerned about some optimal control problems associated to the evolution of two isother-mal, incompressible, immiscible fluids in a two-dimensional bounded domain. The Cahn-Hilliard-Navier-Stokes model consists of a NavierStokes equation governing the fluid velocity field coupled with a con-vective CahnHilliard equation for the relative concentration of one of the fluids. A distributed optimalcontrol problem is formulated as the minimization of a cost functional subject to the controlled nonlocalCahn-Hilliard-Navier-Stokes equations. We establish the first-order necessary conditions of optimality byproving the Pontryagin maximum principle for optimal control of such system via the seminal Ekelandvariational principle. The optimal control is characterized using the adjoint variable. We also study anothercontrol problem which is similar to that of data assimilation problems in meteorology of obtaining unknowninitial data using optimal control techniques when the underlying system is same as above.

Keywords:AMS subject classifications :

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Paper Presentation

Numerical Solution of Lane-Emden type Equations Using Multilayer PerceptronNeural Network MethodAkanksha Verma, Manoj Kumar

Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj-211004, (U.P.)India

[email protected]

In this paper, we discuss the Multilayer perceptron artificial neural network method for the solution ofsecond order non-linear singular differential equations of Lane-Emden type. Our aim is to produced opti-mal solution of Lane-Emden equations with less computation using multilayer perceptron artificial neuralnetwork method in comparison to other existing methods. Several test examples have been considered toillustrate the proposed method. The results obtained to prove that this method has capability to become aneffective approach for solving Lane-Emden problems with less computing time and memory space.

Key words: Multilayer perceptron Artificial Neural Network, Singular Initial Value Problem, Lane-Emden equation, Error back propagation, Quasi Newton method.

AMS Subject Classification: 65N20

Computational Simulation for Time-Fractional Diffusion Equation with NeumannBoundary Conditions

A.S.V. Ravi Kanth, Neetu GargDepartment of Mathematics National Institute of Technology Kurukshetra, Kurukshetra-136119, India Email:

[email protected], [email protected]

In this paper, computational simulation for a class of time-fractional diffusion equation with Neumannboundary conditions is presented. We construct a numerical scheme by combining L1 approximation forCaputo time-fractional derivative and exponential B-spline approximation for spatial derivatives. The pro-posed scheme is unconditionally stable. The numerical examples are presented to confirm the efficiencyand applicability of the proposed scheme.

Keywords Time-fractional diffusion equation, Caputo derivative, Exponential B-spline method, Stabil-ity.

AMS subject classification: 35R11. 65M12.

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On Solution of Fractional Order Advection-Diffusion Equation in Porous MediaPrashant Pandey

Department of Mathematical SciencesIndian Institute of Technology (BHU), Varanasi, 221005, India

address: [email protected]

In the present article, an operational matrix method with Laguerre polynomials is applied to solve aspace-time fractional order non-linear Cahn-Hilliard equation, which is used to calculate chemical potentialand free energy for a non-homogeneous mixture. Constructing operational matrix for fractional differen-tiation, the collocation method is applied to convert Cahn-Hilliard equation into an algebraic system ofequations, which have been solved using Newton method. The salient features of the article is to findingthe stability analysis of the proposed method and the pictorial presentations of numerical solution of theconcerned equation for different particular cases and showcasing of the effect of advection and reactionterms on the nature of solute concentration of the considered mathematical model for different particularcases..

Keywords: Fractional Calculus, Convergence Analysis, Sub-diffusion, Porous Media, Laguerre Poly-nomials

AMS subject classifications :35Q35, 35B35, 35B30

An exact l1 penalty function method for multi-dimensional first-order PDEconstrained control optimization problem

PreetiDepartment of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004,

Jharkhand, [email protected]

In this paper, we use the exact l1 penalty function method to solve a multi-dimensional first-order PDEconstrained control optimization problem. The relationships between an optimal solution to the aforesaidproblem and its associated penalized problem with the exact l1 penalty function are established. Further, weshow that an optimal solution to the considered problem is a minimizer of its associated penalized problemunder the hypothesis of convex Lagrange functional. In addition, the theoretical results are justified withsome examples.

Keywords: Exact l1 penalty function method Multi-dimensional control optimization problem Neces-sary optimality conditions.

AMS subject classifications : 26A51, 49J15.

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Numerical solution of Lane-Emden type equations using Adomian decompositionmethod with unequal step-size partitions

UMESH, Manoj KumarDepartment of Mathematics, Motilal Nehru National Institute of Technology Allahabad,

Prayagraj-211004 (U.P) [email protected], [email protected]

In this paper, Modified Adomian decomposition method (MADM) for solving Lane-Emden type equa-tions with unequally space partitions is presented. To prove the robustness and effectiveness of the proposedmethod various examples are considered. This method overcomes the singular behavior of the problemsand exhibits the approximations of high accuracy with a large effective region of convergence.

Keywords: Modified Adomian decomposition method, Adomian polynomials, Singular ordinary dif-ferential equations

AMS subject classifications : 65N20

Solution of Riemann problem for non-ideal magnetogasdynamic flowPooja Gupta

Department of Mathematical Sciences Indian Institute of Technology (B.H.U.) Varanasi 221005, India, E-mail ID:[email protected]

The present paper concerns with the analytical solution of the Riemann problem for magnetogasdynamicequations governing an inviscid unsteady one-dimensional flow of non-ideal polytropic gas subjected to thetransverse magnetic field with infinite electrical conductivity. By using the Lax entropy condition and R-Hconditions, we derive the elementary wave solutions i.e. shock wave, simple wave and contact discontinu-ities without any restriction on the magnitude of initial data states and discussed about their properties. Fur-ther, the density and velocity distribution in the flow field for the cases of compressive wave and rarefactionwave is discussed. Here we also compare/contrast the nature of solution in non-ideal magnetogasdynamicflow and ideal gas flow.

Keywords: Riemann problem; Non-ideal; Magnetogasdynamics; Shock wave; Simple wave

Wave interaction with a tunnel in a sea with bottom undulationMANISHA, Dr. RAMANABABU KALIGATLA

Department of Applied Mathematics IIT (ISM) DHANBAD Dhanbad- 826004, Jharkhand, India, Emails:[email protected], [email protected]

A boundary value problem for linear wave interaction with a tunnel in a sea with bottom undulationis studied by the method of eigenfunction expansion and modified mild-slope equation. The tunnel is as-sumed to be rectangular shape and, trapezoidal and circular undulations are considered as breakwaters inthe present study. The effect of bottom undulation on waves and thereby effect on tunnel is analyzed. Solu-tions are obtained by means of separation of variables and those are matched at the interface boundaries bythe conservation of mass flux and continuity of pressure and velocity. The important scattering coefficientssuch as reflection and transmission coefficients are obtained by solving system of equations. Forces are ontunnel are calculated and depicted for wave and structural parameters. Moreover, a definite range of wave

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incident angles is demonstrated for obtaining the critical angle which provides the least reflection and mostforce on the tunnel.

Keywords: Submerged tunnel, Submerged breakwater, Eigenfunction expansion, Modified mild-slopeequation, Reflection coefficient.

AMS subject classifications : 34L10

Subgrid multiscale stabilized finite element analysis for various transport equationsManisha Chowdhury, B.V. Rathish Kumar

Indian Institute of Technology Kanpur Kanpur, Uttar Pradesh, [email protected]

Finite element method (FEM) is a well-known numerical scheme for solving partial differential equa-tions of boundary value problems in the areas of structural analysis, heat and mass transfer, fluid flowetc. Finding analytical solution of various types of transport equation such as advection-diffusion-reaction(ADR) equation with variable coefficients, coupled Stokes and ADR equations, coupled Navier Stokes andADR equations are very difficult and challenging task. Due to wide range of applications of these transportproblems in the fields of bio-medical engineering, chemical engineering, environmental sciences etc, anal-ysis of numerical schemes,such as FEM for the approximate solution of these equations are attractive topicsof research. In this talk a stabilized finite element method for solving transport equations will be presented.Here subgrid scale approach along with algebraic approximation to the subscales has been chosen to sta-bilize the Galerkin finite element method. Both a priori and a posteriori finite element error estimates inL2 norm will also be discussed. Numerical results will be presented to verify the theoretically establishedexpressions.

Keywords : Transport equation Subgrid multiscale finite element method a priori error estimate aposteriori error estimate

Numerical solution for two dimensional space-time fractional reaction diffusionequation

Sachin KumarDepartment of Mathematical Sciences,

Indian Institute of Technology(B.H.U) Varanasi 221005, India.E-mail address: [email protected]

In this article, an operational matrix method with Genocchi polynomials is applied to solve a two di-mensional space-time fractional order nonlinear reaction-diffusion equation. An operational matrix forfractional order differentiation is derived. Applying collocation method and using the said matrix, frac-tional non-linear partial differential equation is reduced to a system of algebraic equations, which can besolved using Newton iteration method. The salient features of the article are the pictorial presentations ofthe numerical solution of the concerned equation for different particular cases to show the effect of reactionterm on the solution profile and also the change of its behavior when the system approaches from standardorder to fractional order. The accuracy of our proposed method is validated through the error analysis ofthe obtained numerical results with the existing analytical results for two spatial fractional order nonlinearequation.

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Keywords: Fractional Calculus, Diffusion equation, Sub-diffusion, Porous Media, Genocchi Polyno-mials.

AMS subject classifications : 35Q35, 35B35, 35B30

Mathematical Modeling of Surface wave transference in a piezo-composite mediausing WKB technique

Sonal Nirwal, Sanjeev A. SahuDepartment of Applied Mathematics, IIT (ISM) Dhanbad, Jharkhand, 826004, India, Email:

[email protected]

This paper proposes an analytical solution (using asymptotic approximation) for the propagation ofsurface waves in a smart piezo-composite structure. The considered structure is a three-layered system inwhich the uppermost piezoelectric (PE) layer is accomplished by a functionally graded piezoelectric mate-rial (FGPM) layer and piezomagnetic (PM) half-space. The Wentzel-Kramers-Brillouin (WKB) asymptoticmethod is adopted to solve the differential equations. Influence of various affecting parameters on phasevelocity curve of different modes has been shown graphically.

Keywords: Asymptotic approximation, FGM, Surface wave.

AMS subject classifications : 74J15, 74A40, 74D05, 74G10, 74H10.

Modelling of Aeration Efficiency At Gabion WeirKM. Luxmi, Nand Kumar Tiwari, Subodh Ranjan Vajesnayee

National Institute of Technology Kurukshetra, Haryana-136119, [email protected], nand [email protected], [email protected]

Gabion weir consists of a porous medium filled with different shape and size of coarser materials. Theturbulence generated by gabion weir will promote the aeration efficiency in the form of large number andbigger forms of bubbles.Aeration is defined as the process of oxygen transfer from atmosphere to water.From this process, the amount of oxygen in water is enhanced and measured as dissolved oxygen (DO)in terms of ppm. Dissolved oxygen is one of the best indicators of water quality. This paper attempts toinvestigate the prediction of aeration efficiency of gabion weir by using AI- based modelling techniques.The output values of aeration efficiency through gabion weir were computed using ANN, Linear regression,Gaussian process and randomforest by taking mean size, porosity, discharge, drop height as input parame-ters. Data is taken by conducting experiments in NIT laboratory. Comparing these modelling techniques, itwas found that ANN has been giving better results than other considered techniques. The findings of thispaper will help in choosing better gabion weir model and modelling technique for best result.

Keywords: Gabion Weir; Aeration Efficiency; Dissolved Oxygen (DO); Porosity; Gaussian Process;Random Forest; ANN; Linear Regression.

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Modelling of scour around spur dykesAmit kumar, Subodh ranjan vajesnayee, and Nand kumar Tiwari

M.Tech Civil Engineering, National Institute of Technology Kurukshetra, Haryana-136119, [email protected], [email protected], [email protected]

Spur dykes are typical man-made hydraulic structures and widely used in allu- vial rivers to defendagainst the effects of disaster and helps in river restoration. Spur dykes are generally built perpendicular orat an angle to the channel bank to protect it against scouring. Spur dykes impact the ow and bed load dy-namics around itself and creates variation in ow pattern and bottom pro

le according to the relationship between the ow characteristics and bed congu- rations. This paper attempts to investigate the scouring around the spur dykes by increasing the

roughness and changing the angle of spur dykes. By using the AI- based modelling technique, It has beenpredicted the scouring around the spur dykes by changing the roughness, and dimension of spur dykes.In this study, the output value of scour around spur dykes due to increasing its surface roughness werepredicted using ANN and Gaussian Process by taking parameters like mean size(d50), velocity, angle, andcontraction ratio of spur dykes.

Keywords: ANN, Gaussian process, scouring, spur dykes, roughness, D50, constriction ratio.

Modelling the delay dynamics of malware propagationSangeeta Kumari

Department of Applied Mathematics, Indian Institute of Technology(Indian School of Mines), Dhanbad, [email protected]

To understand the transmission dynamics of malware propagation in wireless sensor networks, an at-tempt has been made. An e-epidemic delay model with the non linear incidence rate and sigmoid typerecovery rate has been proposed. Existence and stability analyses of the equilibria are performed. Attentionhas been paid to the occurrence of Hopf bifurcation. Numerical simulations is performed for validatingthe theoretical analysis with the help of MATLAB. The impact of the control parameters on the systemdynamics is investigated. Most effective measures are suggested based on the obtained results to controlthe propagation of malicious entities.

Keywords: Delay differential equation, Wireless sensor network, Hopf bifurcation, Malware propaga-tion, Stability Analysis.

AMS subject classifications : 37C75, 65P30, 37M10, 37M05.

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Analysis of a density dependent model with discrete delaysAnuraj Singh, Ankit Parwaliya and Ajay kumar

ABV-Indian Institute of Information Technology and Management, Gwalior, M.P., [email protected], [email protected], [email protected]

A two dimensional model with finite number of discrete delay has been investigated.The Permanence,persistence,positivity,andboundedness of the delayed model has been determined under certain conditions.Phenomenon of Hopf bi-furcation has been determined for different combination of delays. It is resulted that delay cause Hopfbifurcation and further complex dynamics in the system. By using central manifold theorem and normaltheory the direction and stability of Hopf bifurcation is determined. The analytical findings have been vali-dated by exhaustive numerical simulation which exhibits a wide range of complex dynamics in the system.

Keywords: Delay, Global Stability, Hopf bifucation, Permanence.

Approximate analytical solution for shock wave in rotational axisymmetric perfectgas: Isothermal flow

G. Nath, Sumeeta SinghDepartment of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj 211004, Uttar

Pradesh, India, Email: [email protected]

The propagation of cylindrical shock wave in rotational axisymmetric perfect gas under isothermal flowcondition is investigated. Mathematical model for the considered problem using PDEs is presented. Dis-tribution of gasdynamical quantities are discussed. The density, azimuthal fluid velocity and radial fluidvelocity are assumed to be varying according to power law with distance from the axis of symmetry in theundisturbed medium. Approximate analytical solutions are obtained by expanding flow variables in powerseries of (C/U)2, where C is the sound speed in undisturbed fluid and U is the propagation velocity of shockwave. Zeroth and first order approximations are discussed by the aid of power series method. Solutions forzeroth order approximation are constructed in approximate analytical form. The effect of flow parametersnamely: adiabatic exponent and ambient density variation index q are studied on the flow variables. Key-words: Shock wave, Power series method, Isothermal flow, Perfect gas, Rotating medium, Modeling usingPDEs

AMS subject classifications : 76L05, 76U05, 76M55.

MULTIBODY MODELLING OF A RAIL VEHICLE USING MR SUSPENSIONSYSTEM

Deepak Goyal, Sultan Singh, Anil KumarDepartment of Mechanical and Industrial Engineering, IIT Roorkee, India.

[email protected]; [email protected]; [email protected]

The improvement in critical speed of rail vehicles has been ever needed. This article presents a multi-body dynamics approach for evaluating critical speed of a rail vehicle. 17 degrees of freedom are usedfor mathematical modeling of a LHB rail vehicle by considering lateral vehicle dynamics. The degrees offreedom represent lateral and yaw movements of all the 4 wheelsets, lateral, yaw and roll movements ofbogies and car body. Eigen value approach is opted for predicting the stability behavior of themodel. Inuence of design parameters on critical speed is investigated. A sensitivity analysis hasbeen performed to

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assess the in uence of all the dampers on critical speed. The most suitable position for replacing the existingpassive damper with magnetorheological (MR) damper has been identi

ed. Bouc-wen model for MR damper is implemented in MATLAB/SIMULINK. MR model is coupledwith multibody model of the rail vehicle, as a result the behavior of the rail vehicle equipped with MRdamper is analysed. A comparative study for critical speed between MR damper and passive damper sus-pension is done.Improvement in critical speed of rail vehicle has been observed.

Keywords: LHB COACH , CRITICAL SPEED , SENSITIVITY ANALYSIS, VEHICLE STABLITY,MR DAMPER.

Size-dependent vibration of microplate resonators based on the modified couplestress theory and three-phase-lag heat conduction model

Harendra Kumar and Santwana MukhopadhyayDepartment of Mathematical Sciences, Indian Institute of Technology (B.H.U.), Varanasi-221005.

harendra.rs.,[email protected]

Thermoelastic damping (TED) is a significant energy loss factor at room temperature in micro-scaleresonators. The prediction of TED is important in the designing of high quality of micro-electromechanicalsystem (MEMS) resonators. In the present work, an analytical expression for the quality factor (Q) of TEDis presented by applying modified couple stress theory (MCST) considering plane stress condition and thethree-phase-lagging (TPL) heat conduction model. As case study, the effect of the length-scale parameter onthe quality factor of TED in Kirchhoff microplate resonators are discussed in detail. To study the behaviorof TED, the material of the microplate resonator is considered as Silicon. The variation of TED as functionsof the normalized frequency, microplate thickness, reference temperature have been investigated. The effectof phase-lag parameters on TED has also been shown. The results of the present model are compared tothose obtained by the classical continuum theory. The current results show that when the material lengthscale parameter increases, the quality factor increases significantly from the classical continuum theory.

Keywords: Thermoelastic damping; Quality factor; Size effects; Microplate resonator; Modified couplestress theory; Three-phase-lag heat conduction model.

Stability Analysis of a Delay Induced Dynamical Model on Oncolytic VirotherapyHitesh K. Singh and Dwijendra N. Pandey

Department of Mathematics Indian Institute of Technology Roorkee Roorkee, 247667, [email protected], [email protected]

In this paper, we have studied a non-linear delayed dynamical model that illustrates the interaction be-tween an oncolytic virus and the cancerous cells. An oncolytic virus is a virus that selectively kills tumorcells without harming healthy cells. The model includes two kind of cancerous cells, infected cells (infectedby an oncolytic virus) and uninfected ones. We have thoroughly analyzed the stability of all the equilibriumpoints of the system by finding the roots of the corresponding characteristic polynomials which are the ex-ponential polynomials with the coefficients involving delay variable. The necessary stability conditions areestablished in order to stabilize the system in equilibrium. The existence of Hopf bifurcation is shown withdelay as bifurcating parameter. In order to verify the analytical results, numerical simulations are carriedout using two MATLAB solvers namely ode45 and dde23.

Keywords:

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On Existence of Solution of First Order Retarded Differential equations withpiecewise constant delays

Aradhana Bandekar, Y. S. ValaulikarGoa University,Taleigao Plateau ,Panaji, Goa-403206, India.


In this paper, a nonlinear boundary conditions has ben proposed and analysed. We discusses the ex-istence of a solution for a first order Retarded Differential equations with piecewise constant delays andwith Nonlinear Boundary Conditions between Lower and Upper Solutions. It is observed that there existsatleast one solution between coupled lower and upper solution and also between coupled lower and uppersolution in reverse order. This results were obtained by using Arzela Ascoli Theorem , Schauder’s FixedPoint Theorem and L1-Caratheodary conditions. We have examined all possible cases that the equationcould go through.

Keywords: Retarded Differential equations,piecewise constant delays, Nonlinear Boundary Conditions,Lower and Upper Solutions.

AMS subject classifications : 28A75,33E30, 34B15,,34K10

Evolution of weak shock wave in two-dimensional steady supersonic flow in dustygas

Rahul Kumar ChaturvediDepartment of Mathematical Sciences

Indian Institute of Technology (B.H.U.) Varanasi 221005, [email protected]

The present paper concerns with the propagation of weak shock waves in a dusty gas governed by thequasilinear hyperbolic PDEs. Using the method of wavefront analysis the transport equations governingthe evolution of weak discontinuities are derived which lead to determine the shock formation distance andconditions which ensure that there will not evolve any shock wave on the wavefront. Also the influence ofdust particles, ratio of specific heats and upstream flow Mach number on the shock formation distance isdiscussed.

Keywords: Hyperbolic PDEs; Weak shock; Wavefront analysis; Dusty gas.

Existence and regularity of solutions of fractional differential equations involvingHilfer fractional derivative of order 1 < α < 2 and type 0 ≤ β ≤ 1

Anjali Jaiswal, D. BahugunaDepartment of Mathematics, Indian Institute of Technology Kanpur, Kanpur-208016, India.

[email protected]

In this paper we investigate the regularity of a solution of a linear problem involving Hilfer fractionalderivative. We define the mild solution of an abstract Cauchy problem and obtain conditions under which amild solution becomes a strong solution. We also study a semilnear fractionl evolution equation and give asuitable definition of a mild solution and establish some existence results for a mild solution.MSC 2010: 34G10, 34A08, 34G20, 34A12.Keywords: Hilfer fractional derivative, strong solution, mild solution, solution operator, fixed point theo-rem.

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On First Integral Method and Lie Symmetry of meta-mKdV equationMahima Poonia, K. Singh

Department of Mathematics Jaypee University of Information Technology Waknaghat, Distt.-Solan-173234(H.P.),India.

[email protected]

In this paper, the meta-mKdV equation is investigated using the first integral method and Lie symmetry.In Lie symmetry, similarity variables are constructed from the Lie symmetry generators which lead to theordinary differential equation. Using this method, the governing equation is reduced to the Abels equationof second kind. The First integral method provides polynomial first integrals. Using these first integralsthe exact solutions of given equation are derived. Applying this method to the meta-mKdV equation, twoimplicit and some exact travelling wave solutions are obtained. These solutions are completely new contri-butions.

Keywords: The first integral method; Lie Symmetry; meta-mKdV equation.

AMS subject classifications : 35Qxx, 35E99, 35G25

On Monotone Method for a First Order Neutral Differential EquationMamta Kumari, Y. S. Valaulikar

Department of Mathematics, Shree Damodar College of Commerce & Economics, Comba, Margao, Salcete, Goa403 601, India.

[email protected]

This paper discusses the existence of solution for periodic boundary value problem of a first order neutraldifferential equation with piecewise constant deviating argument by using the monotone iterative technique.

Keywords: Neutral differential equations, piecewise constant deviating argument, positive solution,periodic boundary value, monotone iterative technique.

AMS subject classifications : 34K20, 34K40.

Space time fractional nonlinear partial differential system: Exact solution andconservation laws

Baljinder Kour, Sachin KumarDepartment of Mathematics and Statistics,

Central University of Punjab, Bathinda-151001, Punjab, [email protected]; [email protected]

The object of the present article is to study space time fractional generalized Hirota Satsuma coupledKorteweg-de Vries (HSCKdV) system for exact solution using power series method corresponding to Liesymmetry reduction of HSCKdV system. The exact solution obtained in power series form further analyzedfor convergence. Conservation laws of the HSCKdV system are constructed by using the new conservationtheorem and generalized fractional Noether’s operator.

Keywords: Fractional generalized Hirota Satsuma coupled Korteweg-de Vries equations, power seriessolution, conservation laws.

AMS subject classifications : 35R11, 34A05, 35C10, 35L65.

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Solution of Partially Singularly Perturbed System of Initial and Boundary ValueProblems Using Non-Uniform Haar Wavelet

Akmal Raza, Arshad KhanDepartment of Mathematics, Jamia Millia Islamia, New Delhi-110025, India.

[email protected],[email protected]

An efficient non-uniform Haar wavelet method is proposed for the numerical solution of system of firstorder linear partially singularly perturbed initial value problem on piecewise uniform Shishkin mesh andρ−mesh. Further, we apply same technique for solving system of second order linear partially singularlyperturbed boundary value problem on piecewise uniform Shishkin mesh and q−mesh. Our method pro-duces better results in comparison to uniform Haar wavelet, classical finite difference operator method andparameter uniform methods. We demonstrated two test problems to support the theory, accuracy and effi-ciency of the non-uniform Haar wavelet method.

Keywords: System of Differential Equations; Non-Uniform Haar wavelet; Shishkin Mesh; Singularperturbation; Initial and Boundary Value Problems.

Existence, Uniqueness and Regularity of Mild Solutions of Fractional OrderNavier-Stokes Equations with Finite Delay

Md Mansur Alam, Shruti DubeyDepartment of Mathematics

Indian Institute of Technology MadrasChennai-600 036, India.

[email protected], [email protected].

In this work, we consider time-fractional Navier-Stokes equations (NSE) with the external force involv-ing finite delay over a bounded domain Ω ⊂ R3 having sufficiently smooth boundary. We transform thesystem of equations (NSE) to an abstract Cauchy problem and then investigate local existence and unique-ness of the mild solutions for the initial datum φ ∈ C

([−r, 0];D(A

12 )), where A is the Stokes operator.

With some suitable restriction on initial datum we establish the global existence and regularity of the mildsolutions. We use semigroup theory, some tools of fractional calculus and Banach contraction mappingprinciple to establish our results.

Keywords: Fractional calculus, Navier-Stokes equations, delay differntial equations, analytic semi-group, Mild solutions, fractional power of operators.

MSC 2010: 34A08, 34K37, 35D99, 76D05, 76D03

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A new approach of operational matrices for hyperbolic partial differentialequations

Somveer Singh, Mani MehraDepartment of mathematics, IIT Delhi, India

[email protected],[email protected]

A new approach based on operational matrices of Legendre wavelets is introduced for the class of firstorder hyperbolic partial differential equations with the given initial conditions. Operational matrices ofintegration of Legendre wavelets are derived and utilized to transform the given PDE into the linear systemof equations by combining collocation method. Convergence analysis and error estimation the presentedtechnique are also investigated. Some numerical experiments are performed to demonstrate accuracy andefficiency of the proposed method

Analytical Solution of 1-D Advection-Dispersion Equation with an AdditionalSource/Sink term in the Semi-infinite Aquifer using Dispersion Theory

RohitKumar, Manish Chaudhary and Mritunjay Kumar SinghDepartment of Applied Mathematics Indian Institute of Technology (Indian School of Mines) Dhanbad - 826004

(Jharkhand)[email protected]

Mathematical model describing pollutant transport in semi-innite aquifer is often represents advection-dispersion equation (ADE). In this present problem, ADE is

considered with a source/sink term incorporated in one of the functional form. The aquifer is initiallycontaminant free and one additional source term is considered at the inlet boundary. Flux type boundarycondition is at the outlet boundary. Time-dependent velocity and dispersion is considered to add more re-alism in this problem. A closed form solution is obtained using Laplace transform and Matlab is used toobtain the graphical representation. A numerical solution is obtained by Crank-Nicolson scheme. Theresults are compared among both the solutions and found a good agreement between them. The effect ofsource/sink term as a function in the 1-D ADE is explained. The proposed model may be used as a prelim-inary predictive tool in a groundwater resource and management.

Keywords: Aquifer, Advection dispersion equation, Contamination, Source-Sink, Time-dependentdispersion and velocity.

AMS subject classifications : 76Rxx, 76Sxx

Exponentiable objects in Q-TOPHarshita Tiwari

Department of Mathematical Sciences Indian Institute of Technology (B.H.U.) Varanasi 221005, India, E-mail:[email protected]

In this paper, we have defined the exponential Q-topology on the power-set of two Q-topological spacesin the category Q-TOP of Q-topological spaces and Q-continuous maps (where Q is a fixed member of afixed variety of -algebras), and studied the exponentiable objects in the category Q-TOP.

Keywords: Exponentiable object; Q-topology; -algebra.

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Lp Spectra of Strongly Carleman Pseudo Differential Operators associated withintegral transform

Pragya ShuklaDepartment of Mathematical Sciences Indian Institute of Technology (B.H.U.) Varanasi 221005, India, E-mail:

[email protected]

In this paper, we have defined Lp Spectra of Strongly Carleman Pseudo Differential Operators associ-ated with integral transform and studied its various properties like minimal, maximal operators and essentialspectrum.

Keywords: Pseudo Differential Operators; Minimal operators; Maximal operators.AMS subject classifications :

Metrical fixed point theorems via locally finitely T-transitive binary relations undercertain control functions

Aftab Alam, Mohammad Arif and Mohammad ImdadDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002, India.

[email protected], [email protected] and [email protected]

In this paper, we extend relation-theoretic contraction principle due to Alam and Imdad to a nonlinearcontraction using a relatively weaker class of continuous control functions employing a locally finitely T -transitive binary relation, which improves the corresponding fixed point theorems especially due to: Alamand Imdad (J. Fixed Point Theory Appl. 17 (2015) 693-702), Agarwal et al. (Applicable Analysis, 87 (1)(2008) 106-116), Berzig and Karapinar (Fixed Point Theory Appl. 2013:205 (2013) 18 pp), Berzig et al.(Abstr. Appl. Anal. 2014:259768 (2014) 12 pp) and Turinici (The Sci. World J. 2014:169358 (2014) 10 pp).

Keywords: locally finitely T - transitive binary relations; control functions; R-connected sets.

Some Results on Summation-Integral-type Operators and Their PropertiesRishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology Surat(Gujarat-395007), India

Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, MadhyaPradesh 484887, India

Emails : [email protected], meher [email protected], [email protected]

In this paper, we study the Szasz-Mirakyan- Kantorovich type operators and obtain the rate of conver-gence with the help of local approximation results by using modulus of smoothness, second order modulusof continuity, Peetre’s K-functional and functions belonging to the Lipschitz class. The weighted approx-imation properties are discussed for computing the order of approximation and related theorems are alsoproved. To check the asymptotic behavior of the said operators, we prove the Voronovskaya type theorem.The convergence of the Szasz-Mirakyan- Kantorovich type operators is discussed. Graphical approach isalso given and the convergence shown via graphically and numerically. At last we take example to show theapproximation of the operators to the function by numerically, which is illustrated by table and comparisonof the said operators with the Szasz-Mirakyan- Kantorovich operators is took place in sense of absolutenumerical error.

Keywords: Szasz-Mirakjan- Kantorovich, Korovkin-type approximation results, modulus of smooth-ness, Peetre’s K-functional, weighted modulus of continuity.

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Kantorovich type generalization of modided Szasz-Mirakjan OperatorsAnkita R Devdhara, Vishnu Narayan Mishra

SVNIT, Surat, [email protected], [email protected]

In this paper, we generalize the modided Sza asz-Mirakjan operators in Kantorovich form. We discussmoments and central moments of the operators. We prove some local approximation results for the opera-tors.

Keywords: Szasz-Mirakyan operators, Korovkin’s theorems, Rate of convergence, Voronovskaya re-sult.

AMS subject classifications :

θ∗-WEAK CONTRACTIONS AND DISCONTINUITY AT THE FIXED POINTATIYA PERVEEN

Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India, Email: [email protected]

In this paper, the notion of -weak contraction is introduced, which is utilized to prove some fixed pointresults. These results are helpful to give a positive response to certain open question raised by Kannan[Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractivedefinition which does not force the mapping to be continuous at the fixed point. Some illustrative exam-ples are also given to support our results. As applications of our result, we investigate the existence anduniqueness of a solution of integral equations of Volterra type.

A New Type of Paranorm Intuitionistic Fuzzy Zweier I-convergent DoubleSequence Spaces

Hira FatimaDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002, India.

[email protected]

Fuzzy set theory was introduced by Zadeh [Fuzzy sets, Inform Control, (8)(1965), 338-353] which is apowerful hand set for modelling uncertainty and vagueness in various problems arising in field of scienceand engineering and has a wide range of applications. Fuzzy topology is one of the most important anduseful tools and it proves to be very useful for dealing with such situations where the use of classical theoriesbreaks down. In this article, we introduce the paranorm type intuitionistic fuzzy Zweier I-convergent doublesequence spaces 2Z

I(µ,ν)(p) and 2Z

I0(µ,ν)(p) for p = (pij) a double sequence of positive real numbers and

study the fuzzy topology on the said spaces.

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Relation-theoretic multi-valued θ-contraction]Relation-theoretic fixed point resultsfor Multi-valued (θ,R)-contractions with an Application

Mohammad Imdad , Md Hasanuzzaman and Waleed M. Alfaqih

Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.Department of Mathematics, Hajjah University, Hajjah, Yemen.

[email protected], [email protected] and [email protected]

The aim of this paper is to introduce a relatively new concept of multi-valued (θ,R)-contractions andutilize the same to prove some fixed point results in metric spaces endowed with an amorphous binary re-lation. Illustrative examples are also furnished to exhibit the utility of our results proved herein. Finally,we utilize some of our results to investigate the existence and uniqueness of a positive solution for Volterratype integral equation.

Keywords: Fixed point, θ-contractions, multi-valued θ-contractions, binary relations, integral equa-tions.

Optimal control analysis of an e-epidemic model including firewall effectPrerna Singh, Ranjit Kumar

IIT(ISM) Dhanbad, [email protected], [email protected]

A mathematical model has been proposed that studies the virus propagation of a distributed attack ona targeted network. The model is composed of two different classes of computer nodes-attacking and tar-geted. A simpler model is further obtained from these systems by nondimensionalisation, and its dynamicalproperties are discussed. The firewall security is taken as a media coverage factor in this work and it is dis-covered that it helps to diminish the virus propagation in the network upto some extent. We then carry outthe optimal control analysis of the model system and give results regarding the effect of control measuresin controlling the virus propagation in a network. The aim of introducing control theory in this work is toprovide a measure for minimizing the virus transmission in a network. Numerical experiments are carriedout to justify the analytical findings.

Keywords: Firewall, distributed attack, optimal control.

AMS subject classifications : 92D30; 34D08; 34D23; 34D45; 65L07.

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Solution of Differential Algebraic Equations using Coded Differential TransformMethod

Anil Kumar and Giriraj MethiDepartment of Mathematics & Statistics,

Manipal University Jaipur-303003, Rajasthan, [email protected]; [email protected]

Aim of the paper is to obtain numerical solutions of some differential algebraic equations using CodedDifferential Transform Method (CDTM). We have compared our series solutions with other researcher us-ing multi quadric method. We have used Mathematica for numerical solutions and graphical illustrations.CDTM avoids linearization, discretization, complex calculations and save lots of time.

Keywords: Differential algebraic equations, Coded differential transform Method, Numerical solution,Mathematica

AMS subject classifications : MS34-04; MS34L99; MS37-04

Dynamic modeling and control of divided wall distillation multicomponentseparation

Manali Kokare, C. S. Mathpati, Ajit Kumar, S. S. JogwarDepartment of Chemical Engineering, Institute of Chemical Technology, Mumbai.

[email protected], [email protected], [email protected],[email protected]

Distillation is one of the most widely used separation method in chemical and allied industries. Thedesign of distillation unit involves system of ordinary differential equations related to overall mass, compo-nent, energy balance and thermodynamic equilibria of the system. Distillation is energy intensive processand design optimization is essential for energy saving as well as consistent quality. Divided wall distillationsystem is an optimized distillation method which involves separation of multicomponent mixture in singleunit where pre-fractionation and main column are separated by a wall which leads to saving in capital aswell as operating cost. The divided wall distillation is nonlinear in nature so the model predictive controlleris useful in which three component purities are controlled. In the proposed work, dynamic model of thesystem has been simulated in Matlab for the separation of (n-butanol)-(water)-(n-butyl levulinate). Theeffectiveness of the developed controller is checked for a step change in n-butanol purity.

Keywords:Divided wall distillation, globally linearizing controller, dynamic model, system of ordinarydifferential equations

AMS subject classifications : 34B60 (Under ODE: applications)

48

ASYMPTOTIC ANALYSIS OF BOUNDARY OPTIMAL CONTROLPROBLEMON A GENERAL BRANCHED STRUCTURE

S. AIYAPPAN,A. K. NANDAKUMARAN , AND ABU [email protected],[email protected],[email protected]

We consider an optimal control problem posed on a domain with a highly oscillating smooth boundarywhere the controls are applied on the oscillating part of the boundary. There are many results on domainswith oscillating boundaries where the oscillations are pillar-type (non-smooth). The literature on smoothoscillating boundary is very few and recently Aiyappan et. al have studied a homogenization problem onsuch oscillating domain by developing new unfolding operators. In this article, we use appropriate scal-ing on the controls acting on the oscillating boundary leading to different limit control problems; namely,boundary optimal control and interior optimal control problem. In the last part of the article, we visualizethe domains as a branched structure and we introduce unfolding operators to get contributions from eachlevel at every branch.

Keywords:Optimal control, Asymptotic analysis, Unfolding operator, Oscillating boundary domain,Homogenization

AMS subject classifications : 80M35, 80M40, 35B27, 49J20

Approximate controllability of multi-term time-fractional differential inclusionswith nonlocal conditions

Ashish Kumar, Dwijendra N. PandeyIndian Institute of Technology, Roorkee-247667


A set of sufficient conditions for the approximate controllability for a class of multi-term time fractionaldifferential inclusions with the nonlocal condition of the form

cD1+βy(t) +n∑j=1

αjcDγjy(t) ∈ Ay(t) +Bu(t) + F (t, y(t)) t ∈ [0, b]

y(0) + g(y) = σ,

y′(0) + h(y) = χ.

has been established in this article.Keywords:approximate controllability, multi-term time-fractional delay differential system, (β, γj)−

resolvent family, fixed point theorems, differential inclusions.


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Approximate Controllability of Semilinear Fractional Evolution Systems withmultiple Delays in Control

Abdul Haq, N. SukavanamDepartment of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India, Pin-247667.

[email protected]

This work studies the controllability of a class of fractional evolution differential equations with Riemann-Liouville fractional derivatives and with multiple delays in control. We establish suitable assumptions toprove the existence and uniqueness of mild solutions. Approximate controllability of the system is shownusing sequence method. Finally, an illustrative example has been provided.

Keywords: Riemann-Liouville fractional derivatives, fractional evolution systems, delay system,mild solution, approximate controllability.

AMS subject classifications : 93B05

CONTROLLABILITY OF NONLOCAL FRACTIONAL ORDERINTEGRO-DIFFERENTIAL SYSTEMS WITH TIME VARYING DELAY

Ajay Kumar, N. SukavanamDepartment of Mathematics, Indian Institute of Technology Roorkee Roorkee-247667, India e-mail:

[email protected]

In this article, we established some new set of sufficient conditions for the controllability of nonlocalfractional order integro-differential systems in Banach space with time varying delay under the assumptionthat semigroup operator is non-compact. The theory of fractional calculus, strongly continuous semigroup,and Nusbaum fixed point theorem are the main tools used in this problem. An example is given to verifythe application of our proposed results.

Keywords: Controllability, Fractional control delay systems, Semigroup Theory, Nusbaum FixedPoint Theorem.

AMS subject classifications : 93B05, 93C10.

Development of Higher-order Implicit-Explicit Robert-Asselin Type Time FiltersPraveen K. Maurya, Manoj K. Rajpoot

Department of Mathematics Rajiv Gandhi Institute of Petroleum Technology Jais 229 304, U.P., India, e-mail:[email protected]

A class of new hybrid implicit-explicit (IMEX)time filters based on three time- level leapfrog temporalintegration scheme are developed. The developed filters are used for the dispersive and non-dispersivemodel systems by considering the space-time discretization together. As, the leapfrog time-stepping methodis most commonly used in ocean and atmospheric modelling, however, it also admits a spurious mode innumerical computations. The developed hybrid IMEX time filters are based on the optimized values whichare capable in suppress- ing the computational mode(s) more effectively without affecting the physi- calmode. Finally, the developed IMEX filters are tested for one-dimensional non-dispersive convection andtwo-dimensional dispersive rotating shallow water equation (LRSWE), and by solving the incompressibleflow problem governed by Navier-Stokes equation at different Reynolds numbers.

Keywords: IMEX time filters; Spurious dispersion; Grid staggering; Rotary shallow water equa-tion; Navier-Stokes equation.

AMS 2010 Classifications: Primary 65Mxx; Secondary 65Txx.

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Modelling hydraulic characteristics of Gabion weir by soft computing techniquesSiddharth Sonkar1, N.K.Tiwari2, and Subodh Ranjan Vajesnayee3

1,2,3M.Tech Civil Engineering, National Institute of Technology Kurukshetra, Haryana-136119, [email protected]

e-mail: [email protected] A conventional weir essentially consists of an impermeable bodyconstructed by concrete and the main function of a weir is to raise the water level and efficiently regulatethe ow. Gabion is a cage, cylinder, or box filled with rocks, concrete, or sometimes sand and soil for use incivil engineering and other purposes. In this paper,soft computing based modelling techniques were usedto estimate the hydraulic characteristics of Gabion weir and results were compared with conventional solidbroad crested weir. The modelling techniques employed for analysis are Artificial Neural Network(ANN)and Gaussian Process (GP). The parameters used as input are water head at upstream, discharge,mean sizeof gabion materials , porosity,etc. and output as coefficient of discharge.

Keywords: Gabion weir,ANN, GP and Hydraulic Characteristics.

Effect of radiative heat transfer on the growth and decay of acceleration waves innon-ideal magnetogasdynamics

Shobhit Kumar SrivastavaIndian Institute of Technology (B.H.U.) Varanasi 221005, India.

[email protected]

In the present paper, the evolutionary behavior of weak shock waves propagating in an unsteady one-dimensional flow in non-ideal radiating gas under the effect of transverse magnetic field is examined. Forthe effect of thermal radiation, the radiative transfer equations are approximated under the optically thinlimit. It is observed that a linear solution in the characteristic plane may exhibit a non-linear behavior inthe physical plane. The transport equation governing the evolution of weak shock waves is obtained whichintroduces the conditions for shock formation. The time for the rst breaking of the wave is determined.Also, the effect of radiative heat transfer on the growth of compressive waves and decay of expansive wavesin ideal and non-ideal magnetogasdynamics regime is discussed.

Keywords: Thermal radiation; Non-ideal gas; Acceleration waves; Magnetic eld; Shock formation.

Wind turbine blade section optimization using a quantitative studyM.Balachandar, B.U Raja Ramakrishnaa and N.Ramanan

Sri Sai Ram Institute of Technology,Chennai,Tamilnadu,India , R&D, Synce engineeringservice,Chennai,Tamilnadu,India

[email protected], [email protected], [email protected]

Recently there has been an increase in the demand for the utilization of clean renewable energy sources.This is due to increase in the oil prices and increased awareness of human induced climate change. Windenergy has been shown to be one of the most promising sources of renewable energy. The variation hasbeen made with the cross sections of the wind turbine blades. The chosen airfoil is NACA five digit series.Two different series were chosen (NACA 63412 and NACA 63415). These airfoils were studied using asimulation software. Then analyzed using CFD software. Various graphs depicting the lift, angle of attackand drag co-efficient were studied to conclude the air foil having the highest lift. Later the finalized airfoilshape was fitted as one single wind turbine using a simulation software. The modified air foil was man-ufactured from Nutmeg Hickory wood. The given material provides better stability and finish and hence

51

was chosen. The power driven was found using calculation. The observed results were verified using thecomputed results from the software. The results shows that for low speed range of 2.5m/s - 9m/s generates1.28kW of power.

Keywords: CFD, NACA 63415, wind turbine, air foil, renewable energy,power

Hybrid impulsive effects on quasi-synchronization of neural networks withparameter mismatch and mixed time-varying delays

Rakesh KumarDepartment of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi-221005 Emails :

[email protected]

This article is deeply concerned about the effects of hybrid impulses on quasi-synchronization of neu-ral networks with mixed time-varying delays and parameter mismatches. The hybrid impulsive controllerhas been designed to deal with the difficulties in achieving the quasi-synchronization under the effects ofhybrid impulses which occur all the time, but their density decreases gradually with time. In addition tohybrid impulses, the new concept of average impulsive interval and average impulsive gain have been ap-plied to cope with the simultaneous existence of synchronizing and de-synchronizing impulses. Based onthe Lyapunov method together with some mathematical techniques and the extended comparison principlecombined with the formula of variation of parameters for mixed time-varying delayed impulsive system,the delay-dependent sufficient criteria of quasi-synchronization have been derived for two separate cases,viz., a Ta < ∞ and a Ta = ∞. Finally, the efficiency of the theoretical results has been illustrated byproviding two numerical examples.

Keywords: Neural networks, Quasi synchronization, Hybrid impulses, Parameter mismatch, Mixedtime-varying delays.

Novel divergence measure for refined single valued neutrosophic sets and its utilityin decision making

Adeeba Umar, R. N. SaraswatDepartment of Mathematics and Statistics Manipal University Jaipur, Jaipur -303007, Rajasthan, India.


Neutrosophic set which is a branch of neutrosophy, studies the scope, characterization and origin of theneutralities and their interconnection with various ideational expansion. Neutrosophic set is an influentialframework which has been proposed recently. In this communication, a novel divergence measure for re-fined single valued neutrosophic sets is introduced with the proof of its validity. An application of noveldivergence measure is shown with an illustration for decision making in medical investigation and projectselection.

Keywords: Divergence measure, refined single valued neutrosophic sets, medical diagnosis, decisionmaking.

AMS subject classifications : 94A15, 62B86, 94A17

52

Analysis of Surface Seismic Waves in Piezomagnetic Layered StructureSuman Goyal, Sanjeev Anand Sahu

Department of Applied Mathematics, IIT (ISM) Dhanbad (826004), Jharkhand, [email protected] , [email protected]

We propose an analytical solution for the transference of surface seismic waves in a piezo-compositesmart structure. A model describing the propagation of the considered wave in the piezomagnetic layeredstructure is considered. The model is comprised of piezomagnetic layer lying on inhomogeneous elastichalf-space. The inhomogeneity in the half-space is due to exponential variation of elastic constants withthe depth. The governing equations are presented in form of direct Sturm-Liouville problem. Frequencyequations in the form of determinant have been obtained for both the magnetically open and short cases.The influences of layer thickness, presence and absence of piezomagnetic coefficient on the phase velocityof surface wave are depicted through graphs. The results may be useful in designing and optimization ofSurface Acoustic Wave (SAW) devices.

Keywords:Love-type wave, inhomogeneity, Sturm-Liouville, Smart Material.

AMS subject classifications : 74J15, 74D05, 74G10, 74H10.

Velocity Profile of Shear Horizontal (SH) surface waves in Bi-layeredFGPM/Porous Piezoelectric Plate

Shreeta Kumari, Sanjeev A. Sahu1, Kamlesh K. PankajDepartment of Applied Mathematics, IIT(ISM), Dhanbad-826004, Jharkhand, India.

[email protected], [email protected], [email protected]

The present problem is confined to study the SH-wave propagation in a functionally graded piezoelec-tric plate fused together with porous piezoelectric plate. The functionally graded material is assumed tobe varying quadratically. Separation of variable method is used to get the solution for the displacementand stress components. Solutions of the constitutive equations are obtained in terms of modified Besselsfunction of the first and second kind. Dispersion relation is obtained for both; electrically open and shortconditions. Effects of thickness of the plates, gradient coefficient, dielectric coefficients and piezoelectriccoefficients have been discussed and shown distinctly through graphs. Findings of the present investigationmay lead to the theoretical foundation for designing the SAW devices of higher efficiency.

Keywords: Functionally graded piezoelectric material, Porous-Piezoelectric material, SH-wave, Dis-persion.

AMS subject classifications : 74J15, 74D05, 74G10, 74H10

53

Thermal analysis of convective-radiative pin fin with MATLABs inbuilt tool Pdepeconsidering temperature dependent properties

Sarvjeet Singh, Rohit K. SinglaDepartment of Mechanical Engineering, Thapar Institute of Engineering and Technology, Patiala, India.


The present work investigates the performance of the nonlinear longitudinal circular pin fin with all tem-perature dependent thermal parameters. The involved temperature dependency is either linear or nonlinearfor different parameters of conduction, convection, and radiation. The solution of the problem is evaluatedwith various boundary condition from easier one, i.e., constant temperature, insulated, etc. to realistic,i.e., heat gain or lost by convection and radiation. The mathematical non-linear equations was solved withthe MATLAB based code of Pdepe. The stability of solution has been veried. The numerical results ofthe present technique were validated with the literature and found to be very well in agreement with theavailable results in the literature. The study investigates the effect of various parameters on the temperaturedistribution of the nonlinear longitudinal circular pin fin.

Keywords: Pin fin, Conduction, Convection-Radiation, Pdepe tool.

Kumar.tex

Effect of Solar Flare on climate change by Solar Flare Wave Model and ItsApplication

Sumit Bainjwan, Vishal DhakanePandit Deendayal Petroleum University, GandhinagarPandit Deendayal Petroleum University, Gandhinagar.


In the last few hundred years, the number of sunspots has gradually increasing leading to Global Warm-ing. Evidence suggests that solar activity has affected the global climate adversely. Sunspots are storms onthe sun’s surface that are marked by intense magnetic activity and play host to solar flares and hot gassyejections from the sun’s corona. Solar Flares consist of magnetized plasma flares which emerge from thesun and influences galactic rays that may in turn affect atmospheric phenomena on Earth, such as cloudcover. During solar bursts and associated solar flares and hot gassy ejections from the coronal mass excre-tion, the outer atmosphere of the earth is subjected to large amounts of energy. The heat wave producedby the flurry eruptions in the sun are energetic particles which fall in the upper layers of the atmosphereand convey energy at point of incidence. The action creates spectacular Aurora Borealis around the poleswhich heat the atmosphere significantly. The mean temperature of earth can be explained by variation ofshort wave arriving at surface of earth and influence of long term change in radiation, this paper focus onmodeling and analysis of solar wave which could be used to analyze the global warming phenomenon. Themodel is subjected to observational data which could be examine methodically leading predictive control toanalyze and take possible steps to mitigate the Global warming.

Keywords: Solar Flares, Global Warming, Non-Linear Wave Equation, Coronal Mass Ejections, Plas-mas, Radiation, Atmosphere, Energetic Particle.

Kumar.tex

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Modelling Aeration Efficiency of Hydraulic Jump at Under Sluice GateNirali Vashishth, Subodh Ranjan Vajasneyee, and N K Tiwari

Department of Civil Engineering, National Institute of Technology Kurukshetra, Haryana-136119, [email protected], [email protected], [email protected]

Hydraulic jump is the most frequently occurring hydraulic phenomena in the river observed when waterat high velocity discharges into a zone of lower velocity which follows an abrupt rise creating turbulencein the water surface thereby dissolving and increasing the dissolved oxygen (DO) in the river. The amountof DO is a key indicator of quality of water. Higher is the DO better is the quality of water as it meansminimal presence of organic matter. The aim of this paper is to compute the aeration efficiency of hydraulicjump at under sluice gate using AI-based modelling techniques namely SMO Regression, Meta and Treesfor the values taken from the data set of published results. The techniques are compared based on statisticalperformance evaluation parameters and agreement diagrams and it was found that Meta gave better resultsthan others. The findings of this paper will help in selecting the best fit technique for modelling of aerationefficiency of hydraulic jump at under sluice gate.

Keywords: hydraulic jump, aeration, dissolved oxygen, sluice gate.

Interference of Closely Placed Bridge Piers On Local ScourAnuj Kataria1 and Baldev Setia2

1M.Tech Civil Engineering, National Institute of Technology Kurukshetra, Haryana-136119, India, e-mail:[email protected] 2Professor, Department of Civil Engineering, National Institute of Technology

Kurukshetra, India.e-mail: [email protected]

Bridge is a communication provided when the road is obstructed on account of a river, water bodies etc.Most of the bridge failed due to the hydraulic related issues in general scouring around bridge elements.Scouring is a natural phenomenon that occurs due high velocity resulting in removal of sediment particlesfrom the bed, bank of streams and bridge piers. Extensive work on scour around isolated pier is availablein literature but relatively lesser work is available on scour around closely placed bridge piers. The presentstudy is concerned with the experimental investigation of interference of bridge piers on local scour byvarying pier spacing. The experimental work was conducted in a ume of length 15 m, width 0.61 and depth0.70 m in the Water Resources Engineering laboratory at National Institute of Technology, Kurukshetra,In- dia. A set of 20 experiments have been conducted under clear water condition. There are two pierarrangements, namely Tandem and Side by side arrangement that were tried during the experimental study.A single experiment was also conducted to measure the scour depth at upstream face of isolated pier, whichformed the basis of reference for the studies on group of piers. Scour depth in tandem arrangement for twopiers touching each other was found to be 5.17 percent more than that at the isolated pier. At a clear spacingof 16 times the diameter of pier, maximum scour depth at any of the two piers was found to be same as thatat isolated pier. In case of two piers in side by side arrangement, scour depth was found to be 62 percentmore than that at isolated pier at no clear spacing between the two equal piers.

Keywords: Local scour, Bridge pier, Arrangements, Interference, Scour depth.

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The influence of vegetation type and cover on rain garden hydrologicalperformance

Anuj kumar1, Krishna Kumar Singh2

Department of Civil Engineering, National Institute of Technology Kurukshetra, Haryana-136119, [email protected]

Rain gardens are the best storm water management tool these days and frequently used all over the globeespecially in urban areas to reduce urban storm water impacts. Infiltration characteristics of three small raingardens (1 m2) constructed in the hydraulics lab of NIT Kurukshetra campus with different slope profileswere monitored for nearly 9 months, covering 5 observations over the whole period. And water applied tothe Gardens through a constant volume cylindrical tank. The final result indicates that the rain garden withthe flat profile having the highest infiltration rate. This year few modifications were made in these rain gar-dens, like the size of the two gardens get doubled and the vegetation cover also changed and the observationwith different type of vegetation had taken. In the present study, three vegetation types were considered:native scutch grass (cynodon dactylon) and chandni flower plants as well as daisy flower plants. Overall,results indicate that the rain garden with the higher density of scutch grass vegetation cover infiltrate thewater most expeditiously. And the effect of size on the hydrological performance of the rain garden is veryminor or it can be neglected.

Keywords: Rain garden, Infiltration rate, flat profile

Non-linear Deformation of Thin Elastic Model Membrane Driven by ElectrostaticForces

Amar Shrivastava and Paritosh MahataDepartment of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi - 835215, Jharkhand, India.

[email protected]

Deformation of thin elastic membrane driven by electrostatic forces has important implications in thefield of engineering and biological sciences. For example, in cell-biological systems, peripheral proteinsbend the cell membrane into curved structure due to electrostatic interactions between them. This is animportant phenomenon for several cell-biological processes like endocytosis and exocytosis. Malfunction-ing of these processes produces diseases like cancer and Parkinson’s. To analyze the binding mechanismbetween the protein and cell membrane, the out of plane deformation of cell membrane is analyzed whiletreating it as an elastic membrane. In addition to this, the membrane deformation, driven by electrostaticforces plays an important role in many industrial applications like electrophotography, powder technology,semiconductor and pharmaceutical industries.

In this work, we analyze large and non-linear deformation behavior of a thin elastic membrane sheetinteracting electrostatically with a rigid curved domain in the presence of dielectric fluid. The membranehas negative charge distribution on its upper surface. A rigid curved domain with uniform positive chargedistribution at its concave face interacts with the membrane electrostatically and deform it. Mechanicaldeformation of the membrane is coupled with the electrostatic interaction in its equilibrium configuration.Large and non-linear mechanical deformation of the membrane is predicted by the Neo-Hookean strainenergy function. The electrostatic forces acting between membrane and curved domain are calculated byusing Debye-Huckel equation. The non-linear ordinary differential equations obtained from the equilib-rium configurations of the membrane are solved numerically to calculate the deformations of membrane. Itis observed that the membrane deformation is proportional with the increasing charge density of the rigidcurved domain. Increase in inverse Debye length (which signifies the strength of electrostatic field) of thedielectric fluid decreases the membrane deformation. Though the present study is focused on the elastic

56

deformation of thin membrane, but it can also form a basis for understanding the deformation of complexbiological lipid membrane.

Keywords: Non-linear deformation, thin membrane, electrostatic interaction

Integral Equation technique for solution of diffraction of obliquely incident waterwaves by rectangular asymmetric trench

1Amandeep Kaur, 1S. C. Martha, 2A. Chakrabarti1Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab 140001, India,

2Department of Mathematics, Indian Institute of Science, Bangalore 560012, India,Email: [email protected]

The problem involving diffraction of obliquely incident water waves by a rectangular trench is examinedfor its solution with the aid of a system of integral equations of first kind. The resulting integral equationsare solved by using suitably designed polynomial approximations of the unknown functions. The numericalvalues of physical quantities associated with the water wave problem are found to be in excellent agreementwith the known results where a Galerkin type of approximation has been used to obtain the solutions.

Life Cycle Analysis (LCA) of Low Volume Rural Hill RoadsAkhilesh Nautiyala, Sunil Sharmab

PhD Scholar, Civil Engineering Department, NIT Hamirpur, 177005 India,Assistant Professor, Civil Engineering Department, NIT Hamirpur, 177005 India.


Road maintenance projects involve limited amount of funds to be allocated judiciously, for this preciseLife Cycle Assessment (LCA) of pavements is crucial. A precise LCA of can save huge amount of moneyand time by applying satisfactory maintenance and rehabilitation techniques at the suitable time to the mostsuitable roads. This paper present an approach to forecast behaviour of pavements in rural hill roads inits overall life cycle and then predict its performance throughout its service life. Pavement condition rat-ing and traffic volume are two major factors considered in this study to determine the overall performanceof pavement. Rutting, Ravelling, Cracking, Patching and Pothole are five major defects taken to evalu-ate overall condition of pavement. Linear regression analysis was used to develop a relationship betweenpavement age and pavement condition index (PCI), which gives a scientific relationship to predict remain-ing service life of pavement’s in rural roads in hilly regions. Linear regression analysis was performed todevelop correlation between PCI and pavement age which gives relationship in the form of an equation:y = −25.62ln(x) + 116.16, where y is the pavement age and x is the current PCI. Correlation coefficientof 0.8899 was obtained for this equation which shows that the curve is a good fit. The average service lifeof rural roads in the study area was obtained as 21.65 years.

Keywords: Life Cycle Assessment, Remaining service life, Pavement condition index, Rural hill roads,Liner regression analysis

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Flow Characteristics at the Confluence of WJC and SYL CanalsPradeep kumar1 and Baldev Setia2

1M.Tech Civil Engineering, National Institute of Technology Kurukshetra, Haryana-136119, India, e-mail:[email protected]

2Professor, Department of Civil Engineering, National Institute of Technology Kurukshetra, [email protected] Presenter

Haryana is among major agricultural states of India with approximately 2.9mha of cultivable land undersurface irrigation aided mainly by a network of canal system. Development of water for irrigation can becited as one of major contrib- utors to Haryana’s agriculture success. At one of the con uences in thisnetwork, two canals Western Jamuna Canal(WJC) and Satluj Yamuna Canal(SYL) meet near Karnal a cityin Haryana at 29.692171N, 76.956648E. While WJC with a bed width 76.25m carries 320.24cumec, theSYL with bed width of 16.104m carries 175.52cumec. Owing to geometric and discharge differences, thecon uence is not smooth and results in formation of eddies resulting in scouring of bed and banks at thespecific con uence point. This follows as a damaging the right bank of canal. The Present study analysesthe causes of the scouring at the confluence with the help of momentum equation with different magnitudesof Froude Number, Discharge ratio, Depth ratio, Confluence angle, etc. The momentum equation has beendeveloped analytically and solved using MATLAB. Results show that there is decrease in depth ratio with anincrease in discharge ratio at a given Froude Number. Hence with the understanding of field data and Flowcharacteristics gives a reasonable solution regarding erosion, scour and sedimentation in the downstreamcon uence canal. Being a field problem there are some limitations of the work like, the availability of

eld data from not more than one source at confluence point.Keywords: Canal con uence, Momentum equation, MATLAB, Depth ratio, Discharge ratio.

TREND ANALYSIS OF HYDROLOGICAL PARAMETERS OF TWOAGRARIAN DISTRICTS OF HARYANA, INDIA

Mridula Sharma1, Arun GoelDepartment of Civil Engineering, National Institute of Technology Kurukshetra, Haryana-136119, India.


Hydro-geological parameters and land-use pattern vary spatio-temporally and have a profound effect ongroundwater level and quality of any region. Kurukshetra and Kaithal are two prominent agrarian districtsin Haryana, India which have suffered sharp decline in ground water levels below ground in freshwateraquifer areas and rise in water levels in saline-water aquifer areas which is detrimental for agriculture,economy and environment. Therefore, in order to ascertain sustainability of irrigated agriculture, in thepresent study, the ground water levels of these districts of Haryana, including areas with both saline-waterand fresh-water aquifers are studied in co-relation with other hydrological parameters data of last 37 years(1981-2017) including rainfall, temperature, wind speed etc. The statistical analyses of past trends has beendone annually and seasonally using Mann-Kendall test and Sens slope estimation technique which is vitalfor sustainable planning of water-resources and cropping pattern of the area.

Keywords: Rainfall, Hydrology, Ground water, Mann-Kendall test, Sens slope.

AMS subject classifications : 315 (Data Analysis)

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GEOMETRIC PROPERTIES OF THE EXTENDED τ GAUSSHYPERGEOMETRIC FUNCTION

R. ROY AND R. K. JANADepartment of Applied Mathematics and Humanities, S. V. National Institute of Technology, Surat, 395007, India.

e-mail : [email protected]

In this paper, we have considered the normalized form of extended τ Gauss hypergeometric function,which is defined as 2R1(z) = 2Rτ

1((a; p), b; c, z) = Γ(c)Γ(b)

∑∞0

(a;p)nΓ(b+τn)Γ(c+τn)

zn

n!, where p ≥ 0, τ > 0, |z| <

1;R(c) > R(b) > 0, when p = 0. We obtained several conditions so that the extended τ Gauss hypergeo-metric function has some geometric properties including univalency, starlikeness and convexity inside theunit disk |z| < 1.

Keywords: Analytic function, Univalent function, Close-to-convex function, Starlike function.AMS subject classifications : 33E12, 30C45.

Theoretical Investigation of Networks of Interacting Exclusion ProcessesTripti Midha, Arvind Kumar Gupta

Department of Mathematics, Indian Institute of Technology Ropar, [email protected]

Motivated by the biological and vehicular transport processes, we investigate a network consisting of avertex V from which several lattices, undergoing the totally asymmetric simple exclusion process with inter-actions, converge and diverge together. The vertex V act as an exit and entry reservoir, respectively, for thesegments arriving and leaving from it. The interactions in the bulk of every lattice are theoretically handledwith the two-cluster meanfield framework. We calculate the effective entrance and exit rates, respectively,for the outgoing and incoming segments to the vertex V, as a function of its average particle density, byignoring the nearest-neighbor correlations for the sites at the boundaries. The theoretical calculations forthe particle density, correlation profiles and phase diagrams for the entire network match efficiently with theextensively performed computer Monte Carlo simulations. We theoretically compute the general existenceconditions for the various phases in a phase diagram and found that their existence highly depends on thetotal number of outgoing, incoming segments and the interaction energy among the particles. We find thatthe correlations weaken in a network with more number of incoming or outgoing segments.

Keywords: Exclusion processes, microtubule network, cluster mean-field theory, Monte Carlo simula-tions

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CNA

On solvability of some nonlinear functional-integral equations with applicationsAmar Deep and Deepmal

PDPM-Indian Institute of Information Technology, Design and Manufacturing, Jabalpur - 482005 (MP), [email protected]

Using the concept of measure of noncompactness in Banach algebra, we establish some existenceresults for a generalized nonlinear functional-integral equation, which contains several known functional-integral equations as a particular case. Our results unify and improve some known results in the recentliterature. For application, an example of a functional-integral equation is also provided to illustrate ourmain result.

Keywords: Measure of noncompactness, Fixed point, Functional-integral equation, Banach alge-bra.

2010 Mathematics Subject Classification. 90C39, 47H10.

Effect of Solar Flare on climate change by Solar Flare Wave Model and ItsApplication

Sumit Bainjwan, Vishal DhakanePandit Deendayal Petroleum University, GandhinagarPandit Deendayal Petroleum University, Gandhinagar.


In the last few hundred years, the number of sunspots has gradually increasing leading to Global Warm-ing. Evidence suggests that solar activity has affected the global climate adversely. Sunspots are storms onthe sun’s surface that are marked by intense magnetic activity and play host to solar flares and hot gassyejections from the sun’s corona. Solar Flares consist of magnetized plasma flares which emerge from thesun and influences galactic rays that may in turn affect atmospheric phenomena on Earth, such as cloudcover. During solar bursts and associated solar flares and hot gassy ejections from the coronal mass excre-tion, the outer atmosphere of the earth is subjected to large amounts of energy. The heat wave producedby the flurry eruptions in the sun are energetic particles which fall in the upper layers of the atmosphereand convey energy at point of incidence. The action creates spectacular Aurora Borealis around the poleswhich heat the atmosphere significantly. The mean temperature of earth can be explained by variation ofshort wave arriving at surface of earth and influence of long term change in radiation, this paper focus onmodeling and analysis of solar wave which could be used to analyze the global warming phenomenon. Themodel is subjected to observational data which could be examine methodically leading predictive control toanalyze and take possible steps to mitigate the Global warming.

Keywords: Solar Flares, Global Warming, Non-Linear Wave Equation, Coronal Mass Ejections, Plas-mas, Radiation, Atmosphere, Energetic Particle.

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Entropy Generation in the Flow of Sisko Nanofluids over a Stretching SheetAnkita Bisht and Rajesh Sharma

Department of Mathematics, National Institute of Technology, Hamirpur, Hamirpur 177 005, Himachal Pradesh,India.


The main motive of the present article is to investigate the entropy generation in MHD Sisko nanofluidflow towards linear stretching of the sheet. The governing Sisko nanofluid flow equations comprise mo-mentum, energy and nanoparticle volume fraction are reduced to nonlinear ordinary differential equationsby using suitable similarity variables. The coupled nonlinear ordinary differential equations are then solvednumerically by using finite difference method in MATLAB software. The impact of different physicalparameters on entropy generation number, velocity, Bejan number, and temperature are presented graphi-cally. The obtained results indicate that the entropy generation number (N∗G) increases with increases inthe Brinkman number (Br∗) and magnetic parameter (M∗) while decreases with the material parameter forSisko fluid (A∗) whereas Bejan number (Be∗) enhances for large values of the material parameter for Siskofluid (A∗) while diminishes for the magnetic parameter (M∗) and Brinkman number (Br∗). Moreover,increasing trends are observed for both (N∗G) and (Be∗) for higher values of diffusion parameter (γ∗). Ve-locity profile increases while the temperature profile decreases for large values of the magnetic parameter.It can be observed from the present analysis that the obtained results are beneficial in understanding theentropy generation (or irreversibility) in non-Newtonian fluid flows.

Keywords: Sisko nanofluid, Entropy generation, Finite difference method, Numerical solution.

AMS Subject Classification: 76A05, 76M20, 76N20, 76W05, 35G30

Adomian Decomposition Method for the solution of a Parial Differential Equationsof Fractional Order

Pratibha Verma and Manoj KumarDepartment of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Allahabad,

Prayagraj211004, Uttar Pradesh, [email protected] and [email protected].

In this paper, we investigate the method for solving linear and non-linear partial differential equations offractional order. The Adomian Decomposition Method is one of the reliable and popular method for solvinglinear and non-linear differential equations and provides solutions in the form of series. In this study, ourmain purpose is to achieve more accurate and fast convergent solution with less iterations. Here we adoptTwo-Step Adomian Decomposition Method (TSADM) for solving linear and non-linear partial differentialequations of fractional order and compared with Standard Adomian decomposition method and ModifiedAdomain Decomposition Method. It is successfully applied to autonomous linear and non-linear partialdifferential equations with variable coefficients. It is shown that TSADM is more effective and promisingmethod with one iteration and provides exact solution of both the problems without discretization and lin-earisation.

Keywords: Adomian decomposition method, Modified Adomain Decomposition Method , Two StepAdomain Decomposition Method, Fractional Partial Differential Equation.

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A new efficient numerical scheme for variable order fractional sub-diffusionequation

Sarita Nandal, Dwijendra Narain PandeyDepaertment of Mathematics, IIT Roorkee, Roorkee-247667, India, [email protected],

[email protected]

In this paper, we propose to construct a new efficient finite difference scheme for variable order frac-tional sub-diffusion wave equation. Fractional derivative will be considered in the sense of Caputo andapproximated using L2 − 1σ formula which gives second order convergence for α(t) ∈ (0, 1). For spa-tial dimensions, we will consider a compact difference operator which improves the convergence order toO(h4), where h is spatial mesh size. Next, we will prove the stability, solvability, and convergence of ourconstructed scheme using discrete energy method with help of L2-norm. Our proposed scheme is new andefficient in terms of convergence orders in both time and spatial dimensions. Then, a few examples will beprovided to demonstrate the accuracy and efficiency of the proposed scheme. This scheme can further beimplemented easily to non-linear and time delay oriented problems.

AMS subject classification: Analytical and numerical methods for ODEs and PDE.

Key words: Variable order fractional derivative, L2-1σ formula, Compact difference scheme, Stability,Convergence.

Transverse Hydromagnetic and Media Permeability Effect on Mixed ConvectiveFlow in a Channel Filled by Porous Medium with asymmetric wall heating

conditionKm. Renu, Ashok Kumar

Hamvati Gandan Bahugana Garhwal, [email protected], [email protected]

An analytical as well as numerical study of steady, fully developed unidirectional non-Darcy mixedconvective flow in a vertical channel with transverse hydromagnetic effect is reported in this article. Thefluid in channel is assumed electrically conducted and flow is due buoyancy forces and an external pressuregradient. The non-Darcy Brinkman-Forchheimer extended model is considered to characterized the flowin porous media. Chebyshev spectral collocation method is used to solved the governing equations andget the magnificent agreement with the analytic solution for the special case. The governing parametersfor this problem are media permeability (Darcy number,Da, Forchheimer number, F ∗), Hartmann number(M), Heat generating/absorption parameter (H), and mixed convective parameter (Gr

Re). From the numerical

investigation, it is found an unnatural deviation in the velocity, temperature and Nusselt number after thethreshold value of positiveH (heat generating case). The Nusselt number is a linear function of negativeH .Further, on the basis of other fixed controlling parameters, the velocity, temperature and Nusselt number areincreasing on increasing M up to certain value and beyond it reducing asymptotically. The flow strengthand heat transfer rate decreases on decreasing media permeability on reducing Da and increasing F ∗.

Keywords - Magnetohydrodynamics, Mixed-convection, Non-Darcy Brinkman-Forchheimer extendedmodel, Chebyshev Spectral collocation method, Gauss-Chebyshev quadrature formula.

Classification - 76Dxx, 76Fxx, 76Sxx, 76Wxx, 76Rxx

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Numerical study of entropy generation in porous medium vertical channelsubjected to mixed convection

Paresh Vyas, Kusum YadavUOR, Jaipur, Rajasthan, India.


This paper is aimed to analyze entropy generation in a vertical plate channel filled with porous medium.The flow is modified by buoyancy force, viscous and ohmic dissipations. One wall of the channel is sub-jected to convective flux whereas other wall is kept at uniform temperature. The governing partial differ-ential equations are reduced to ordinary differential equations by using similarity transformations and theresulting boundary value problem is solved numerically by finite difference scheme. The effects of perti-nent parameters on the entropy generation number, global entropy and Bejan number have been reportedgraphically and discussed.

Keywords: entropy, buoyancy force, porous medium, mixed convection, vertical channel.

Curvelet optimized method for solving partial differential equations on generalmanifolds

Deepika Sharma, Kavita GoyalSchool of Mathematics, Thapar Institute of Engineering and Technology, Patiala-147004, India Emails:

[email protected] [email protected]

In this work, a dynamically adaptive curvelet method has been developed for solving partial differentialequations (PDEs) on the general manifolds. Approximation formulae for Laplacian-Beltrami (2) opera-tor is derived using the closest point method. The grid on which the equation is solved is obtained usingcurvelets. The CPU time taken by the proposed method is compared with the CPU time taken by the closestpoint method and it is observed that the proposed method performs better. To best of our knowledge the use-ful properties of curvelet is for the first time exploited to solve PDEs on general manifolds. The method istested on three test problems namely reaction-diffusion equation on a sphere, Schnakenberg model evolvingon the surface of ellipsoid and the well-known Fitzhugh-Nagumo equations. The numerical results showthat the method can accurately capture the emergence of the localized patterns at all the scales and the nodearrangement is accordingly adapted. The convergence of the method has also been verified.

Keywords; Multiresolution analysis (MRA); Adaptive node arrangement; Curvelet; Numerical method;Partial differential equations.

AMS subject classification : 65M99, 35J25

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Solution of inverse fractional Fisher’s equation by differential quadrature methodG. Arora, Pratiksha

Lovely Professional University, Punjab, [email protected], [email protected]

This work is an attempt to solve the inverse problem on fractional Fisher equation. A method is pro-posed to find the numerical solution of the problem, comprising of Lubich’s approach to discretize the timefractional derivative and differential quadrature method with modified B-spline basis function to approxi-mate the space derivatives A stable numerical solution is obtained for this problem and then a comparisonis made with the existing results. The obtained results are presented in form of tables and figures.

keyword: Fractional Fisher’s equation, differential quadrature method, discretization, fractional differ-ential equation, inverse problem.

MSC [2010] : 26A33, 34A08, 35R11, 65L20

Uncertainty propagation using Wiener-Bspline wavelet expansionNavjot Kaur and Kavita Goyal

School of Mathematics, Thapar Institute of Engineering and Technology, Patiala-147004, India Emails: [email protected] [email protected]

In this paper, we have constructed a scheme combining generalized Polynomial Chaos (gPC) expansionand B-spline wavelets. To begin with, semi-orthogonal compactly supported B-spline wavelets are con-structed for the bounded interval [0, 1] which is used as a PC expansion for possible stochastic processes.To compute the deterministic coefficients of expansion, we have applied both semiorthogonal Galerkin pro-jection and pseudo-spectral projection of uncertain data and the solution variables. Then, to determine thebehaviour of the stochastic process, the system of equations obtained from projection are integrated usingfourth order Runge-Kutta method. The scheme is illustrated through model problems of real life impor-tance. It has been observed that the wavelet function based expansion shows superior results as comparedto scaling function based expansion.

Keywords : Uncertainty quantification; B-spline wavelets; generalized Polynomial Chaos (gPC);Stochastic differential equation.

AMS subject classification : 65M99, 35J25.

Entropy Generation Analysis For A Micropolar Fluid Flow Due To A MovingSurface

Paresh Vyas, Manvi AdhaUniversity of Rajasthan, Jaipur, Rajasthan, India.


In this paper, an analytical solution has been developed for micropolar fluid flow in porous medium.The flow is caused by convection due to moving surface and buoyancy. The governing equations are solvedby perturbation method. The velocity and thermal fields are used to compute entropy generation. Profilesfor entropy generation and bejan number are portrayed and discussed.

Keywords: micropolar fluid flow, porous medium, entropy

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Mathematical analysis of surface wave propagation in Functionally GradedMaterial using WKB approximation

Sonali Mondal, Sanjeev A. SahuDepartment of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004,


This paper aims to study the Love-type surface waves propagation in a composite structure comprisingof functionally graded material (FGM) layer and porous piezoelectric (PP) substrate. The FGM layer issupposed to be under constant tensile initial stress. Wentzel Kramers Brillouin (WKB) approximation tech-nique and variable separable method are used for the wave solutions. Dispersion relations are obtained usingsuitable boundary conditions for the two cases i.e. electrically open and electrically short case. Numericalexample is given in support of findings. Effects of gradient coefficient of the FGM layer, initial tensilestress as well as the width of the FGM layer have been shown graphically. The present study contributestowards designing and optimization of underwater acoustic devices. Mathematics Subject Classification(2010). 74B10 74J15.

Keywords : Functionally Graded Material, Surface waves, WKB approximation, Porous piezoelectric-ity.

Data bounded WENO reconstructions of high order schemesRitesh Kumar Dubey, Sabana Parvin

Research Institute & Department of Mathematics, SRM Institute of Science and Technology, Chennai, [email protected] [email protected]

High order accurate shock capturing Weno schemes are mainly based on high order WENO recon-structions. These reconstructions lack significantly in terms of rigor mathematical results except in someparticular cases.The main aim of this work is to establish estimates on stability mainly data boundednessof such reconstructions. More precisely, conditions on non-linear WENO weights are provided on the re-gion of a smoothness measurement which is again a function of consecutive gradient ratio, so as to makeWENO reconstruction data bounded in that regions. Data boundedness i.e Boundedness of the polynomialreconstruction by its adjacent values, will helps in preservation of extrema in WENO polynomial solution.Numerical results for various test problems are given and compared.

Keywords: Hyperbolic conservation laws, WENO reconstructions, Non-linear weights, Data depen-dent stability, Data-bounded polynomials.

AMS subject classifications : 65M06, 65D05, 35L65.

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Solution of singular fractional Lane-Emden type equations by an analyticaltechnique

Anoop Kumar, SeemaDepartment of Mathematics and Statistics School of Basic and Applied Sciences Central University of Punjab,

Bathinda, Punjab-151 001, India.Email: [email protected], [email protected].

This paper deals with the approximate solution for the singular fractional Lane-Emden equations usingVariational iteration method(VIM). The fractional derivative are described in Caputos sense. The obtainedresults shows that VIM is effective and convenient.

Keywords: Variational iteration method, Lane- Emden equations, Lagrange multiplier.

AMS subject classifications : 30C70, 35N99, 35J05.

NUMERICAL APPROACH FOR A COUPLED SYSTEM OF SINGULARLYPERTURBED CONVECTION-DIFFUSION PROBLEM WITH NON-SMOOTH

DATAAarthika K, V. Shanthi

Department of Mathematics, National Institute of Technology, Tiruchirappalli-620 015, Tamilnadu, [email protected], [email protected].

The time-dependent weakly coupled linear system of singularly perturbed one-dimensional parabolicconvection-diffusion partial differential equation with a discontinuous source term is analyzed in this pa-per. We build a numerical technique by handling an efficient finite difference scheme to achieve a reliableapproximation of the solution. This method involves an appropriate piecewise-uniform mesh to generateuniformly convergent numerical estimates to the solution. The execution of the linear system successfullyexperimented which validates the analytical results.

Keywords: convection-diffusion, non-smooth data, piecewise-uniform mesh, singular perturbation,weakly coupled system, uniform convergence

AMS subject classifications : 35B25, 35R05, 65N06

THRESHOLDING FUNCTIONS INVOLVED IN THE WAVELET BASEDDENOISING METHOD

Princess Raina and Zaheer AbbasDepartment of Mathematical Sciences, Baba Ghulam Shah Badshah University Rajouri

[email protected]

Every scientist or engineer dealing with the real world data knows very well that, in general, signals donot exist without noise - Gaussian Noise, Impulsive Noise(salt-and- pepper noise or spike noise), SpeckleNoise. So to obtain the correct information, the signals hve to be denoised for which there are abundance ofmethods available in the literature. Among these methods, the wavelet based methods are very effective andhave been very successfully applied in many areas of science and technology. The wavelet method involvesthree steps - a linear forward wavelet transformation, a nonlinear thresholding step and a linear inversewavelet transform. The second step uses a function, called as thresholding function. Donoho and Johnstone

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proposed two types of thresholding functions - hard and the soft thresholding functions. However, thesethresholding techniques suffer from certain drawbacks and hence a number of thresholding functions havebeen introduced by the researchers since then. In this paper, we shall present a detailed report on the variousthreshholding functions available in the literature after presenting various types of noises, wavelet denoisingmethod and a brief introduction to wavelets.

One-dimensional solute migration model with first-order production term insemi-infinite porous media

Affreen Akhter, Mritunjay Kumar SinghDepartment of Applied Mathematics, Indian Institute of Technology, Indian School of Mines), Dhanbad 826004,

Jharkhand, [email protected], [email protected]

In the present study developed an analytical solution for one-dimensional contaminant migration modelin homogeneous as well as heterogeneous semi-infinite porous media. The effect of linear isotherm,sink/source term, porosity, density and first-order production term are considered into account for obtainedthe exact analytical solution of contaminant migration. Initially, a not solute-free domain is assumed asa linear combination of the initial source concentration with the effect of zero order production term withspace dependent is considered. Temporally dependent linear function is taken in one end of the boundaryand other end of the boundary concentration gradient is assumed to be zero. Laplace Integral TransformTechnique (LITT) is used to demonstrate the analytical solution. An asymptotically and exponentially de-creasing function is considered to illustrate the proposed solutions.

Keywords: Advection, Dispersion, Linear Isotherm, Solute, Analytical Solution.

STUDY OF FRACTIONAL THERMOELASTIC PROBLEM WITH MOVINGHEAT SOURCE

Jaya Bikram, G.D. Kedar1Department of Mathematics, RTM Nagpur University, Nagpur, India.

[email protected]

In this paper, we have studied one dimensional problem of thermoelastic rod with moving heat source.The heat conduction equation is taken in space-time fractional derivative form. Finite Riez fractional andCaputo derivative are considered in heat conduction. The integral transforms are used to determine thetemperature distribution. The numerical results are presented and illustrated graphically.

Keywords: Fractional heat conduction equation, generalized Mittage Leffler function, thermal stresses,fractional thermoelasticity.

AMS subject classifications :

68

Numerical Solution of Fractional Order Non-Conservative Advection-DiffusionEquation

Anup Singh and S. DasDepartment of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi-221005, India

[email protected]

In this article, the Laplace transform method is used to solve the advection- diffusion equation havingsource or sink term with initial and boundary conditions. The solution profile of normalized field variablefor both conservative and non-conservative systems are calculated numerically using the Bellman methodand the results are presented through graphs for different particular cases. A comparison of the numericalsolution with the existing analytical solution for standard order conservative system clearly exhibits thatthe method is effective and reliable. The important part of the study is the graphical presentations of theeffect of the reaction term on the solution profile for the non-conservative case in the fractional order aswell as standard order system. The salient feature of the article is the exhibition of stochastic nature of theconsidered fractional order model.

Keywords: Advection; Diffusion; Laplace transformation; Non-conservative system


Finite element analysis of semilinear time-fractional diffusion equationDileep Kumar∗a, Sudhakar Chaudharyb, V.V.K Srinivas Kumar∗

∗ Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016,India, [email protected]

b Department of Mathematics, Institute of Infrastructure Technology Research and Management, Ahmedabad,Gujarat, India,

[email protected]

This work is devoted to the finite element analysis of semilinear time-fractional diffusion equation.Grunwald-Letnikov approximation is used to approximate time-fractional derivative. We propose fully-discrete scheme to solve semilinear time-fractional diffusion equation and discuss its existence-uniquenessof solution. For linearizing the nonlinear fully-discrete problem, Newton’s method is used. We derive apriori error estimate for the fully-discrete solution in L2(Ω) norm. Numerical results are presented whichconfirms the theoretical findings.

Keywords: Fractional diffusion equation, finite element methods, Newton’s method, Grunwald-Letnikovapproximation, Error estimates

AMS subject classifications : 65N12, 65N30, 35K61

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Effect of Aspect Ratio on Natural Convective flow in a Rectangular EnclosureOccupied by Anisotropic Porous Medium

Ashok Kumar, Ajay Kumar∗1, Km. Renu and M. S. Rawat1Department of Mathematics, H N B Garhwal University (A Central University) Srinagar -246174, India

[email protected], [email protected],[email protected] and [email protected]

A compreherensive numerical study of natural convective flow in rectangular enclosure occupied byanisotropic porous medium using spectral element methods is presented . In this study the main emphasizeis given on the effect of aspect ratio on fluid flow and heat transfer rate. The flow is induced by the non-uniform partial heating at the bottom wall and cooling at vertical walls anlong with the adiabatic top wall.The non-uniform partial heating is given on the one third part in middle of the bottom wall and the restpart of the bottom wall is adiabatic. The flow in porous medium is characterized by the non-Darcy modelin which media is taken hydrodynamically anisotropic and thermaly isotropic. The numerical results arepresented in terms of stream function, isotherm, local as well as average heat transfer rate. The numericalresults presented here shows that the heat transfer rate as well as flow streanth is reducing on increasing theaspect ratio. The maximum values stream fuction is also reducing on enhancing the Aspect ratio.

Keywords: Spectral Element Method, Natural Convection, Porous Media, Partial Heating

AMS subject classifications : Numerical Method in Fluid Mechanics 76Z99, Fluid Mechanics 76D33& Flows in Porous Media 78A99

NUMERICAL SOLUTION OF DAMPED FORCED OSCILLATOR PROBLEMSBY OPERATIONAL MATRIX OF INTEGRATION

Dr. Mithilesh Singh1, Seema Sharma2, Sunil Rawan3

1Rajkiya Engineering College, Churk, Sonbhadra, Uttar Pradesh2Kanya Gurukul Campus, Haridwar, Uttarakhand

3Gurukula Kangri Vishwavidyalaya, Haridwar,[email protected],[email protected],[email protected]

In this paper, the operational matrix of integration Bernoulli orthonormal polynomials has been used todetermine the numerical solution of damped forced oscillator problem. The integral operator on Bernoulliorthonormal polynomials has been applied to determine the operational matrix of integration. Numeri-cal examples of two different problems of spring are given to illustrate the efficiency and accuracy of themethod and compared with exact solution.

Keywords: Orthonormal Bernoulli polynomials; Operational matrix; Damped forced oscillator

AMS subject classifications : 65L05,34B60

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Flow of a Hydromagnetic Fluid through a porous medium between permeable bedswith damping effects.Ravi Kumar and B.G. Prasad

Post Graduate Department of Mathematics, Patna University, Patna-800005, [email protected]; [email protected]

The Navier-Stoke’s equations and Darcy’s law have been used to study the flow of a hydromagneticfluid under a uniform magnetic field, with suction and injection through the lower and the upper permeablebeds. The pressure gradient is taken as e−(n1+in2)t, where n1 and n2 being positive constants. Analyticalsolutions for the velocity field and the volume flux have been obtained. For n2 = 0 the problem reducesto that discussed by Prasad and Kumar (2011) and for n1 = 0 and porosity of medium tending to zero, theproblem reduces to that discussed by Malathy and Srinivasan (2008).

Finite element solution of a problem on coupled thermoelasticity for functionallygraded material by two different approaches for time domain

Om Namha Shivay∗ and Santwana MukhopadhyayDepartment of Mathematical Sciences, IIT (BHU), Varanasi-221005

∗Corresponding author; [email protected]

The present work is concerned with the modified Green-Lindsay thermoelasticity theory involvingstrain-rate. This theory has been proposed very recently to modify the Green-Lindsay model of thermoelas-ticity and overcome its drawback by introducing both temperature and strain-rate terms in the constitutiverelations of coupled thermos-mechanics. We consider a problem involving coupled thermo-mechanical in-teractions inside a functionally graded hollow disk due to a thermal shock applied at the inner boundarywhich is assumed to be stress free. The material properties of the disk are assumed to change along theradial direction according to a volume fraction rule with a power of non-homogeneity index term. We for-mulate the problem by considering the basic governing equations of GL and modified GL thermoelasticitytheories in a unified form to derive a non-linear system of coupled partial differential equations. We solvethis system by applying a Galerkin’s approach of FEM for the space domain and derived the time differen-tial system of equations. We apply two different methods; namely, the FE approach and Newmark methodto obtain the solution time domain. Further, to show the advantages of the present methods over transFEmethods, the CPU time to obtain the solutions by the present formulations are compared with the CPU timeto obtain the solution by trans-finite element method. The variation of different physical field variables withspace and time have been discussed for different values of the nonhomogeneity index by highlighting thedifference in the results under GL model and modified GL model.

Keywords: Coupled Thermoelasticity Theory; Temperature-rate Dependent theory; Functionally GradedMaterials (FGM); Finite Element Method; Trans-finite Element Method

AMS subject classifications : 74A60

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Simulation of Heat transfer of Ferro fluid in Cylindrical Micro-ChannelRamesh kumar1∗, Harry Garg2, S.K Dhiman1

1Department of Mechanical Engineering, Birla Institute of Technology Mesra, Ranchi, India, 8352152Central Scientific Instruments Organization (CSIR-CSIO), Chandigarh, India, 160030

1,2∗[email protected]; [email protected]; [email protected]∗CORRESPONDING AUTHOR

In the present work the computational fluid dynamics and differential method is used to study the flowbehaviour and heat transfer rate of kerosene based Ferro fluid. The Ferro fluid is mixture of magnetic par-ticles and based fluid therefore treated as mixture phase. The numerical simulation results are obtained inthe form of different parameter e.g. Nusselt Number, Reynolds number and heat transfer coefficient.

Keywords: Heat transfer, Ferro fluid, Magnetization, Kelvin body forces

Computational Analysis of Bed of a Mobile ChannelAtul Ailawadhi1 Baldev Setia2,

1M.Tech. Student, Department of Civil Engineering, National Institute of Technology, Kurukshetra, Haryana2Professor, Department of Civil Engineering, National Institute of Technology, Kurukshetra, Haryana


The process of sediment transport being a topic of utmost importance has been emphasized on, sincelong. Understanding of the process has undergone significant transformations through laboratory experi-mentations and field observations. However, its solutions through the use of computational tools, thoughhaving a wide scope, have not been fully developed. Some significant work in this direction has been re-ported in the works of Wen Xiong (2017), Shi Liu (2017), ZHU Zhi-wen (2012), etc. In the present paperthe transport process has been modelled with the help of a three-dimensional simulation model of a flumewith mobile sand bed using the principles of CFD. The data used for simulation was obtained from theexperimental works carried out in another study in the laboratory of NIT Kurukshetra. The flow has beensimulated by employing the k-? turbulence model and the sand-water coupling being modelled by Euler-Euler model with two-phase flow. Navier-Stokes Equation was solved independently for both the phasesand all three- mass, momentum and energy conservation laws were applied. The volume fraction methodhelped in determining the flux exchange of the sand phase from the bed and has been followed by updatingthe bed boundary using dynamic meshing technique. The bed levels at various time steps have been ob-tained using the threshold value of the critical bed shear stresses. The computed values have been comparedwith the laboratory results and satisfactorily good co-relation has been observed in terms of bed levels andincipience velocity for the fine sand particles as well.

Keywords: CFD-Computational Fluid Dynamics; critical bed shear stress; incipience velocity.


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Numerical study on MHD flow of nanofluid due to a rotating disk with heatgeneration and partial slip effect

V. K. Chaurasiya, Ramayan Singh and Rajat TripathiDepartment of Mathematics, National Institute of Technology, Jamshedpur-831014, Jharkhand, India.

[email protected]

In the present study, our aim is to study the heat and mass transfer mechanism in Von Krmn swirlingflow problem of nanofluid due to a rotating disc with the consideration of magnetic field and heat genera-tion effect. The well-known Buongiorno model exhibits the characteristics of Brownian motion and ther-mophoresis. Using Karman similarity transformations, the governing partial differential equations (PDEs)are transformed into the non-linear and coupled ordinary differential equations (ODEs) which are thensolved by a numerical method for the broad range of the involved parameters. The effects of the magneticparameter, heat generation parameter and slip coefficients on the heat and mass transfer are discussed. Theeffect of relavent parameters on the velocities (radial and azimuthal) and temperature distributions is rep-resented by plotting graphs. Expressions of wall skin friction and rate of heat transfer at the surface of thedisk are calculated and are presented in the tabular form. It is noted that the velocities (radial and azimuthal)are reduced on increasing the magnetic field and slip coefficient. The temperature of fluid is enhanced forheat generation parameter.

Fibonacci collocation method to solve nonlinear space-time fractional orderadvection-reaction-diffusion equation

Kushal Dhar DwivediDepartment of Mathematical Sciences IIT(BHU), Varanasi-221005, India.

[email protected]

In this article, a new algorithm is proposed to solve the fractional order nonlinear one-dimensional so-lute transport system. The spectral collocation technique is considered with the Fibonacci polynomial asa basic function for approximation. The Fibonacci polynomial is used to obtain derivative in terms of anoperational matrix. The proposed algorithm is based on the fact that the terms of the considered problemare approximated through a series expansion of double Fibonacci polynomials and then collocated those onspecific points, which provide a system of non-linear algebraic equations which can be solved using New-tons method. To validate the accuracy of the proposed method, it is applied to solve three different problemshaving analytical solutions. The comparison of the results through error analysis depicted through tablesclearly shows the higher accuracy of order of convergence of the proposed method in less CPU time. Thesalient feature of the article is the graphical exhibition of the movement of solute concentration for differentparticular cases due to presence and absence of reaction term when the proposed method is applied to theconsidered fractional order nonlinear space-time advection-reaction-diffusion model.

Keywords: Fibonacci polynomial, Spectral method, Fractional-order, Diffusion equation, Operationalmatrix


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Abhishek Verma,N K Singh 1 1Department of Mechanical EngineeAbhishek Verma,N K Singh

Department of Mechanical Engineering, NIT Kurukshetra, [email protected]

Structures experience various forces exerted over them in routine. Thus they are designed in order tobear them all in certain limits modified with some factors of safety. Wind forces are one of the most impor-tant of such forces especially in high rise buildings and tall structures like towers, etc. The same has beensimulated through computational technique using CFD based software package Ansys Fluent available inCFD lab of NIT Kurukshetra. In the same process, k-omega SSD model has been used as a standard flowturbulent model. The wind forces have been tracked in the vicinity of the structure at NUMERICAL SIM-ULATION OF FLOW AROUND VARIOUS STRUCTURAL SHAPES the faces treated as walls for thefluid-structure interaction. The study involved comparison of the drag force magnitude and the vortices forvarious structural shapes feasible for construction. The observation of vortices in the nearby areas and themagnitude of forces has been compared with various other studies and has been found in good accordancewith each other.

Keywords: CFD- Computational Fluid Dynamics; Ansys Fluent; Aerodynamics Drag and Lift;Turbulent Flow

Numerical study of inclined stretchable partially heated enclosure filled withnanofluid

Pentyala Srinivasa Rao, Anil KumarDepartment of Applied Mathematics, Indian Institute of Technology (ISM) Dhanbad 826004, India, e-mail:

[email protected]

In this article, we analysed numerically the heat transfer behaviour of nanofluid due to buoyancy forceinside a two-dimensional inclined partially heated stretchable square cavity filled with nanofluid. Thismodel is used to test the performance of stretchable walls and inclination on stream function and tempera-ture field inside the cavity. The proposed governing equations are numerically solved by Implicit alternatedirection finite difference method for modified Rayleigh number (103 ≤ Ra ≤ 105), Prandtl number(Pr= 0.1; 0.7; 3), volume fraction(0 ≤ φ ≤ 0.3), stretching parameter (0.01 ≤ τ ≤ 1.2) and inclination.It is found that the convective heat transfer and mean Nusselt number both are effected with variation ofstretching parameter and inclination. Therefore, the details of results are graphically presented to show thatthe effect of stretching parameter on flow strength, heat transfer and mean Nusselt number for laminar flowin the cavity.

Keywords: Nanofluid, Natural convection, Stretching sheet, Moving boundaries, Enclosure.AMS subject classifications : 76DXX; 76RXX; 80AXX.

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CP

Dynamic modeling and control of divided wall distillation multicomponentseparation

Manali Kokare, C. S. Mathpati, Ajit Kumar, S. S. JogwarDepartment of Chemical Engineering, Institute of Chemical Technology, Mumbai.

[email protected], [email protected], [email protected],[email protected]

Distillation is one of the most widely used separation method in chemical and allied industries. Thedesign of distillation unit involves system of ordinary differential equations related to overall mass, compo-nent, energy balance and thermodynamic equilibria of the system. Distillation is energy intensive processand design optimization is essential for energy saving as well as consistent quality. Divided wall distillationsystem is an optimized distillation method which involves separation of multicomponent mixture in singleunit where pre-fractionation and main column are separated by a wall which leads to saving in capital aswell as operating cost. The divided wall distillation is nonlinear in nature so the model predictive controlleris useful in which three component purities are controlled. In the proposed work, dynamic model of thesystem has been simulated in Matlab for the separation of (n-butanol)-(water)-(n-butyl levulinate). Theeffectiveness of the developed controller is checked for a step change in n-butanol purity.

Keywords:Divided wall distillation, globally linearizing controller, dynamic model, system of ordinarydifferential equations


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DE

Existence of mild solutions for neutral fractional functional integro-differentialequations with non instantaneous impulses of order α ∈ (1, 2)

Pallavi Bedi, Anoop KumarDepartment of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab,

Bathinda, Punjab-151 001, [email protected], [email protected].

In this manuscript we establish the existence of mild solutions for neutral fractional functional integro-differential equations with non instantaneous impulses and state dependent delay of order α ∈ (1, 2) of theform.

cDαt

[u(t) +

∫ t

0

(t− s)α−1

Γ(α)g(s, uρ(s,us)

)ds

]= Au(t) + f

(t, uρ(t,ut), Bu(t)

), (0.0.4)

t ∈ (si, ti+1] ⊂ J = [0, T ], i = 0, 1, 2, ..., N.

u(t) = φi(t, u(t)); u′(t) = ψi(t, u(t)), t ∈ (ti, si], i = 1, 2, ..., N. (0.0.5)

u(t) = q1(t); u′(t) = q2(t), t ∈ [−d, 0]. (0.3)

where cDαt denotes the Caputo′s fractional derivative of order α ∈ (1, 2) and A : D(A) ⊂ X −→

X is the sectorial operator defined on a complex Banach space X, 0 = t0 = s0 < t1 ≤ t2 < ... < tN ≤SN ≤ tN+1 = T are prefixed numbers and φi, ψi ∈ C

((ti, si] × X;X

)∀i = 1, 2, 3..., N. The functions

f : J × PCo × X −→ X; g : J × PCo −→ X and ρ : J × PCo −→ [−d, T ] are continuous functions.The history function ut ∈ PCo = C

([−d, 0], X

)and is defined as ut(θ) = u(t+ θ), θ ∈ [−d, 0]. The maps

q1(t), q2(t) ∈ PCo and u′(t) denotes the derivative of u(t)w.r.t to ′t′ and φi, ψi ∈ C((ti, si]×X;X

)∀i =

1, 2, 3..., N.The term B(x)(t) =

∫ t0K(t, s)x(s)ds where K ∈ C(D,R+) is the set of all positive functions which are

continuous on D = (t, s) ∈ R2 : 0 ≤ s ≤ t < T.The existence results are proved with the help of analytic operator functions and fixed point theorems. Anexample is offered to demonstrate the application of results obtained.

Keywords: Fractional differential equations; non instantaneous impulse conditions; fixed point theo-rems; state-dependent delay; sectorial operator; analtyic operator functions.

AMS subject classifications : 34A08, 34K40, 34A37, 26A33, 34A12.

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CHARACTERIZATION OF POLARIZED SHEAR WAVES INPOROUS-PIEZOELECTRIC MEDIUM OVER A HETEROGENEOUS ELASTIC

SUBSTRATE CONTAINING POINT SOURCESUBHASHIS KARMAKAR*, SANJEEV A. SAHU

Dept. of Applied Mathematics, IIT(ISM), Dhanbad, 826004E-mails: [email protected], [email protected]

In the present study a model consisting of porous piezoelectric layer lying over a heterogeneous half-space has been considered. An analytical approach has been adopted by using Greens function methodto solve the inhomogeneous linear differential equations for horizontally polarized shear wave (SH-wave)propagation. Point source, situated at the interface of two media has been considered to influence thepropagation of SH-waves. It is found that the angular frequency of SH wave depends considerably onthe material properties (thickness of the layer, elastic parameter, piezoelectric constant, heterogeneity, andporosity). Obtained results are presented graphically to exhibit the influence of parameters on the phaseand group velocity of considered wave. A special case is also presented by reducing the upper layer toa piezoelectric layer. Numerical example has been illustrated by taking Lead Zirconate Titanate (PZT-1,PZT-5H and PZT-7)as the upper layer. Results may be useful to investigate the dispersion characteristics ofsurface seismic waves in smart materials.

Keywords: Greens function, Porous piezoelectric layer, Point source, SH-wave

AMS subject classifications : 34L10, 35Q74, 74J15.

Smooth stable manifold for delay equations with arbitrary growth ratesLokesh Singh*, Dhirendra BahugunaIndian Institute of Technology, Kanpur

[email protected]

Invariant manifolds play crucial role in understanding the dynamics of differential equations. Perronand Lyapunov developed a method to get the stable invariant manifold for hyperbolic trajectories with theassumption that solution operator satisfies [uniform] exponential dichotomy. Later on, in 2005 L. Barreiraand C. Valls generalized the notion of uniform exponential dichotomy to nonuniform exponential dichotomyfor nonhyperbolic trajectories and proved the existence of stable invariant manifold for nonautonomousdifferential equations. In this talk, first I will give the generalization of nonuniform exponential dichotomy.Later, assuming the generalized nonuniform exponential dichotomy, I will prove the existence of Smoothstable invariant manifold for semiflows generated by a nonautonomous differential equations with infinitedelay of the form given by

x′ = Ax(t) + Lxt + f(t, xt), xs = φ,

on some Banach space X .

Keywords: Stable Invariant Manifold, Nonautonomous system, Nonuniform Exponential dichotomy

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Approximation of fixed points and the solution of delay differential equation vianew iterative scheme

Javid Ali, Faeem AliDepartment of Mathematics, Aligarh Muslim University, Aligarh- 202002, India

[email protected]

The purpose of this paper is to introduce a new iterative scheme, called F iterative scheme for approx-imating fixed points of contraction mappings in an arbitrary Banach space. We also prove that F iterativescheme is T -stable and converges faster than the iterative schemes S, Picard-S, Vatan, Thakur-New,M∗,Mand many more. As an application, we approximate the solution of a delay differential equation by usingF iterative scheme. Also, we give two numerical examples to support our analytic proofs and illustrate theefficiency of purposed iterative scheme.

Keywords: F iterative scheme, contraction mappings, fixed points, convergence results, Banach spaces,delay differential equations

AMS subject classifications : 47H09, 47H10.

Classification of Some Functional Differential Equations with Constant Coefficientsto Solvable Lie AlgebrasJervin Zen Lobo, Y.S Valaulikar

Department of Mathematics, St. Xaviers College, Mapusa, Goa - 403507, IndiaDepartment of Mathematics, Goa University, Talegao Plateau, Goa - 403206, India


In this paper we shall apply symmetry analysis to some functional differential equations with constantcoefficients. The determining equations of the admitted Lie group are constructed in a manner differentfrom that of the existing literature for delay differential equations. We define the standard Lie bracketand make a complete classification of linear functional differential equations with constant coefficients, tosolvable Lie algebras. We also classify some non-linear functional differential equations with constant co-efficients, to solvable Lie algebras.

Keywords: Delay differential equations, determining equations, group analysis, neutral differentialequations, solvable lie algebras.

Mathematics Subject Classification (2010): 17B30, 34K06, 76M60, 58J70.

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MD

Speech analysis based emotion-aware healthcare systemAkshita Abrol, Praveen K. Lehana

Department of Electronics Jammu University Jammu, J& K, India.Email: [email protected]

One of the most important use of speech communication in health care would be to detect an illnessthrough the analysis of speech of a patient. Glottal analysis of speech constitutes an integral part of clinicalinterpretation. It helps in determination of emotional expression and its relation to the overall state of thespeaker. Emotional or mood disorders such as clinical depression constitute potentially crippling illnesses.Depressive disorders are among the leading causes of disability in the world and have been linked to highrates of suicides. This paper discusses the relation of emotional impairment in speech with the clinical stateof the speaker. With the advent of big data oriented wireless technologies including Internet of Things inthe next generation networks, emotional health care monitoring specifically for children and elderly andmentally ill people is receiving considerable attention. Emotional impairment is considered to be one ofthe hallmark features of Schizophrenic speech which has further been investigated in this paper. It has beenconcluded that objective classification of emotional speech to detect an illness would contribute to person-alized and seamless state-of-the-art health care technologies in near future.

Keywords: Emotional impairment, depression, speech, healthcare, next generation networks.

Analysing the efficiency of hexagonal microfluidic fuel cellJyoti Lalotra, Praveen K. Lehana

Department of Electronics Jammu University Jammu, J& K, India, Email: [email protected]

The greed of power and energy has blindfolded the human race by triggering the never ending processof depletion of energy resources on earth. It has alarmed to search for alternative sources of energy as aconsequence of deteriorating climatic changes and rapid depletion of fossil fuels. It is time to shift to greenenergy otherwise with the pace of polluting and utilizing natural resources the earth will not sustain more.Besides this, combustion of fossil fuels is slowly changing the composition of atmosphere and it may leadto climatic disasters. Developing alternative renewable and safe resources is a goal of energy engineering tosafeguard the future of coming generations. Further, major part environmental pollution is contributed byusing conventional techniques for generating electricity. A recent device for tackling these problems is thefuel cell. It is like a battery which generates energy from an electrochemical reaction. Both batteries andfuel cells convert chemical energy into electrical energy. Battery supplies energy only for some specifiedtime, fuel cell has the efficiency to supply energy indefinitely as long as the supply of hydrogen and oxy-gen is maintained. Fuel cells have higher efficiency than other conventional alternatives. Proton exchangemembrane (PEM) based fuel cells use Hydrogen and Oxygen for generating electric voltage. The onlyby-product of this fuel is the water. In this paper, different microfluidic structures have been investigatedfor enhancing the efficiency. The investigations have shown that hexagonal structure is a better option for

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supplying gases and placement fuel cell as arrays.

Keywords: Efficiency, PEM, Fuel cell.

Varying Trends of Smart BandagingPriti Rajput, Praveen K. Lehana

Department of Electronics Jammu University Jammu, J& K, [email protected]

Living tissue inheritably has the ability of self-healing on getting wounded or misaligned. The healingmechanism starts within seconds of getting injured. The damaged blood vessels send a signal to the bloodcell platelets that race together and form a clot to prevent further blood loss. The clots turn to scab with time.The blood vessels open to allow fresh nutrients and oxygen into the wound that speeds healing and whiteblood vessels joins in to fight infection. Oxygen rich red blood cells arrives at the wound site to build upthe damaged tissue. With time the tissue heals completely and is same as it was before. Bodys mechanismtakes a fixed time to heal the wound depending upon the conditioning of the wound and immune system.Sometimes it takes more than a year to heal the wound and in that case manmade modes are required to healthe wound at a pace. A wound heals on its own in living tissues unless it becomes chronic. Bandages are amean to aid healing. The traditional mechanisms of healing the wounds involve examining it by removingthe bandages regularly that hinders the healing mechanism. With advancement in technology, the traditionaltechniques are being replaced by smart methods of wound management. Researchers throughout the worldare working on smart bandage technology. The current fast and technological world demands a bandagethat needs to be monitored at home for spread of infection or restorative process. Different bandages havebeen under development in various research institutes across the globe. The smart bandages react to thevarying level of oxygen, pH, moisture, or infection at the wounded area. Its great relief to the woundedsoldiers in the battle field as it helps to monitor the wound in the absence of doctors. The paper presents areview of various smart bandages developed by different researchers and the prototype of one developed byus using herbal ingredients.

Keywords: Bandages, infection, microfluidics, moisture, wounds.

Varying Trends of Smart BandagingVerasis Kour, Praveen K. Lehana

Department of Electronics Jammu University Jammu, J& K, [email protected]

Internet of Things (IoT), a novel technology that connects day-to-day objects with the internet, forleveraging the usefulness of data, has started to find its applications in numerous domains including auto-mobile, aviation, healthcare, logistics, manufacturing, industries, transport etc. Additionally, the conceptof machine health and status monitoring is being incorporated widely in industrial as well as domestic en-vironment owing to its various advantages such as detection of anomalies, reducing the maintenance costs,eliminating the machinery breakdown, performance optimization, fault detection, and machinery conditionmonitoring. Techniques such as analysis of machines electromagnetic field signature, noise and vibrationsignature, current signature, machinerys temperature profile analysis, etc are usually used for monitoringthe health of a machine. Integration of machinery maintenance with IoT, would serve as a powerful tool,leading to enhanced capabilities and increased potential, offering wider opportunities in terms of machineryhealthcare. Data collection in real time through various sensors and actuators, transfer of this data to the

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internet, its analysis, extraction of information, exchange of this information among wider section of ma-chinery via the internet as well as machine-to-machine communication opens doors for investigating noveltechniques for efficient machinery healthcare using IoT.

Keywords: Internet of Things, machinery health monitoring, condition monitoring, status monitoring,machine learning.

Impact of rigid surface on dispersion and damping characteristic of Love-typewave propagating in an initially stressed piezoelectric layer

Shishir Gupta, Rachaita Dutta, Soumik DasDepartment of Applied Mathematics IIT(ISM), Dhanbad, India.

shishir [email protected], [email protected] [email protected]

In this article, an investigation regarding Love-type wave propagation through initially stressed piezo-electric layer deals with the effect of overlying fractured porous medium saturated with liquid and an un-derlying fiber-reinforced half-space with initial stress. Two individual cases for the interposed piezoelectriclayer have been analysed; one is electrically open circuit and other one is electrically short circuit. More-over, behaviour of Love-type wave propagation is determined in presence of rigid surface. Displacementcomponents are acquired by using method of separation of variables. Frequency equations in both casesappear to be complex which are dissociated into real and imaginary expressions indicating dispersion andattenuation properties of Love-type wave respectively. Impact of total porosity, volume fraction of fractures,initial stress parameters, dielectric constants, piezoelectricity parameter and fiber-reinforcement parametersare portrayed through various graphical implementations. In every graph of dispersion and attenuation, bothcases of piezoelectricity have been compared by taking variation in above discussed parameters.

Keywords: Love-type wave, fractured porosity, initial stress, piezoelectricity, fiber-reinforcement.

AMS subject classifications : 74J15.

Discharge characteristic of multi-cycle triangular labyrinth weirSubhankar Das, Parthajit Roy

M.Tech Student, National Institute of Technology, Silchar, India,Assistant Professor, National Institute of Technology, Silchar, India .

[email protected], parthajit [email protected]

In rivers and canals, weirs are the most common and useful water retaining structure and it allows owof excess water over its crest. The flow over a weir is largely governed by its length and head over theweir crest. Labyrinth weirs are more efficient than conventional weirs due to increased crest length. In thisstudy, ANSYS Fluent software was used to investigate the effect of included angle and number of cycleson the performance of the labyrinth weir. The grid-independent study was done to check the sensitivity ofthe mesh in the numerical results and a fine mesh (10mm) was selected for numerical study with 1.874%discretization error. Standard k-ε turbulence model was used to consider the turbulence effects. The volumeof fluid (VOF) model was used for tracking the free surface. The discharge performance obtained fromthe computational fluid dynamic (CFD) analysis shows a good agreement with the results obtained throughlaboratory experiments. Comparison of the results shows that single cycle labyrinth weirs are more efficientthan multi-cycle labyrinth weir. The results encouraged to use of ANSYS Fluent and computational fluiddynamics methods for further analysis.

Keywords: Labyrinth weir, Computational fluid dynamics, Free surface flow

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Geometrical changes in journal bearing due to piezoelectric actuatorsAayush Trivedia, Wolfgang Seemannb, and Mohammad Talhac

a,cSchool of Engineering, Indian Institute of Technology Mandi, HP, 175005, India bInstitut fiir TechnischeMechanik, Karlsruher Institut fiir Technologie, Karlsruhe, Germany.

[email protected]

In this study, an analytical solution to find the deformation in journal bearing under the action of piezo-electric actuators is obtained. Here, steel AISI 4340 is taken as bearing material and PZT-4 is taken asmaterial for piezoelectric actuators. The differential equation relating the bending moment and displace-ment of thin curved rods are coupled with the stress-charge form of reverse piezoelectric effect. The two-dimensional plane stress condition is used for additional simplifcation of the model. The present results arevalidated with the finite element method-based package COMSOL multiphysics. It has been observed thatthe results tend to converge at higher values of radius to thickness ratios of the bearing, and lower breadthto height ratios of the piezoelectric actuators.

Keywords: Piezoelectric actuators, journal bearing, FEM, deformation analysis, thin curved rods.

Studies of Hyperloop Vehicle for Transportation: A ReviewV.K. Srivastav1, Aditya Priyanka1, Abhishek Kumar1, Shudhanshu Kumar1, Anand Raj1

1 Mothari College of Engineering Mothari, Bihar

This paper presents a critical review of hyperloop vehicle that is useful for next generation transporta-tion. The Hyperloop concept is proposed as quicker, cheaper alternative to high speed rail.It is seen fromliterature that computational simulation play an important role to simulate the air flow around the capsuleconsidering the effect of the axial-flow air compressor and the levitation cushion on the air flow. In thispaper, provide all the boundary conditions in tabular from that was used in both computational as well asexperimental papers. The present work will also compare different hyperloop models used by the .

Keywords: Hyperloop, Computational Fluid Dynamics(CFD), Tube transport system, Tube Vehi-cle.


1 Motihari College of Engineering Motihari, [email protected]

This paper presents a critical review of hyperloop vehicle that is useful for next generation transporta-tion. The Hyperloop concept is proposed as quicker, cheaper alternative to high speed rail.It is seen fromliterature that computational simulation play an important role to simulate the air flow around the capsuleconsidering the effect of the axial-flow air compressor and the levitation cushion on the air flow. In thispaper, provide all the boundary conditions in tabular from that was used in both computational as wellas experimental papers. The present work will also compare different hyperloop models used by the re-searchers.


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Bivariate Bernstein-Schurer-Stancu type GBS operators based on (p, q)-integersMohd. Ahasan and M. Mursaleen

Department of mathematics, Aligarh Muslim University, Aligarh-202002, [email protected]

The purpose of this paper is to construct (p, q)-analogue of Bernstein-Schurer-Stancu type GBS oper-ators for approximating B-continuous functions and establish the uniform convergence theorem for thesenew operators. In terms of mixed modulus of continuity, the rate of convergence for these new operators isdetermined.

Keywords: (p, q)-integers, Bernstein-Schurer-Stancu type operators, GBS operators, Positive lin-ear operators, B-continuous functions and Mixed modulus of continuity.

AMS subject classifications : 41A10, 41A25 and 41A36

Uncertain eigenvalue analysis of finite element modelled functionally gradientarches

Mohammad Amir#, Mohammad Talha∗

School of Engineering, Indian Institute of Technology Mandi, HP, 175005, [email protected]

Uncertain eigenvalue analysis of the functionally gradient arches using finite element method is pre-sented in this study. The system parameters, like material properties of each constituent’s material, andvolume fraction index are taken as uncorrelated random input variables. These random input variables aremod- elled using first order perturbation technique (FOPT). An efficient stochastic finite element modelbased on FOPT is developed and employed to examine the second-order statistics (mean and standard de-viation (SD)) of the vibration response of the functionally graded curved beams. The efficacy and accuracyof the present formulation is ensured by comparing the present results with results obtained by Monte Carlosampling (MSC) method. Few new numerical results are calculated which can be used as benchmark forfurther studies.

Keywords:First order perturbation technique (FOPT), Stochastic finite element method (SFEM),Monte Carlo sampling (MSC) method, Uncertainty quantification, FG curved beams etc.


1 Motihari College of Engineering Motihari, Bihar



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Second-order statistics of the elastic buckling of skewed functionally gradient plateswith material uncertainties

Mohammed Shakir1∗ and Mohammad Talha 2

1,2School of Engineering, Indian Institute of Technology, Mandi-175005, [email protected]

The manufacturing of functionally gradient materials (FGM) are highly sophisticated due to large num-ber of design parameters are associated in the fabrication processes and led uncertainties in their materialproperties. These materials offer immense capability and excellent performance in a vast range of en-gineering applications, such as in Aerospace, Mechanical and Marine engineering. In the present work,second-order statistics of the elastic buckling of skewed FGM plates has been studied subjected to uniaxialand biaxial loadings. The effective material properties of the gradient plates are customized in the transversedirection only according to the power-law distribution of the volume fractions of the constituents. Youngsmoduli, Poissons ratios and power law index are considered as random system parameters. The plate kine-matics is based on Reddys higher order shear deformation theory. An efficient C0 stochastic finite elementbased on the first-order perturbation technique (FOPT) is proposed to access second-order statistics of thebuckling load. Convergence and comparison studies have been performed to assess the adequacy of thepresent mathematical model. The numerical results have been presented with different system parameters,and its dispersion with respect to various random variables.

Keywords: Functionally gradient skewed plate, material uncertainty, finite element method, first-order perturbation technique.

Estimation of mean rainfalls using Geostatistical techniques in Kabul River Basin,Afghanistan

Shamsullah Sultani1 1∗, Arun Goel 2

1.∗Master of technology student, Civil Engineering Department, National Institute of Technology Kurukshetra,Haryana-136119, India email: [email protected]

2. Professor, Civil Engineering Department, National Institute of Technology, Kurukshetra, Haryana-136119, India.drarun [email protected]

Rainfall is part of Hydrologic cycle, it has much spatial variability over the basin. The amount of rainfallreceived at periodic intervals like weeks, months, seasons and years indicates its distribution. Rainfallmagnitude varies in space and time so it needs suitable implements to anticipate accurate mean values inspace as well as in time. Many rainfall estimation methods are available in which interpolation is veryhelpful. In this study two geostatistical interpolation techniques (kriging, cokriging) and one deterministictechnique IDW (Inverse Distance Weighted) have been applied to estimate monthly (January-December),seasonal (spring, summer, autumn, winter) and annual rainfalls in Kabul River Basin, Afghanistan. It ishighly mountainous region ranging from 400-6000 meters lies in the northeast quarter of the country andincludes eight provinces and the capital Kabul city. Interpolation has been conducted for a period of 1958-1978 by using ground data obtained from 15 rain gauge stations. Among all three methods, kriging andcokriging produced good results with nearly zero Mean Error (ME) and least Root Mean Square Error(RMSE) where IDW produced results out of limits. Elevation was used as co-variant in cokriging methodto improve the results but due to lack of density of stations and correlation between two variables (rainfalland elevation) the outcome has not been improved considerably. Geographic Information System (GIS)with geostatistical extension has been used.

Keywords: Kabul River Basin, Afghanistan, Kriging, Cokriging, IDW, Rainfall

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COMPUTATIONAL AND EXPERIMENTAL STUDIES OF FLY ASH BRICKV. K. Srivastav1 R. K. Singh1, R. Kumar1, A Kumar1, A. K. Chhotu1, A. R. Paul2

1Motihari College of Engineering, Motihari, Bihar2Motilal Nehru National Institute of Technology Allahabad, Prayagraj, Uttar Pradesh.

[email protected]

This paper is studied compressive strength of fly ash bricks both computationally as well as experi-mentally. The experiment is performed in the Department of Civil Engineering, MCE Motihari. However,computational work is done using Ansys Software. In India, It is seen that more than 50the electricity isproduced through coal fired thermal power plant and in this process about 65of the total coal produced inIndia. Electricity formed through coal is cheap, reliable and most widely used in India but it has much badeffect on human health because of disposal interns of fly ash. Fly ash are deposited in big pond which cre-ates a bad impact on environment as well as human health so recycling of fly ash is the biggest challenge forresearchers. The fly ash bricks are reasonably lighter in weight and stronger as comparison of clay bricks.Therefore, the present work is focused on to compute the strength of fly ash bricks. The computed resultshows good agreement with the experimental results.

Keywords : Fly ash brick, Finite Element Method, Strength of Fly Ash Bricks.

3D Stress Analysis of Reinforced Concrete SleeperTejas M. Gondhalekar1 and S. K. Panigrahi2

1PG student, Defence Institute of Advanced Technology (Deemed University), Pune, India 2Professor, DefenceInstitute of Advanced Technology (Deemed University), Pune, India.

[email protected]

Railway is a significant and widespread means of conveyance for people and cargo. One of the mostvital part of railway system is sleeper which is rested beneath the rails and supports the track. Its function isto transfer and mete out the loads coming from the above to the ballast and later to ground and transverselysecure the rails to maintain the correct gauge-width. Till this time many materials have been used in makingof sleeper. But the problems such as biodegradation and splitting in timber, corrosion and electrical conduc-tivity for steel and excessive brittleness for cast iron constricted the use of these materials and shifted theresearch towards the concrete sleeper. In the railway track structure the strength of sleeper determines thetype of locomotive to be used over that path. In near future due to time constraints the railway transportationis going to increase. This condition necessitates the appropriate use of exhaustive analysis for the designanalysis of railway sleeper. In the present work, a three dimensional stress analysis has been carried outwith the help of ANSYS under the vertical static loading finite element based model. Also it is shown thatthe loading capacity of the sleeper is strongly affected by the longitudinal reinforcements. This paper alsopresents the study of dynamic behaviour of railway sleeper subjected to transient concentrated load. Thisload also takes into account the dynamic load factor for the analysis. Numerical finite element solutions tothis fundamental transient dynamic load problem are obtained.

Keywords: Concrete sleeper, finite element method, Stress correlation, longitudinal reinforce-ment, transient load, impact factor.

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Triple-diffusive convection with more realistic two temperature model fornanofluidsUrvashi Gupta

Dr. S.S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University,Chandigarh-160014, India.

dr urvashi [email protected].

Triple-diffusive convection for nanofluids in which driving density differences are caused due to thevariation of three diffusive components nanoparticles, heat and solute; using more realistic two temperaturemodel i.e. separate thermal energy equations for fluid phase and nanoparticle phase has been investigated bymaking use of the method of superposition of basic possible modes and single term Galerkin method. Thesystem of partial differential equations are converted to ordinary differential equations which are solvedusing Normal mode technique and single term Galerkin method. A complex system with local thermalnonequilibrium (LTNE) effects among the fluid and particle phases along with the Brownian motion andthermophoresis to account for nanoparticles has been considered. Numerical computations are carried outusing the software Mathematica for permissible range of values of various parameters under consideration.An additional solute concentration equation supplements the conservation equations due to the existenceof solute which introduces two additional non-dimensional parameters whereas three additional parameterscame into existence due to the consideration of LTNE effects. The critical Rayleigh number remains con-stant for smaller values of interphase heat transfer parameter, decreases for intermediate values and againreaches to constant value for higher values of the parameter. It implies that stabilizing and destabilizingeffects are observed only for the intermediate values of Nield parameter. Further Lewis Number, soluteRayleigh number, concentration Rayleigh number and modified diffusivity ratio tend to enhance the im-pact of destabilization while modified thermal diffusivity ratio inhibit the destabilizing impact though veryslightly.

Keywords: Nanofluids; Binary convection; Thermophoresis; Rayleigh Bnard problem; Localthermal non-equilibrium.

Design of wind turbine for the application of desalination processS.Ramachandran1 ,S.Vasanth1∗,S.Devarajan1

1Sri Sai Ram Engineering college,Chennai,Tamilnadu, [email protected]

In this research work , design, development and performance analysis of a cluster of wind energy baseddesalination units are proposed. The design shall be made for small scale of desalinated water per day perunit depending on the requirement. Various blade profiles shall be used to optimize the profles. NACA0015 airfoil profile is used for the windmill which rotates at a very low speed of 1m/s. A high pressurereciprocating pump is used for pumping seawater through high pressure RO Membrane to get the desali-nated water. Glass Fiber Reinforced Polypropylene material is used for the fabrication of the blades ofthe windmill. This would facilitate the studies on the performance various NACA profiles for optimizedfor various units of desalination depending on the sites. Also suitable materials for the fabrication of theturbine blades would be suggested based on Carbon Fiber Reinforced Plastics (CFRP) blades. CFD wasused for the analysis of air ow and the results are presented.

Keywords: CFD, NACA 0015, wind turbine, turbine blades, desalination

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Enhancing software reliability through the generalized inflection S-shaped failurerate with testing effort in growth modelVishal Pradhan1, Ajay Kumar1 and Joydip Dhar1

1Department of Applied Sciences, ABV-Indian Institute of Information Technology and ManagementGwalior-474015 India.

[email protected]

This paper presents a methodology for estimating software reliability incorporating generalized inflec-tion S-shaped failure rate using the testing effort function. Here, testing effort function is involved in failurerate function. Further, we consider both the perfect and imperfect debugging environment. In the reliabilitygrowth model, we also develop for both detection and correction process. A software project manager hasto conduct testing activities economically and efficiently with limited testing resources due to the limiteddelivery, cost, and testing effort. Therefore, we reckon the testing effort function (TEF) that classified asdetection and correction effort. Here, we estimate the values of unknown parameters of TEF, detectionmodel and correction model separately by least square estimation. All the measures of performance arecalculated using real data-sets and comparison made between the existing model and the proposed models.It is observed that the performance of the proposed model is better. Release time of software with a trade-offbetween reliability and cost is also calculated.

Keywords: Software reliability growth model (SRGM), Testing effort function, Optimal release,Generalized Inflection S-shaped.

Experimental and numerical study of blood ow characteristics in human coronaryartery with plaque

Wasim Saliha,Pradeep Kumarb, Parmod Kumarc, Mohammad Talha ∗

School of Engineering, Indian Institute of Technology Mandi, HP, 175005, [email protected]

The present study investigates the characteristics of blood ow in human coronary artery with plaqueusing combined experimental and numerical simulations. A computational model has been developedusing uid ow solver AN- SYS Fluent. In the present framework blood is considered as Newtonian uidand the corresponding governing equations are discretised using Eulerian approach based finite volumemethod. Two different set of plaque con

gurations with concentrated, and uniform distribution along the circumference have been simulated.The computational results have been verified with the corresponding experiments. It has been observedthat central line velocity in axial direction takes sudden rise at the throat of uniformly distributed plaque.Similar rise of central line velocity is observed in concentrated plaque also, however it has shown localiseductuation in velocity magnitude at other locations as well. The detailed study will include the comparison ofvelocity and pressure distributions for wide range of ow conditions. These analysis have great importancein designing of cardiovascular devices in order to circumvent heart related problems.

Keywords: Coronary Artery, Plaque, Blood ow, Numerical simulations, Expermental Setup

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Numerical simulation for radial stress and displacement of jet engine Exhaust pipeY.K.Singh1 and S. K. Panigrahi2

1 PG student, Defence Institute of Advanced Technology (Deemed University), Pune, India 2 Professor, DefenceInstitute of Advanced Technology (Deemed University), Pune, India.

Exhaust pipe is used in exhaust section of jet engine. Exhaust pipe is subjected to combined mechanicaland thermal loads like internal pressure and high temperature of exhaust gases and the ambient conditions.Exhaust pipe is actually thick cylindrical angular pipe cross-section. In this research a basic 3D model thatcan be used to study the effects of temperature and internal pressure of exhaust gases on the radial stressdistributions and radial displacement fields in circular angled cylinder. A linear distribution of temperaturethrough the thickness is considered for thick cylindrical exhaust pipe. The analytical model will be studiedon the thick walled cylinders theory using FEA. Results of this analytical study will be used to study thecritical cross-section of Exhaust pipe. To sustain very temperature of exhaust gases the material should havegood thermal resistance properties, the common alloy used for Exhaust pipe is stainless steel or INCONEL718. The alloy with good results will suggested for manufacturing of exhaust pipe.

Keywords: Exhaust pipe, Jet engine, Thermal and Mechanical load 3D-Finite Element Analysis(FEA), Steel and Nickel Alloys.

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MM

Cross-diffusion induced Turing and non-Turing patterns inRosenzweig-MacArthur model

Nayana MukherjeeDepartment of Mathematics & Statistics, IIT Kanpur, Kanpur, India.

[email protected]

Pattern formation is widely studied in spatio-temporal prey-predator models with only selfdiffusionterms. Models with cross-diffusion, in addition to self-diffusion terms, take care of the situation in whichpresence, absence, abundance or scarcity of one species affect the movement of a population of anotherspecies in a given domain. In this talk, I consider cross-diffusion induced pattern formation in a prey-predator model with Rosenzweig-MacArthur type reaction kinetics in a one-dimensional spatial domain.Spatio-temporal prey-predator model with Rosenzweig-MacArthur type reaction kinetics and self-diffusionis unable to generate Turing patterns rather produces traveling wave, periodic traveling wave, modulated pe-riodic traveling wave and spatio-temporal chaotic patterns. However, addition of density dependent cross-diffusion term leads to satisfaction of Turing instability conditions and generation of stationary Turingpatterns. Also the dynamics of the patterns generated by the self-diffusion model is preserved. Further,cross-diffusion term affects the speed of traveling waves produced in the self-diffusion model. The focus ofmy talk is to investigate the bifurcation of traveling wave solution into Turing patterns and transition of onepattern into another in the presence of cross-diffusion.

Keywords: cross-diffusion; Turing instability; traveling wave; stationary pattern; spatiotemporal chaos;bifurcation.

AMS subject classifications : 35B36, 37L10, 34D30

POPULATION DYNAMIC CONSEQUENCES OF FEARFUL PREY IN ASPATIOTEMPORAL PREDATOR-PREY SYSTEM

Ranjit Kumar Upadhyay, Swati MishraDepartment of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad,

Jharkhand-826004, [email protected]

of responses spanning the physiology, morphology, ontogeny and the behavior of scared organisms. Toexplore the effect of fear and its dynamic consequences, we have formulated a predator-prey model with thecost of fear in prey reproduction term. Spatial movement of species in one and two dimensions have beenconsidered for the better understanding of the model system dynamics. Stability analysis, Hopf-bifurcation,direction and stability of bifurcating periodic solutions have been studied. Conditions for Turing pattern for-mation have been established through diffusion-driven instability. The existence of both supercritical andsubcritical Hopf-bifurcations have been investigated by numerical simulations. Various Turing patterns are

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presented and found that the change in the level of fear and diffusion coefficients alter these structuressignificantly. Holes and holes-stripes mixed type of ecologically realistic patterns are observed for smallvalues of fear and relative increase in the level of fear may reduce the overall population size.

Keywords: Predator-prey interactions, Fear effect, Anti-predator response, Stability, Hopf-bifurcation,Pattern formation.

AMS subject classifications : 92D25, 92D40, 34A34, 35B36.

A Mathematical model for Human Papillomavirus and its impact on cervicalcancer in India

R Praveen Kumar, K MurugesanaaDepartment of Mathematics National Institute of Technology, Tiruchirappalli-620015, Tamil Nadu, India.

[email protected], nand [email protected], [email protected]

In this article, We develop a mathematical model for Human Papillomavirus transmission and its impactof cervical cancer in India. The existence and stability of the system are discussed. Using next-generationmatrix method we obtain the basic reproduction number and show that the disease-free equilibrium be-comes asymptotically stable under certain conditions. Finally, numerical simulation is applied to study thesystem.

Keywords:

Predator-prey system: Herd behavior and anti-predator traits contribute inenriching the evolution of stronger prey defence

Rajat Kaushik, Sandip BanerjeeIndian Institute of Technology Roorkee, Roorkee-247447, Uttrakhand (India).


In this paper, we focus on a stage-structured predator-prey model with herd behavior and anti-predatorphenomenon. It is our purpose in this paper to illustrate the combined effects of the herd behavior andanti-predator strategy on the predator-prey ecology. By constructing the model equations, we present ananalytical study of the system and the occurrence of Hopf and transcritical bifurcation for the anti-predatorrate as a bifurcation parameter. Finally, the extinction of predators is explored via numerical simulations,that is the prey population survives successfully in the habitat due to their defense mechanism and anti-predator behavior.

Keywords: Herd behavior; Anti-predator strategy; Asymptotically stable; Hopf bifurcation.

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Effect of porosities with and without fractures on propagation of SH wave: casewise study

Shishir Gupta, Soumik Das, Rachaita [email protected]

A mathematical model is presented in this article for a comparative study between SH wave propaga-tion in corrugated double porous stratum and that in corrugated single porous medium. Among the twocases, the first one depicts propagation of SH wave through fluid saturated creased porous layer havingfractures and resting over a half-space consisting of void pores, whereas in the second case, only liquidsaturated porous medium with corrugated boundaries has been considered for SH wave propagation whilethe half-space remains unchanged. Effects of heterogeneity and anisotropy on wave propagation have beenanalysed in both cases. Method of separation of variable is used to attain the complex frequency equationaccording as both cases and those complex dispersion relations are separated into two equations that illus-trate dispersion and attenuation properties of SH wave. In every graphical execution, double porosity andsingle porosity have been compared in terms of wave velocity and attenuation coefficient by using variationof several parameters such as inhomogeneity parameter, position parameter, fluctuation parameter, flatnessparameter, total porosity and ratio of rigidity modulus.

Dynamical behaviour of predator-prey systems with variation of Allee function inpredator’s growth: Structural sensitivity analysis

Deeptajyoti SenDepartment of Mathematics and Statistics, IIT Kanpur, Kanpur, India.

[email protected]

Prey-predator model with Allee effect in predator’s growth is one of the important research areas inMathematical biology now a days as it capture some realistic features . This due to the fact that the complexbehaviour exhibited by such model also agrees with the experiment held in laboratory. Allee effect occursin predator’s growth due to various reasons such as lack of consumption of prey, unable to find suitable mateetc. Now Allee functions, to model Allee effect on predator growth, have certain properties. In this talk, Iwish to compare the dynamics of the system with genreal form of Allee function in predator’s growth. Theresults will be elaborated with some base functions (such as ay

b+y, , a

b(1 − exp(−by)) etc) which has same

charecteristic as that of Allee function and perturb them slightly by variation of the parameters. Finally Iwill present the comparative dynamics resulting from the variation of Allee effect function using structuralsensitivity analysis .

Keywords: Allee effect, functional response, Bifurcation,StabilityMSC: 37L10, 34D30

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MODELLING OF SEDIMENT EXCLUDERDibyendu Das1, N.K.Tiwari2,Subodh Ranjan vajesnayee3

1,2,3Department of Civil Engineering,National Institute of Technology Kurukshetra, Haryana. e-mail:[email protected]

A tunnel-type sediment excluder is commonly used at the headwork of a canal for preventing excesssediment from entering the off-taking canal. In such excluders the sediment-laden water, which flowsmainly near the bed, is made to flow through the tunnels provided at the canal bed. It may be then dischargedback into the river downstream through the undersluice bays. Comparatively sediment-free water in the toplayers is allowed to enter the canal. Presently, the only hydraulic principle utilized in its design is thatenergy loss is kept to a minimum and a minimum velocity of flow is ensured through the tunnel for thenondeposition of the coarse material.This paper attempts to investigate the efficiency of Sediment Excluderat the headwork of canal by decreasing the number of tunnels,change the sediment size and concentrations.By using the AI based modelling techniques,It has been predicted the efficiency of Sediment Excluder bychanging number of tunnels,sediment size and concentrations. In this study the output value of efficiency ofSediment Excluder due to decreasing number of tunnels were predicted using ANN and Gaussian Processby taking Parameters like Geometric mean,discharge,concentrations,efficiency of Sediment Excluder.

Keywords: ANN, Gaussian process, Geometric mean, concentrations, Efficiency of Sediment Ex-cluder.

FEM Analysis of Adhesively Bonded Composite PatchesV.Divakar1 and S. K. PanigrahiR2

1,2Defence Institute of Advanced Technology (Deemed University), Pune, [email protected]

Structural adhesives as a medium of bonding as opposed to other securing strategies such as screwsand rivets presents various favorable circumstances like lightweight, larger area of contact. This paperdeals with the numerical simulation of these adhesively bonded joints in Aluminum 2024 T3 Aircraft Skinhaving corrosion grind out at center with pessimistic load range. The FEA model generated is validatedby comparing the stresses with the results available in the literature. Variation due to change in MaterialAnisotropy, Patch shape, Ply Sequences and its impact on stresses are studied in this paper. The MaximumPrincipal stress in Aluminium Skin, Critical Failure Indices in Adhesive as well as Composite Doubler dueto out-of plane bending moments are determined for different fibres made of Graphite and Boron in Epoxymatrix with varied laminate stacking sequence viz. unidirectional [0]13, cross-ply [(0/90)3(0)(90/0)3] andangle ply [(+45/45)3(0)(45/45)3].

Results show that judicious choice of the above mentioned parameters in Composite Doubler Patchallows for a noteworthy increment of the static strength compared to previously corrosion damaged alu-minium plate and facilitates a cost-effective method to broaden the lives of the part.

Keywords: Composite materials; Composite repair; Patch repair; adhesively bonded patch; Car-bon fibre reinforced polymer; Failure indices.

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Solving a variational inclusion problem with its corresponding resolvent equationproblem involving XOR-Operation

1Rais Ahmad,2Javid Iqbal,2Shakeel Ahmed,1Saddam Husain1Department of Mathematics Aligarh Muslim University, Aligarh 202002, India. 2Department of Mathematical

Sciences Baba Ghulam Shah Badshah University Rajouri,Jammu and Kashmir-185234, [email protected]

In this paper, we consider a variational inclusion problem involving XOR-operation with its resolventequation problem involving XOR-operation. We suggest separate iterative algorithms for solving both theproblems. The existence and convergence results are proved for variational inclusion problem and forcorresponding resolvent equation problem in ordered Hilbert spaces. We claim that results of this paper arenew and refinement of previously known results

Keywords: Resolvent, Existence, Convergence, XOR-Operation, Equation.AMS Subject Classification: 49J40, 47H06, 49J53, 47J20.

Modeling and Simulation of Nylon Liner Shaped Charge JetsYadav Ombir Singh∗, Nimje S.V and Choudha P.K.

[email protected]

Warhead an integral part of ammunition, which causes desired damage to the target by converting theenergy released by rapid decomposition (detonation) of explosives into desired forms like temperature,blast, K.E. to projectiles etc. by a suitable warhead mechanism. Warheads can be designed for omni-directional effects or for a particular direction i.e. directed energy warheads. Shaped charges belong toclass of directed energy warheads and are usually employed in defeating armoured protected targets. Ashaped charge is a cylinder of explosives with an empty cavity with a liner (mostly of metals) on one sideand a detonator at the other end of it. When the explosive is detonated, a high pressure is generated whichcauses the solid liner to collapse and form a jet with velocities in the range of 10 km/s. When this highenergy jet strikes a metal plate, a deep cavity is formed and that is more effective as compared to otherconventional ammunitions against an armoured target. But the conventional shaped charges have somedisadvantages i.e. they are easily detectable by metal detectors and activate the modern Explosive ReactiveArmours (ERA) resulting into failure of its intended task. Also they are very heavy, thus are not suitable forhand held fired ammunitions. Hence, in the current research nylon is used as a substitute for the traditionalmetal liners to achieve short comings of the traditional metal liner shaped charges. Exhaustive numericalsimulations have been carried out for nylon liner shaped charge using commercial software Autodyn. Theobjective of research work is to assess the properties of the nylon jet and to create an empirical relationshipto forecast the jet length, by changing the crucial dimensional parameters such as length-to-diameter ratio,charge diameter, liner thickness, cone angle and stand-off-distance. Results indicate that maximum jet tipvelocity can be achieved for 80 cone angle and liner thickness (2-2.5 mm).

Keywords: Warhead, shaped charge, detonation, ERA.

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Modeling the impact of sanitation and awareness on the spread of infectiousdiseases

Rajanish Kumar Raia, A.K. Misraa∗, Yasuhiro takeuchibaDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221005, India. bCollege of

Science and Engineering, Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa252-5258, Japan.

[email protected]

Sanitation and awareness programs play a fundamental role and are much effective public health in-terventions to control the spread of infectious diseases. In this paper, a nonlinear mathematical model forthe control of infectious diseases, such as typhoid fever is proposed and analyzed by considering budgetrequired for sanitation and awareness programs as a dynamic variable. It is assumed that the budget allo-cation regarding the protection against the disease to warn people and for sanitation increases logisticallyand its per-capita growth rate increases with the increase in number of infected individuals. In the modelformulation, it is assumed that the susceptible individuals contract infection through the direct contact withinfected individuals as well as indirectly through bacteria shed in the environment. It is further assumedthat a fraction of budget is used to warn people via propagating awareness whereas the remaining part isused for sanitation to reduce the density of bacteria. The condition when budget should spend on sanita-tion/awareness to reduce the number of infected individuals is obtained. Model analysis reveals that thesanitation and awareness programs have capability to reduce the epidemic threshold and thus control thespread of infection. However, delay in providing funds destabilizes the system and may cause stabilityswitches through Hopf-bifurcation. Numerical simulations are also carried out to support analytical find-ings.

Keywords: Budget allocation, Delay, Sanitation, Awareness, Hopf-bifurcation, Stability switch.MSC (2010): 34A34, 34D20, 34C23, 92D30.

Modelling of scour around Cylindrical PiersM Vignesh1, Subodh Ranjan Vajesnayee2, and N K Tiwari3

1,2,3Department of Civil Engineering, National Institute of Technology Kurukshetra, India, e-mail:[email protected]

Sediment erosion in the region of bridge piers is a potential hazard to the safety of bridges. The presenceof various roughness heights on the surface of bridge piers was explored as a scour countermeasure. Labo-ratory experiments under clear-water conditions are to be conducted using different roughness heights withdifferent pier diameters under different ow water depths. The test program included a case of a smoothpier to determine the performance of the roughened piers and to benchmark some existing formulas of localscour around bridge piers. This paper attempts to investigate the scouring around the piers by in- creasingthe roughness. By using the AI- based modelling technique, It has been predicted the scouring around thecylindrical piers by changing the roughness and dimension of piers. In this study, the output value of scouraround piers due to increasing its surface roughness were predicted using ANN and Gaussian Process bytaking parameters like mean size(d50), velocity, etc.

Keywords: ANN, Gaussian process, scouring, piers, roughness, D50.

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NA

Continuous wavelet transform of Schwartz tempered distributions in S ′(Rn)

Jay Singh Maurya

Department of Mathematical Sciences Indian Institute of Technology (B.H.U.) Varanasi 221005, India. Email :[email protected]

In this paper we define a continuous wavelet transform of a Schwartz tempered distribution f ∈ S ′(Rn)with wavelet kernel ψ ∈ S(Rn) and derive the corresponding wavelet inversion formula interpreting conver-gence in the weak topology of S ′(Rn) It turns out that the wavelet transform of a constant distribution iszero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constantdistribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribu-tion.

Keywords: Distributions; Generalized functions; Distribution space; Wavelet transform of generalizedfunctions.

Continuous fractional wave packet system in Sobolev type spaceManab Kundu and Akhilesh Prasad

Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004,India.

[email protected], apr [email protected]

In this paper we introduce continuous fractional wave packet system in Sobolev type space and investi-gate their orthogonal properties. The sufficient condition for such system to be orthogonal in Sobolev typespace is investigated. Mathematics Subject Classification (2010). 42C40 42C15.

Keywords: Wave packet transform, Fractional Fourier transform, Orthogonal wave packet, Frame.

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Cech proximity relation and Rough Set TheoryPankaj Kumar Singh, Surabhi Tiwari

Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj211004, [email protected], [email protected]

Zdzisław Pawlak used equivalence relation on a non-empty set to introduce approximation spaces dur-ing the early 1980s to classify objects employing attributes of information systems. It is an extension of settheory for the study of intelligent systems characterized by insufficient and incomplete information. Topol-ogy is a strong root of constructs that can be helpful to enrich the original model of approximation spaces.The study of proximal relation between two sets with respect to their approximations and its application inimage analysis has been discussed in [James Peters et al., 2013], which motivates us to establish proximalrelation between two sets using their respective upper approximations in approximation space. This paperintroduces Cech closure spaces on rough sets by preferring the approach of proximity relation on approx-imation spaces and studies its compactification. Some results have been proved on this advanced nearnessstructure named Cech rough proximity. Examples well support the study. Since this approach identifies thenearness between sets in approximation space, therefore it may prove to be a better tool for such studiesin the field of information science, artificial intelligence, computer science, pattern recognition, etc. 2010AMS subject classification: 54A05, 54A10, 54C60, 54E05, 54E17.

Keywords: Rough sets, proximity spaces, closure space.

A Comparative Study of Monitor function in Mesh ReconstructionPrabhat Mishra and Ritesh Kumar Dubey

SRM IST, [email protected], [email protected]

In this work new monitor functions are proposed using exponential function and compared with theexisting prevailing monitor function in mesh adaptation algorithms for discontinuous flow problems. Dif-ferent time integration methods are used to analyze the non-oscillatory property of the adapted mesh. Itis found that monitor functions designed by exponential function is efficient and yields the solution in lessnumber iterations of the mesh adaptation algorithm.Mathematics Subject Classification(2010): 35L65, 65M50.

Keywords: Adaptive Mesh Reconstruction, Monitor Functions, Conservative scheme.

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1 Motihari College of Engineering Motihari, [email protected]



MESHLESS METHOD FOR THE NUMERICAL SOLUTION OF SPACE ANDTIME FRACTIONAL WAVE EQUATION

Hitesh Bansu ,Sushil KumarS. V. National Institute of Technology, India.

[email protected]

In this article, we have considered a space and time fractional wave equation (STFWE), that is obtainedfrom the classical wave equation by replacing the space and time derivatives with a generalized (Caputo)derivative of fractional order. Furthermore, we have proposed novel and independent discretization forspace and time fractional wave equations (STFWE) using two different basis functions namely, radial basisfunctions(in space) and Chebyshev polynomials(in time). The proposed numerical scheme is truly meshlessand therefore is capable to manage both space and time fractional derivatives concurrently with appropriateinitial and boundary conditions. Finally, we have included few numerical examples to confirm accuracyand performance of the proposed scheme.

Keywords: Radial basis function , Chebyshev Polynomial , Meshless method , Kronecker product, Fractional Wave equation

AMS subject classifications : 26A33 65M70 65N35 35R11 65D25 35L05

Semi-Analytical Solution of Fractional Convection-Dispersion Equation by usingConformable Derivative Approach and Homotopy Analysis Method

Manish Chaudhary∗, Rohit Kumar and Mritunjay Kumar SinghDepartment of Applied Mathematics Indian Institute of Technology (Indian School of Mines) Dhanbad - 826004

(Jharkhand)[email protected]

In this present study, semi-analytical solutions for one-dimensional fractional convection dispersionequation (FCDE) were developed. The concept of conformable fractional derivative of order α ∈ (0, 1]is considered along with Ho- motopy analysis method (HAM) for prediction of pollutant contamination ingroundwater in different porous structures. Initially, the domain is considered to be pollutant free. Theeffect of retardation factor, seepage velocity and generalized dispersion coefficient are included in thesolution of convection dispersion model. In this work, problem is formulated for various types of spatial

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dependency of velocity and dispersion coefficient, that dealt with more realistic phenomenon of the pol-lutant transport in groundwater. FCDE is transformed into the standard convection-dispersion equation withconformal fractional derivative of order α = 1 and compared with the corresponding numerical solutionobtained by Crank-Nicolson Scheme. It shows a good agreement in both solutions. It is observed that thepollutant concentration shows variation with conformable derivative of order α. Hence, this investigationhelps to interpret the accurate description of time dependent behaviour of contaminant transport in porousstructure.

Keywords: Pollutant transport, convection, retardation factor, conformableMathematics subject classification: 76Rxx, 76Sxx

Convergence Analysis of New Hybrid Scheme for Singularly Perturbed ParabolicProblems with Interior Layers

Mr. Narendra Singh Yadav1 Dr. Kaushik MukherjeeDepartment of Mathematics, Indian Institute of Space Science and Technology, Trivandrum-695547, India.

[email protected]

This article deals with a class of singularly perturbed parabolic convection- diffusion problems withdiscontinuous convection coefficient. To obtain better numerical approximation for solving this classof problems, the time derivative is discretized by the backward-Euler method on uniform mesh and forthe spatial discretization, a new hybrid finite difference scheme is proposed utilizing a layer resolvingpiecewise-uniform Shishkin mesh. We prove that the proposed scheme is uniformly convergent in thediscrete supremum norm; and almost second-order accurate in space, regardless of the larger and the smallervalues of the parameter ”. Finally, extensive numerical experiments are conducted to verify the theoreticalresults and also to demonstrate the accuracy of the proposed scheme.

Keywords: singularly perturbed parabolic problem, interior layer, numerical scheme, piecewise-uniform Shishkin mesh, uniform convergence

Fractional calculus for k-Mittag-Leffler function of two variables with the kernel F3Owais Khan

Department of Applied Mathematics, A.M.U., [email protected]

In this paper, we introduced k-Mittag-Leffler function of two variables and investigated its fractionalintegrals and derivatives using Marichev-Saigo-Maeda operators with the kernel F 3. Besides, we obtaincertain interesting particular cases of derived results considering specific values of the parameters.

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Approximation By Modified Lupas Operators Based On (p, q)IntegersM. Mursaleena, Zaheer Abbasb and Mohd Qasimb

aDepartment of Mathematics, Aligarh Muslim University, Aligarh- 202002, India bDepartment of Mathematics,Baba Ghulam Shah Badshah University, Rajouri-185234, JK,India.

[email protected]

The purpose of this paper is to introduce a new modification of Lupas operators in the frame of postquantum setting and to investigate their approximation properties. First using the relations between q-calculus and post quantum calculus, the post quantum analogue of operators constructed will be linearand positive but will not follow Korovkins theorem. Hence a new modification of q-Lupas operators isconstructed which will preserve test functions. Based on these modification of operators, approximationproperties have been investigated. Further, the rate of convergence of operators by mean of modulus ofcontinuity and functions belonging to the Lipschitz class as well as Peetres K-functional are studied.

Keywords: Lupas operators; Post quantum analogue; q analogue; Peetres K-functional; Ko-rovkins type theorem; Convergence theorems.

AMS subject classifications :47H09, 47H10.

HURWITZ-LERCH ZETA FUNCTION AND SOLUTION OF FRACTIONALKINETIC EQUATION

Raghib NadeemDepartment of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University,

Aligarh202002, [email protected]

In the present article, we aim to extend the Hurwitz-Lerch Zeta function φδ,µ;ν(ξ, s, v; p) in terms of ex-tended Beta function. We also study basic properties of this extended Hurwitz-Lerch Zeta function whichcomprises various integral formulas, derivative formula, Mellin transform, generating relation. Fractionalkinetic equation for extended Hurwitz-Lerch Zeta function are also obtained from application perspec- tive.Further, we obtain certain interesting relations in the form of particular cases.

Computation of fractional integrals and derivatives for the product ofMathieu-type series and generalized Mittag-Leffler function

Mohd SaifDepartment of Applied Mathematics, A.M.U., Aligarh.

[email protected]

Fractional calculus, in allowing integrals and derivatives of any positive order (the term ’fractional’kept only for historical reasons), can be considered a branch of mathematical physics which mainly dealswith integro-differential equations, where integrals are of convolution form with weakly singular kernels ofpower law type. In recent decades fractional calculus has won more and more interest in applications inseveral fields of applied sciences. In this line, our main object to investigate image formulas of generalizedfractional hypergeometric operators involving the product of Mathieu type series and generalized Mittag-Leffler function. We also consider some interesting special cases of derived results by specializing suitablevalue of the parameters..

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Turing patterns in a Prey-Predator Model with Hassell-Varley Functional ResponseVikas Kumar and Nitu Kumari

School of Basic Sciences, Indian Institute of Technology Mandi, India.Emails: [email protected], [email protected]

In this article, we have studied a Prey Predator system with Hassell-Varley Functional Response. We as-sume fear in prey due to predator, the birth rate of prey population decreases. Further, we study the spatiallyextended model system to understand the impact of fear on the dynamics. Pattern formation phenomenonis illustrated via numerical simulation, which shows that different diffusive coefficients give differ Turingpatterns. Further, we observe the impact of fear in both temporal and spatiotemporal model systems.

Keywords: Hassell-Varley fuctional response, fear, local stability, Turing instability, Turing patterns.

AMS subject classifications : 92C15, 92B05, 35B36.

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Invited Talks

103

Author Index

A Kumar1, 87A. Chakrabarti, 57A. K. Chhotu1, 87A. R. Paul2, 87A.K. Misraa∗, 96A.S.V. Ravi Kanth, 33Aarthika K, 67Aayush Trivedia, 84Abdul Haq, 50ABDUR RAHEEM, 22Abhilasha, 31ABHISHAKE; GILLES BLANCHARD AND

PETER MATHE, 22Abhishek Kumar1, 84, 85, 99Abhishek Verma, 74ABU SUFIAN, 49Adeeba Umar1, 52Aditya Priyanka1, 84, 85, 99Affreen Akhter, 68Aftab Alam, 45Ajay Kumar, 50, 70Ajay Kumar1 and Joydip Dhar1, 89Ajit Kumar, 48, 75Akanksha Verma, 33Akash Bhavsar, 29Akhilesh Nautiyal, 57Akmal Raza, 43Akshita Abrol, 81Amandeep Kaur, 57Amar Deep and Deepmala, 61Amar Shrivastava and Paritosh Mahata, 56Amit kumar, 38Amit Parmar, 31Anand Raj1, 84, 85, 99ANANTA K. MAJEE, 20and Mohammad Talhac, 84and N K Tiwari3 , 96and Nand kumar Tiwari, 38and Subodh Ranjan Vajesnayee3, 51Anil , 14Anil Kumar, 39, 48

Anil Kumar , 74Anita Devi Thakur , 25Anjali Jaiswal, 41Ankit Parwaliya and Ajay kumar, 39Ankita R Devdhara, 46Anoop Kumar, 67, 77Anuj Kataria1 and Baldev Setia2 , 55Anuj kumar1, 56Anup Singh, 69Anuraj Singh, 39Anuraj Singh , 14Aradhana Bandekar, 41Arun Goel, 58Arun Goel 2 , 86Arvind Kumar Gupta, 13, 59Ashish Kumar, 49Ashok Kumar, 63ATIYA PERVEEN, 46Atul Ailawadhi, 72

B S Lakshmi and S S Phulsagar, 25B.U Raja Ramakrishnaa and N.Ramanan, 51B.V. Rathish Kumar, 3, 36Baljinder Kour, 42Bidhan Chandra Sardar, 15

C. S. Mathpati, 48, 75

D. Bahuguna, 41Deepak Goyal, 39Deepika Sharma, 64Deeptajyoti Sen, 93Devendra Kumar, 12, 24Dibyendu Das1, 94Dileep Kumar, 69Dr. RAMANABABU KALIGATLA, 35Dwijendra Narain Pandey, 63

Faeem Ali, 79

G. Arora, 65G. Nath, 39G.D. Kedar, 68

105

G.D. Veerappa Gowda , 2Gaurav Saxena, 21Ghanshyam G. Tejani, 26Giriraj Methi And Anil Kumar, 27Gnana Bhaskar Tenali , 1Gomathi Bhavani, 21

Harendra Kumar and Santwana Mukhopadhyay,40

Harish Kumar , 8Harshita Tiwari, 44Himanshu Rathore, 18Hira Fatima, 46Hitesh Bansu , 99Hitesh K. Singh and Dwijendra N. Pandey, 40

Indresh Yadav, 17

Jagdev Singh, 24JAIME H. ORTEGA, 5Jay Singh Maurya, 97Jaya Bikram, 68Jervin Zen Lobo, 79Jyoti Lalotra, 81Jyoti Sharma, 19

K Murugesana, 92K. Balaje , 16K. Singh, 42Kamaljeet, 21Kamlesh K. Pankaj, 53Kapil Kumar Sharma, 4Kavita Goyal, 64KM. Luxmi, 37, 54, 61Km. Renu, 63Krishna Kumar Singh2 , 56Kunwer Singh Mathur, 30Kushal Dhar Dwivedi, 73Kusum Yadav, 64

Lokesh Singh, 78

M Vignesh1, 96M. Balachandar, 24M. Krishna Prasad, 18M. Mursaleena, 101M. Senthilvelan, 10M. Tanveer , 16M.Balachandar, 51Mahima Poonia, 42Manab Kundu and Akhilesh Prasad, 97Manali Kokare, 48, 75

Manish Chaudhary and Mritunjay Kumar Singh,44

Manish Chaudhary∗, 99MANISHA, 35Manisha Chowdhury, 36Manoj Kumar, 33Manvi Adha, 65Md Ataur Rahman Khan, 16Md Hasanuzzaman and Waleed M. Alfaqih, 47Md Mansur Alam, 43Md Tarikul Islam, 16Md. Mehedi Hasan Bhuiyan., 16Md. Moniruzzaman Bhuyan, 16Mohammad Amir#, 85Mohammad Anwar Hossain, 16Mohammad Arif and Mohammad Imdad, 45Mohammad Imdad , 47Mohammad Sajid, 2Mohammad Talha∗, 85Mohammed Shakir1∗ and Mohammad Talha 2 ,

86Mohd Saif , 101Mohd. Ahasan and M. Mursaleen , 85Mr. Narendra Singh Yadav1 Dr. Kaushik

Mukherjee , 100Mridula Sharma1, 58Mritunjay Kumar Singh, 68

N K Singh , 74N. Sukavanam , 50N.K.Tiwari2, 51, 94Nand Kumar Tiwari, 37, 54, 61Navjot Kaur and Kavita Goyal, 65Navnit Jha, 9Nayana Mukherjee, 91Neetu Garg, 33Nilesh Kumar Thakur and Archana Ojha , 21Nimje S.V and Choudha P.K., 95Nityananda Roy, 1

Om Namha Shivay, 71Owais Khan , 100

P. Dhanumjaya, 16Pallavi Bedi, 77Pankaj Kumar Singh, 98Pankaj Kumar Tiwari, 27Paresh Vyas, 64, 65Parmod Kumarc, 89Partha Sarathi Mandal, 11Parthajit Roy, 83

106

Pentyala Srinivasa Rao, 74Pooja Gupta, 35Poornesh Kumar Koorata1, 12Prabhat Mishra and Ritesh Kumar Dubey, 98Pradeep kumar1 and Baldev Setia2, 58Pradeep Kumarb, 89Pragya Shukla, 45Prashant Pandey, 34Pratibha Verma and Manoj Kumar, 62Pratiksha, 65Praveen K. Lehana, 81, 82Praveen K. Maurya Manoj K. Rajpoot , 50Prawal Sinha, 4Preeti, 34Prerna Singh, 47Princess Raina and Zaheer Abbas, 67Priti Rajput, 82Prof. A. K. Nandkumaran, 1

R Praveen Kumar, 92R. Kumar1, 87R. N. Saraswat, 52R. P. Gupta , 8R. ROY AND R. K. JANA , 59Rachaita Dutta, 83, 93RAGHIB NADEEM , 101Rahul Kumar Chaturvedi, 41Rais Ahmad , 95Rajanish Kumar Raia, 96Rajat Kaushik, 92Rajeev, 7Rajesh Pandey , 8Rajib Haloi and Subha Pal, 30Raju K. George, 3Rakesh Choudhary and Shalini Jain, 26Rakesh Kumar, 52Ramakanta Meher , 45Ramesh kumar, 72Randhir Singh Baghel, 28Ranjit Kumar, 47Ranjit Kumar Upadhyay, 91Ravi Kumar, 71RENU CHAUDHARY, 20Renuka Rai, 23Rishabh Daal , 7Rishikesh Yadav , 45Ritesh Kumar Dubey, 66Rohit K. Singla, 54Rohit Kumar and Mritunjay Kumar Singh , 99Rohit Tripathi; G. N. Tiwari; Deepak Sharma, 28RohitKumar, 44

Roshan Lal, 5

S. C. Martha, 57S. Kumar2, 7S. S. Jogwar, 48, 75S.C.S. Rao1, 7S.Devarajan1, 88S.Ramachandran1 , 88S.Sundar, 1S.Vasanth1∗, 88Sabana Parvin, 66Sachin Kumar, 36, 42Sandip Banerjee, 92Sandip Rakshit, 32Sangeeta Kumari, 38Sanjeev A. Sahu, 37, 66Sanjeev A. Sahu1, 53Sanjeev Anand Sahu, 53Sanket Tikare, 29Sapna Sharma, 11Sarika, 17Sarita Nandal, 63Saroj Kumar Sahani, 9Sarvjeet Singh, 54Seema, 67Shahna, 17Shamsullah Sultani1 1∗, 86Sheetal Dharmatti , 32Shilpee S. Saxena, 21Shilpee Srivastava, 15Shishir Gupta, 83, 93Shobhit Kumar Srivastava, 51Shreeta Kumari, 53Shudhanshu Kumar1, 84, 85, 99Siddharth Sonkar1, 51Somveer Singh, 44Sonal Nirwal, 37Sonali Mondal, 66Soumik Das, 83, 93Srinivasa Rao Nadiminti1; N. Gayathri Devi1

and A.Kandasamy, 10Subhankar Das, 83SUBHASHIS KARMAKAR, 78Subodh Ranjan Vajesnayee, 37, 54, 61Subodh ranjan vajesnayee, 38Subodh Ranjan Vajesnayee2, 96Subodh Ranjan vajesnayee3, 94Sultan Singh, 39Suman Goyal, 53Sumeeta Singh, 39Sumit Kumar Vishwakarma, 13

107

Sunil Rawan, 70Sunil Sharma, 57Surabhi Tiwari, 98Sushil Kumar, 99Swati Mishra, 91Syed

Abbas, 62

Talat Sultana and Arshad Khan, 17Tejas M. Gondhalekar1 and S. K. Panigrahi2, 87Thomas Goetz , 1Tripti Midha, 59

UMESH, 35URVASHI ARORA AND N.SUKAVANAM, 23Urvashi Gupta , 88

V. K. Chaurasiya, 73V. K. Srivastav1 R. K. Singh1, 87V. K. Srivastav; Aditya Priyanka; Abhishek

Kumar; Shudhanshu Kumar; Anand Raj.,

27V. R. Lakshmi Gorty, 19V. Shanthi, 67V.Divakar1 and S. K. PanigrahiR2, 94V.K. Srivastav1, 84, 85, 99Veena Sharma , 32Verasis Kour, 82Vikas Kumar and Nitu Kumari , 102Vishal Pradhan1, 89Vishnu Narayan Mishra, 45, 46

Wasim Saliha, 89Wolfgang Seemannb, 84

Y. S. Valaulikar , 41Y.K.Singh1 and S. K. Panigrahi2 , 90Yadav Ombir Singh∗, 95Yasuhiro takeuchib, 96

ZAHEER ABBAS, 23Zaheer Abbasb and Mohd Qasimb, 101

108

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