book of abstracts th workshop on current problems in physicswcpp/wcpp13/abstracts.pdf · 2013. 9....

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BOOK OF ABSTRACTS

6th Workshop on Current Problems in Physics:

Zielona Góra - Lviv

23 - 25 September 2013, Zielona Góra, Poland

2

The Workshop on Current Problems in Physics

2013 (WCPP'13) is already the sixth in a series of

meetings which represent annual forum for the

Polish and Ukrainian physicists community to

present their latest scientific results. Usually, the

meetings are attended by representatives of other

countries, too. An important feature of the

conference is the possibility for young scientists

to present their research results and interact

with the more experienced colleagues from other

countries. The Workshop will be held in Zielona

Góra from 23 to 25 September 2013.

The conference is organized under the auspices of

His Magnificence Rector of the University of

Zielona Góra, professor Tadeusz Kuczyński.

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Conference programme

Monday 23.09.2013

Arrival of participants

Tuesday 24.09.2013

9:00-9:10 Opening ceremony

Session I – Chairman: G. Melikidze

special session on integrable systems to celebrate

professor Stanislaw Kasperczuk 70th birthday

9:10-09:30 S. Kasperczuk

09:30-10:00 M. Błaszak

10:00-10:20 A. Maciejewski

10:20-10:40 M. Przybylska

10:40-10:50 Coffee Break

10:50-11:10 P. Rozmej

11:10-11:20 W. Szumiński

Session II – Chairman: V.M. Tkachuk

selected aspects of classical and quantum theory

11:20-11:40 A. Duviryak

11:40-12:00 S. Kondej

12:00-12:20 P. Jachimowicz

12:20-12:40 M. Stetsko

12:40:13:00 A. Kuzmak

13:00-14:00 Lunch

Session III – Chairman: W. Leoński

quantum optics, quantum correlations, quantum information

14:00-14:30 R. Tanaś

14:30-14:50 V. Cao Long

14:50-15:10 A. Kowalewska-Kudłaszyk

15:10-15:30 J. K. Kalaga

15:30-15:45 T. D. Nguyen


Session IV – Chairman: K. Urbanowski symmetry, fundamental interactions, cosmology

16:00-16:30 V. M. Tkachuk

16:30-16:50 Yu. Yaremko

16:50-17:20 A. Szary

17:20-17:40 K. Raczyńska

19:00_____ dinner under Braniborska tower observatory

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Wednesday 25.09.2013

Session I – Chairman: K.W. Wojciechowski

medical applications

9:00-9:20 J. Piskorski

9:20-9:40 S. Żurek

9:40-10:10 G. Garbacz

Session II – Chairman: J. Piskorski

nanotechnology, nanomedicine

10:10-10:25 B. Zapotoczny

10:25-10:40 A. Timoszyk

10:40-10:55 A. Defort

10:55-11:10 J. Mleczko


Session III – Chairman: A. Drzewiński

metamaterials, mechanical properties

11:25-11:55 K.W. Wojciechowski

11:55-12:15 J. Narojczyk

Session IV – Chairman: V. Cao Long spectroscopy, luminescence, materials

12:15-12:45 N. Guskos

12:45-13:05 A. Rovenchak

13:05:13:20 G. Panochko

13:20-14:20 Lunch

Session V – Chairman: V. Cao Long

statistical physics methods, models

14:20-14:35 T. Masłowski

14:35-14:50 M. Zubaszewska

14:50-15:05 A. Durajski

15:05-15:25 M. Jarosik


15:45-16:00 B. Brzostowski

16:00-16:15 M. Wojciechowski

16:15-16:30 D. Woźniak

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ABSTRACTS

6

Classical and quantum Stackel systems

M. Błaszak

Faculty of Physics, A. Mickiewicz University,

Umultowska 85, 61-614 Poznań, Poland

In the talk is presented a theory of separability for a class of Liouville integrable

hamiltonian systems with all constants of motion quadratic in momenta. Then, the so

called minimal quantization procedure is applied and is analyzed the problem of quantum

separability of such constructed quantum systems.

7

Chain-model approximations for the Cr8

molecular magnet. DFT approach.

B. Brzostowski1, M. Wojciechowski

1, D. M. Tomecka

2,

G. Kamieniarz2, V. Bellini

3,4, F. Troiani

3, F. Manghi

3,

M. Affronte3

1 Institute of Physics, University of Zielona Góra,

65-516 Zielona Góra, Poland;

2 Faculty of Physics, A. Mickiewicz University,

61-614 Poznań, Poland;

3 CNR-INFM-National Research Center on nanoStructures

and bioSystems at Surfaces (S3),

Via Campi 213/A, 41100 Modena, Italy;

4 Istituto di Struttura della Materia (ISM) - Consiglio Nazionale delle Ricerche (CNR),

I-34149, Trieste, Italy;

We present a density functional theory (DFT) study of the electronic and magnetic

properties of the Cr8 molecular ring. The all-electron linearized augmented plane wave

method (LAPW) implemented in the Wien2k package and pseudopotential method

implemented in Siesta package are used to calculate the electronic states, exchange

coupling parameters of an infinite chain model system of Cr88. We demonstrate how, under

opportune modifications to the ring cycle structure, different one-dimensional chain models

can be devised, with the capability of mimicking with good approximation the electronic

and magnetic properties of the original Cr8 molecule. Such models offer an unique

opportunity, in virtue of the reduced computational effort, to carry out extensive

investigations of a whole set of molecules belonging to the Cr-based molecular rings

family.

8

Application of functionalized iron oxide

nanoparticles to determine catecholamines

A. Defort, J. Nowak-Jary, J. J. Kozioł

Faculty of Biological Sciences, University of Zielona Góra,

ul. Szafrana 1, 65-516 Zielona Góra, Poland

Magnetic iron oxide nanoparticles provide attractive possibilities in biomedical

application such cell labeling and separation, target drug delivery and biosensor [1,2].

These applications require magnetic nanoparticles to be well-dispersed in liquid media,

chemically stable and uniform in size. Due to the magnetic dipolar attraction, unmodified

magnetite nanoparticles incline to aggregate into clusters and inhibit the advantage of the

specific properties by single-domain. The aggregation associated with magnetite

nanoparticles can be avoided by creating an electrostatic double layer using a surfactant

steric stabilizer or silica coating [3]. In this presentation magnetic nanoparticles (Fe3O4)

are prepared by co-precipitation method and modify by silica using Stöber process [4].

The applications of arylboronic acids as catecholamine sensors are broad, because they

are small and exible molecules. They can form fast and reversible cyclic esters with

compounds containing diol moieties in aqueous media. Arylboronic acids potentially

offer non-invasive continuous blood glucose monitoring, in some cases without the need

for reference measurements. The information can be provided by attachment of the

boronic acid moiety (for example Alizarine S) to a proper reporting unit, which undergoes

a significant change in fluorescence emission [5]. This presentation will focus on the

synthesis of magnetic iron oxide nanoparticles of arylboronic acids and their important

properties which eventually will make them suitable as key elements in future non-

invasive continuous catecholamine sensors such an epinephrine, norepinephrine or sialic

acid [6].

References

[1] J. Chen, Y. Miao, N. He, X. Wu, S. Li, Biotechnology Advances 22 (2004) 505.

[2] J. Lee, Y. Lee, J.K. Youn, Biocatalysts. Small 4 143.

[3] Z. Lu, G. Wang, J. Zhuang, W. Yang, Colloids and Surfaces A: Physicochem. Eng.

Aspects (2006) 140.

[4] Z.Y. Lu, et al., Colloids and Surfaces A: Physicochem. Eng. Aspects 317 (2008) 450.

[5] G. Springsteen, B. Wang, Tetrahedron 58 (2002) 5291.

[6] M. Perry, Q. Li, R.T. Kennedy, Analytica Chimica Acta 653 (2009) 1.

9

The high-pressure superconductivity in hydrogen-

rich compounds

A. Durajski

Institute of Physics, Częstochowa University of Technology,

Ave. Armii Krajowej 19, 42-200 Częstochowa, Poland

Solid molecular hydrogen and the possibility of its metallization has fascinated condensed

matter researchers since the prediction of the pressure required for metallization was

proposed by Wigner and Huntington in 1935 [1],[2]. The possibility of forming metallic

hydrogen using hydrogenated materials was subsequently studied and discussed [3]. The

recent ab initio calculations suggest that the superconducting state in metallic hydrogen-

rich compounds under the pressure has the critical temperatures much higher than the

boiling point of liquid nitrogen. For this reason, the relevant thermodynamic parameters of

the superconducting state in SiH4, Si2H6, SiH4(H2)2, GeH4, GaH4(H2)2 and CaH6, have been

determined within the framework of the Eliashberg theory. It has been shown that for a

wide range of the Coulomb pseudopotential the values of the ratio of the energy

gap to the critical temperature ( ), the ratio of the specific heat jump to the

heat in the normal state ( ) and the ratio connected with the

thermodynamic critical field ( ) significantly exceed the values predicted

by the BCS theory [4], [5]. This fact is connected with strong coupling electron-phonon

interaction and the retardation effects existing in the analyzed systems.

References

[1] E. Wigner, H.B. Huntington, J. Chem. Phys. 3, 764 (1935).

[2] N. W. Ashcroft, Phys. Rev. Lett, 21, 1748 (1968).

[3] N. W. Ashcroft, Phys. Rev. Lett, 92, 187002 (2004).

[4] R. Szczęśniak, A.P. Durajski, Solid State Conunun. 153, 26 (2013).

[5] R. Szczęśniak, A.P. Durajski, J. Phys. Chem. Solids 74, 641 (2013).

10

Dificulties in prediction of the oral drug delivery -

about differences between theory and reality form

pharmaceutical point of view.

G. Garbacz1, W. Weitschies

2

1 Physiolution GmbH,

Walther Rathenau Strasse 49 a, 17489 Greifswald, Germany

2 Center of Drug Absorption and Transport,

Felix-Hausdorff-Strasse 3, 17487 Greifswald, Germany

A reliable estimation of drug delivery behavior is a prerequisite for rational and efficient

development of dosage forms. It is frequently believed that this challenging goal may be

achieved using standard test methods as well as different mathematical models describing

the drug delivery processes. Unfortunately, the clinical data often demonstrate insufficient

predictive power of the available models. The main reasons thereof are the lack of the good

understanding of the gastro-intestinal (GI) physiology as well as the variability on the

conditions on the drug absorption site. Interestingly, both factors cannot be realistically

simulated using compendial test equipment for dissolution testing. We will briefly

introduce the selected aspects of the human GI physiology, evolution and goals of

dissolution testing as well as the development and use of test devices that are intended to

simulate the GI conditions. The data will be discussed in the light of the test results and

experiences obtained with the new dissolution stress test device that simulates physic-

chemical and mechanical conditions of the GI passage of dosage forms developed by our

group.

11

Magnetic resonance study of co-modified (Co,N)-TiO2

N. Guskos1,2

, S. Glenis1, G. Zolnierkiwicz

2, A. Guskos

2, J. Typek

2, P.

Berczynski2, D. Dolat

3, B. Grzmil

3, B. Ohtani

4 and A.W. Morawski

3

1Department of Solid State Physics, University of Athens, Panepistimioupolis,

GR-157 84 Athens, Greece

2Department of Physics, West Pomeranian University of Technology,

Al. Piastow 48, 70-311 Szczecin, Poland

3Department of Chemical and Environmental Engineering,

West Pomeranian University of Technology,

Al. Piastow 17, 70-310 Szczecin, Poland

4Catalysis Research Center, Hokkaido University, Sapporo 001-0021 Japan

The nCo,N-TiO2 (n=1, 5 and 10 wt.%) nanocomposites have been prepared by comodification of commercial

amorphous titanium dioxide via impregnation followed by calcination at 800°C in ammonia atmosphere. The

photocatalytic properties strongly depend on concentration of cobalt ions of the obtained samples. The magnetic

properties of (Co,N)-TiO2 nanocomposites have been investigated by FMR/EPR spectroscopy in 4-290 K range

(Fig. 1). The intense FMR spectra of cobalt nanoparticle agglomerates were dominant in the whole temperature

range for all samples. In addition, intense EPR spectra of trivalent titanium ions were recorded for sample with

n=1% (Fig.1) while for other two samples two orders of magnitude smaller intensities of spectra were

registered. Above a certain treshhold concentration of Ti3+

a drastic deterioration of the photocatalytic properties

is observed, and sample with n = 1% is the worst in this respect.

0 2000 4000 6000 8000

-80000

-60000

-40000

-20000

0

20000

40000

60000

d"/

dH

[A

rb. u

nits]

Magnetic field H [G]

T=4 K

T=290 K

T=10 KTi3+

Fig. Temperature dependence of the FMR/EPR Spectra of (1%Co,N)-TiO2.

12

Pairing mechanism for the high-Tc

superconductivity: symmetries and

thermodynamic properties

M. Jarosik, R. Szczęśniak

Institute of Physics, Częstochowa University of Technology,

Ave. Armii Krajowej 19, 42-200 Częstochowa, Poland

The pairing mechanism for the high-Tc superconductors based on the electron-phonon

(EPH) and electron-electron-phonon (EEPH) interactions has been presented. On the fold

mean-field level, it has been proven, that the obtained s-wave model supplements the

predictions based on the BCS van Hove scenario. In particular: (i) For strong EEPH

coupling and T < Tc the energy gap () is very weak temperature dependent; up to the

critical temperature extends into the anomalous normal state to the Nemst temperature.

(ii) The model explains well the experimental dependence of the ratio R 2(0)/kTc on

doping for the reported superconductors In the terms of the few fundamental parameters.

In the presented paper, the properties of the d-wave superconducting state in the two-

dimensional system have been also studied. The obtained results, like for s-wave, have

shown the energy gap amplitude crossover from the BCS to non-BCS behaviour, as the

value of the EEPH potential increases. However, for T > Tc the energy gap amplitude

extends into the anomalous normal state to the pseudogap temperature. Finally, it has been

presented that the anisotropic model explains the dependence of the ratio R on doping for

the considered superconductors.

13

Quantum chaos of nonlinear oscillator system

and Kullback - Leibler quantum divergence

J. K. Kalaga1, A. Kowalewska-Kudłaszyk

2,

W. Leoński1, V. Cao Long

1

1Quantum Optics and Engineering Division, Institute of Physics,

University of Zielona Góra,

Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland

2Faculty of Physics, A. Mickiewcz University,


We discuss a system containing nonlinear Kerr-like oscillator, driven by a series of ultra

short external pulses. Using Kullback - Leibler quantum divergence K[q|] we define linear

and nonlinear quantum divergences. We analyze behavior of these divergences for various

values of the parameters determining character of system's dynamics and show that they

can be applied as witnesses of quantum-chaotic evolution of the system. We show that the

nonlinear divergence is more sensitive for the quantum-chaotic behavior than its linear

counterpart.

14

Double line interaction

Sylwia Kondej

Institute of Physics, University of Zielona Góra,

ul. Szafrana 4a, 65246 Zielona Góra, Poland

The talk is addressed to the problem of, so called, leaky quantum wires which can be

modelled by delta potential supported by two parallel straight lines. We discuss spectral

properties of such a system, for example, we formulate conditions guaranteeing existence

of discrete eigenvalues. Furthermore, we show that for a certain class of systems with

a mirror symmetry the embedded eigenvalues phenomena holds.

The talk is based on a common work with David Krejčiřík

15

Kerr coupler operating on Werner-like states ―

entanglement creation and evolution

A. Kowalewska-Kudłaszyk1, W. Leoński

2

1 Faculty of Physics, A. Mickiewcz University,


2 Quantum Optics and Engineering Division, Institute of Physics,



We consider a problem of creation of pure entangled states in two-qubit space from initial

Werner or Werner-like state by Nonlinear Quantum Scissors (NQS). NQS systems are

based on Kerr-like oscillators and can operate in optical domain, but there are also

examples of Kerr-like Hamiltonians used in condensed matter systems. NQS are able,

under some assumptions, to restrict substantially the number of states involved in the

dynamics and therefore are called quantum scissors.

Such state reduction can lead to generation of maximally, or almost maximally entangled

states. It was already shown that for two Kerr-like oscillators the system with various types

of interactions (linear, nonlinear and parametric) behave like two-qubit, qutrit-qubit or two-

qutrit system. It was also shown that we are able to generate entangled states from initial

number states within Kerr-couplers.

At present we would like to show that there is also a possibility of creating pure entangled

states even though the system is initially in incoherent combination of a completely mixed

state and a maximally entangled pure state (Werner or Werner-like states). We consider the

influence of various types of damping processes on entanglement creation. The analytical

conditions for obtaining different types of entanglement decay: asymptotic or decay in

finite time and its possible revival after a significantly long time period, are presented.

16

Preparation of quantum states of two spins-

in the Schmidt decomposition

A. R. Kuzmak

Department for Theoretical Physics, Ivan Franko National University of Lviv,

12 Drahomanov St., Lviv, UA-79005, Ukraine

We consider a system of two spins and their interaction is represented by isotropic

Heisenberg Hamiltonian. Our aim is to create arbitrary quantum state of two spins having

started with | state. We can easily prepare this state because it is an eigenvector of the

system of two spins which is located in the magnetic field directed along the z-axis. The

method which we suggest consist of two steps. At the first step, using the evolution

operator with isotropic Heisenberg Hamiltonian we obtain the state which depends on time

of evolution. At the second step, the spins are driven individually by magnetic pulse fields.

Finally, we obtain arbitrary state of two qubits which can be easily represented in the

Schmidt decomposition. This state is defined by time of evolution and parameters which

are determined strength and direction of magnetic fields.

We propose to realize this method on the physical system of atoms which have a nuclear

spin I of 1/2 and one valence electron. Therefore, these systems can be considered as a two-

qubit systems. Factorized initial state | state can be easily prepared for these systems

[1]. We consider the system of 31

P donor in silicon because it is system with high degree of

quantum coherence, and states of this system are measured with high fidelity [1].

References

[1] J.J. Pla et al., Nature 496 (2013) 334.

17

EIT in Lambda configuration: multilevel model

and model with structured continua

V. Cao Long, W. Leoński

Quantum Optics and Engineering Division, Institute of Physics,



We present some new results concerning so-called electromagnetically induced

transparency (EIT) [1] in Lambda scheme. We discuss two different models. One of them

involves discrete levels [2,3] , whereas the second one contains structured continua [4].

Applying multilevel model, we reconstruct multi-peak spectra registered by Warsaw Group

in a sample of cold 85Rb atoms trapped in MOT. Moreover, we show that the nature of the

spectra exhibiting several transparency windows can be explained on a basis of the second

model, that with several autoionizing states, or equivalently, with Fano structured continua.

References

[1] K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen Huy, J. Szonert,

Comp. Meth. Sci. Technol. Special Issue 2 (2010) 131.

[2] K. Kowalski, V. Cao Long, H. Nguyen Viet, S. Gateva, M. Głódź, J. Szonert,

J. Non-Cryst. Solids 355 (2009) 1295.

[3] A. Żaba, V. Cao Long, M. Głódź, E. Paul-Kwiek, K. Kowalski, J. Szonert, D. Woźniak

and S. Gateva Ukr. J. Phys. 14 (2013) 138.

[4] T. Bui Dinh, W. Leoński, V. Cao Long and J. Peřina Jr. Optica Applicata (2013) in print.

18

Necessary conditions for integrability of algebraic

Hamiltonian systems

A.J. Maciejewski

Institute of Astronomy, University of Zielona Góra, Poland

Necessary conditions for integrability of algebraic Hamiltonian systems Abstract: Systems

with Hamiltonian functions algebraic in coordinates and momenta are considered. For such

systems the right hand sides of Hamilton equations typically are not single valued. This is

why the Ziglin or the Morales-Ramis theory cannot be applied directly to study their

integrability. The main idea is following. One can extend the phase space of the system in

such a way that the extended system is meromorphic and Hamiltonian with respect to a

certain degenerated Poisson structure. Although the proposed construction is not unique it

allows to obtain necessary conditions for the integrability in the framework of differential

Galois theory. Applying this approach necessary conditions for integrability of algebraic

homogeneous potentials of rational homogeneity degree are obtained.

19

Magnetic nanoparticles and antigen-antibody

reactions; can magnetic nanoparticles modify

antigen-gen-antibody reaction

J. Mleczko

Institute of Genetics and Microbiology, Uniwersity of Wrocław,

ul. Przybyszewskiego 63/7, 51-148 Wrocław

Magnetic nanoparticles in water solution under external magnetic field modify/change the

local (near their surface) value of pH and temperature and do not necessarily influence on

their value in a bulk solution. Antigen-antibody reactions constitue important group of

biological/biochemical reactions in human/animal organisms and commonly are used in

biomedical tests. Efficiency of antigen antibody reactions significantly depend on pH and

temperature. The magnetic nanoparticles exhibit very low toxicity and because of their

pliability on control by magnetic field they are becoming useful for experimental and

biomedical applications. Magnetic nanopartices could open up possibility of local lowering

or increasing (controlling) of dynamics and efficiency of antigen-antibody reactions in

human body.

20

Partial auxeticity of soft polydisperse dimers at

zero temperature.

J. W. Narojczyk, K. W. Wojciechowski, M. Kowalik

Institute of Molecular Physics Polish Academy of Sciences,

Mariana Smoluchowskiego 17, 60-179 Poznań, Poland

Influence of atomic size polydispersity on Poisson's ratio [1] of cubic systems consisted of

di-atomic molecules (dimers) is studied by computer simulation. The simulations,

performed in the NV T ensemble, are restricted to the static case, i.e. to the zero temperature

(T = 0K). The positions of the dimer centres of mass and their orientations are aperiodic but

the constituting atoms form the (perfect or slightly distorted in the polydisperse case) f.c.c.

lattice. Such a phase, called the degenerate crystal (DC) [2], is illustrated in Figure 1.

a) b)

Figure 1: Example of microscopic structure of DC polydisperse dimer system. The structure

shown consists of 432 dimers and has the polydispersity parameter δ equal to 3%. In (a) the

atoms are drawn in the shades of gray, indicating their size relative to other atoms. The

darker the color, the larger the atomic diameter. The gray cube indicates the periodic box.

In (b) dimer center positions and orientations for the structure in (a) are represented by

points and line segments connecting the atomic centers.

Size polydispersity concerns all atoms in the model. Interactions are short-ranged -

restricted to nearest-neighbouring atoms, i.e. those sharing a common wall of their Voronoi

polyhedra. The atoms interact with soft, repulsive n-inverse-power potential.

Poisson's ratio is the negative ratio of the relative change in the transverse dimension to the

relative change in the longitudinal dimension when infinitesimal change of the longitudinal

stress is applied [1]. For most commonly used materials, the Poisson's ratio is positive. This

means that when stretched (compressed) longitudinally, such a material will shrink

(expand) in transverse dimensions. There are materials however, which behave contrary.

They expand (shrink) transversely when stretched (compressed) longitudinally. They are

called auxetics and for such unusual materials the Poisson's ratio is negative. In the case of

anisotropic materials, Poisson's ratio (ναβ) may depend on both the longitudinal (α) and

transversal (β) direction. It is known that, in general, the disorder of crystalline lattice leads

to the increase of average Poisson's ratio, both in the case of isotropic [3-6] and anisotropic

[7-9] systems. However, in the case of cubic systems a direction exists (β = [1 0]) for

which, polydispersity has the opposite effect, when the sample is deformed in α = [110]. In

this case it has been found, that increasing polydispersity leads to a decrease of the

Poisson's ratio [8, 9], down to negative values. For unconstrained, polydisperse cubic

21

system (f.c.c. spheres), the decrease was insignificant [8], and negligible in the limit of hard

interactions. Negative Poisson's ratio was observed for a range of soft interactions. For

f.c.c. dimers, the increasing polydispersity decreases significantly, down to -0.8,

in the range of hard interactions [9]. Various models of dimers were studied [10] and the

observed effect was found to be robust with respect to model details. Hence, this effect can

be of interest from practical applications perspective.

Acknowledgments

Part of the simulations was performed at Pozna_n Supercomputing and Networking Center (PCSS).

References

[1] L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Pergamon Press, London, 1986.

[2] K. W. Wojciechowski, D. Frenkel and A. C. Brańka, Non-periodic solid phase in a two

dimensional hard-dimer system, Physical Review Letters, 66:3168-3171, 1991.

[3] K. W. Wojciechowski and J. Narojczyk, Inuence of disorder on the Poisson's ratio of

static solids in two dimensions, Reviews on Advanced Materials Science, 12:120-126,

2006.

[4] J. W. Narojczyk and K. W. Wojciechowski, Computer simulation of the Poisson's ratio

of soft polydisperse discs at zero temperature, Materials Science (Poland), 24:921-927,

2006.

[5] J. W. Narojczyk and K. W. Wojciechowski, Elastic properties of two-dimensional soft

discs of various diameters at zero temperature, Journal of Non-Crystalline Solids,

352:4292-4298, 2006.

[6] J. W. Narojczyk and K. W. Wojciechowski, Elasticity of periodic and aperiodic

structures of polydisperse dimers in two dimensions at zero temperature, Physica Status

Solids (b), 245:2463-2468, 2008.

[7] J. W. Narojczyk, A. Alderson, A.R. Imre, F. Scarpa, and K. W. Wojciechowski,

Negative Poisson's ratio behavior in the planar model of asymmetric trimers at zero

temperature, Journal of Non-Crystalline Solids, 354:4242-4248, 2008.

[8] J. W. Narojczyk and K. W. Wojciechowski, Elastic properties of the fcc crystals of soft

spheres with size dispersion at zero temperature, Physica Status Solidi (b), 245:606-613,

2008.

[9] J. W. Narojczyk and K. W. Wojciechowski, Elastic properties of degenerate f.c.c.

crystal of polydisperse soft dimers at zero temperature, Journal of Non-Crystalline

Solids, 356:2026-2032, 2010.

[10] J. W. Narojczyk, K. W. Wojciechowski and M. Kowalik, Partially auxetic properties

of polydisperse soft dimer systems at zero temperature, Journal of Chemical Physics,

submitted.

22

Maximally entangled states generation in kicked

Kerr-like coupler models

T. D. Nguyen, W. Leoński, V. Cao Long,

Quantum Optics and Engineering Division, Institute of Physics,



We discuss a system involving Kerr-like nonlinear coupler [1] excited by a series of ultra-

short external coherent pulses. We show that despite the simplicity of the model, it can

behave in non-trivial way. In particular, we discuss and compare two cases of kicked

nonlinear coupler's model (with and without crosscoupling), showing that the quantum

evolution of the system remains closed within a two-qubit Hilbert space. Hence, the system

can be treated as nonlinear quantum scissors [2]. Moreover, maximally entangled Bell

states can be generated during the system's evolution similarly as in [3]. We show that

despite the presence of damping processes, some amount of entanglement can survive in

the system.

References

[1] N. Korolkova, J. Peřina, Quantum statistics and dynamics of Kerr nonlinear couplers,

Opt. Commun. 136, 135-149 (1997).

[2] W. Leoński, A. Kowalewska-Kudłaszyk, Quantum Scissors-Finite- Dimensional States

Engineering, Progr. Opt. 56, 131-185 (2011).

[3] A. Miranowicz, W. Leoński, Two-mode optical state truncation and generation of maximally

entangled states in pumped nonlinear couplers, J. Phys. B: At. Mol. Opt. Phys. 39, 1683-1700

(2006).

23

Parameters of scalar field dark energy in the light

of Planck 2013 results

B. Novosyadlyj, O. Sergijenko

Astronomical Observatory of Ivan Franko National University of Lviv, Ukraine

The Planck 2013 results [1] together with data on baryon acoustic oscillations (BAO) [2-4]

and distance moduli of SNe Ia [5,6] are used for determination of best-fit parameters and

their confidential ranges for cosmological model with cold dark matter and scalar field dark

energy. The scalar field (xi) defined by the canonical Lagrangian

and generalized linear barotropic equation of state pde = 2

qde+C = wdeqde presents the

dynamical quintessence or phantom dark energy depending on the current value of equation

of state parameter wde and its value in the early or future Universe. The best-fit values of

scalar field dark energy parameters and their confidential ranges, obtained using Markov

chain Monte Carlo method and data [1-6], give the possibility to state that the dark energy

is phantom at confidential level > 1. The confidential level of existence of dark energy of

any type is very high: > 10.

References

[1] Planck collaboration, arXiv:1303.5075.

[2] F. Beutler, C. Blake, M. Colless et al., MNRAS 416 (2011) 3017 .

[3] N. Padmanabhan N., X. Xu, D..J. Eisenstein et al., MNRAS 427 (20120) 2132.

[4] L. Anderson, E. Aubourg, S. Bailey et al., MNRAS 427 (2012) 3435.

[5] M. Sullivan, J. Guy, A. Conley et al., Astrophys. ,/. 737 (2011) 102.

[6] X. Suzuki, D. Rubin, C. Lidman. et al., Astrophys. ,/. 746 ( 2012) 85.

24

Investigation of the local structure of boron

andlithium in some borate compunds by MAS

NMR spectroscopy

B. V. Padlyak1,2

, N. A. Sergeev3, M. Olszewski

3

1Division of Spectroscopy of Functional Materials,


Szafrana Str. 4a, 65-516 Zielona Góra, Poland

2 2Sector of Spectroscopy, Institute of Physical Optics,

Dragomanova Str. 23, 79-005 Lviv, Ukraine

3 Institute of Physics, University of Szczecin,

Wielkopolska Str. 15, 70-451 Szczecin, Poland

The magic angle spinning nuclear magnetic resonance (MAS NMR) spectra of the 11

B, and 7Li isotopes in a series of un-doped glassy and crystalline borate compounds with Li2B4O7,

LiB3O5, LiCaBO3, LiKB4O7 and SrB4O7 chemical compositions were investigated and

analysed. Investigated borate glasses of high optical quality and chemical purity were

obtained from corresponding polycrystalline compounds using standard glass synthesis

according to [1]. The borate single crystals were obtained by Czochralski method. The main

structural units (BO3, BO4, and LiO4 atomic groups) and their proportions in the Li2B4O7,

LiB3O5, LiCaBO3, LiKB4O7 and SrB4O7 glasses and crystals have been established based

on the comparative analysis of the 11

B and 7Li MAS NMR experimental spectra in them.

The obtained results of MAS NMR spectroscopy show good correlation with X-ray

diffraction data for local structure of the cationic sites in borate glasses and crystals with

same chemical compositions [1].

References

[1] B.V. Padlyak, S.I. Mudry, Y.O. Kulyk, A. Drzewiecki, V.T. Adamiv, Y.V. Burak, I.M. Teslyuk,

Mater. Sci.-Poland 30 (2012) 264.

25

The 3He impurity states in 4He

I. Vakarchuk1, G. Panochko

2

1 Department for Theoretical Physics, Ivan Franko National University of Lviv, Ukraine

2 College of Natural Sciences, Ivan Franko National University of Lviv, Ukraine

We consider a set of spinless Bose-particles of mass m with coordinates r1, ... , rN and an

impurity atom of mass M with coordinate r. For the system of “liquid helium + impurity 3He” full- and one-particle density matrices for all temperatures by means of the method of

collective variables in the approximation of pair correlations are found. The contribution to

the full density matrix that takes into account the effect of impurities on the state of the

system at finite temperatures is calculated. At low temperatures this contribution is

considered as a correction to the ground-state energy of the system. The input data for the

numerical calculations are the Fourier coefficients of the two-particle interaction potential

between liquid and impurity which are written via the structure factor S(k) of liquid 4He

obtained from X-rays scattering measurements. The estimation of the effective mass of the

impurity is made.

26

Heart Rate Asymmetry - mathematical,

physiological and medical aspects

J. Piskorski


ul. Szafrana 4a, 65-516 Zielona Góra, Poland

Heart rate asymmetry (HRA) is a newly discovered phenomenon by which the behavior of

decelerations and accelerations of heart rate is different. The variance based HRA states

that the contribution of decelerations to short-term heart rate variability is greater than that

of accelerations, and that the contribution of accelerations to long-term and total variability

is greater than that of decelerations. The structure based HRA states that the runs of

accelerations are longer than those of decelerations. Both types are closely related and turn

out to be physiologically and medically important.

27

The inhomogeneous Suslov problem

M. Przybylska1, L.C. Garcia-Naranjo

2,

A.J. Maciejewski3, J.C. Marrero

4


ul. Szafrana 4a, 65-516 Zielona Góra, Poland 2

3 Institute of Astronomy, University of Zielona Góra,

ul. Szafrana 4a, 65-516 Zielona Góra, Poland 4

We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous

constraints. We show that if the direction along which the Suslov constraint is enforced is

perpendicular to a principal axis of inertia of the body, then the reduced equations are

integrable and possess an invariant measure. Interestingly, the first integral that permits

integration is transcendental and the density of the invariant measure depends on the

angular velocities. Moreover, in this case, using the so-called alpha-method of Painleve one

can identify when all solutions of the system are single-valued and find their explicit form.

28

Unstable states and cosmology

K. Raczyńska

University of Zielona Góra, Institute of Physics,

ul. Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland.

It is known that space regions with unstable false vacuum may originate during the process

of the creation of the Universe [1]. Some of them can survive up to times when their

survival probability has a non-exponential (an inverse power-like) form [2]. The energy of

these false vacuum states at asymptotically late times, (much latter than the transition time,

when contributions to the survival probability of its exponential and non-exponential parts

are comparable), was analyzed in [3]. We analyze properties of the energy of the unstable

false vacuum states at transition time regions in a given model of the unstable state. We

show that at this time region large and rapid fluctuations of this energy occur.

References

[1] S. Coleman, Phys. Rev. D 15, 2929 (1977); C.G. Callan and S. Coleman, Phys. Rev. D,

16, 1762 (1977).

[2] L. M. Krauss, J. Dent, Phys. Rev. Lett., 100, 171301 (2008).

[3] K. Urbanowski, Phys. Rev. Lett., 107, 209001 (2011).

29

Enumeration of plane partitions with a restricted

number of parts

A. Rovenchak

Department of Theoretical Physics, Ivan Franko National University of Lviv,

12 Drahomanov Str., Lviv, UA-79005, Ukraine

The quantum-statistical approach is used to estimate the number of restricted plane

partitions of an integer n with the number of parts not exceeding some finite N. The analogy

between this number- theoretical problem and the enumeration of microstates of the ideal

two-dimensional Bose-gas is used. The conjectured expression for the number of restricted

plane partitions shows a good agreement between calculated and exact values for

n = 10 20.

30

New nonlinear equations in the shallow water

wave problem

A. Karczewska1, P. Rozmej

2, Ł. Rutkowski

2

1 Faculty of Mathematics, Computer Science and Ekonometrics,



2Faculty of Physics and Astronomy, University of Zielona Góra,


The classical problem of irrotational long waves on the shallow water is reconsidered. The

model of ideal fluid moving under the influence of gravity is used with an appropriate

perturbation approach allowing consistent treatment of small parameters. Additionally to

two standard parameters which control amplitude of waves and shallowness of the system,

respectively, the third one, governing the amplitude of the bottom topography is introduced.

Under the assumption that the bottom does not vary rapidly with the horizontal coordinates

the new nonlinear equations describing shallow water waves are derived. Several different

forms of equations have been obtained for different orders in three small parameters. For

the flat bottom KdV equations of different orders, depending of the order of perturbation

are recovered. Some particular examples of numerical solutions to those equations are

presented, as well.

31

Dirac oscillator and nonrelativistic Snyder-de

Sitter algebra

N.M. Stetsko

Department of Theoretical Physics, Ivan Franko National University of Lviv,

12 Drahomanov Str., Lviv, UA-79005, Ukraine

Three dimensional Dirac oscillator was considered in deformed space obeyed to deformed

commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation

relations give rise to appearance minimal uncertainty in position as well as in momentum.

To derive energy spectrum and wavefunctions of the Dirac oscillator supersymmetric

quantum mechanics and shape invariance technique was applied.

32

Non-dipolar magnetic field at the polar cap of

neutron stars: Two Modes of Inner Acceleration

Region

A. Szary

Institute of Astronomy, University of Zielona Góra,

65-516 Zielona Góra, Poland

The analysis of X-ray observations suggest an ultrastrong surface magnetic field at the

polar cap of pulsars. On the other hand, the temperature of the hot spots is about a few

million Kelvins. Based on these two facts we use the Partially Screened Gap (PSG) model

to describe the Inner Acceleration Region (IAR). The PSG model assumes that the

temperature of the actual polar cap is equal to the so-called critical value, i.e. the

temperature at which the outflow of thermal ions from the surface screens the gap

completely.

We have found that, depending on the conditions above the polar cap, the generation of

high energetic photons in IAR can be caused either by Curvature Radiation (CR) or by

Inverse Compton Scattering (ICS). Completely different properties of both processes result

in two different scenarios of breaking the acceleration gap: the so-called PSG-off mode for

the gap dominated by CR and the PSG-on mode for the gap dominated by ICS. The

existence of two different mechanisms of gap breakdown naturally explains the mode-

changing phenomenon. Different characteristics of plasma generated in the acceleration

region for both processes also explain the pulse nulling phenomenon.

33

Constrained N-body problems

W. Szumiński



We consider a problem of mass points interacting gravitationally whose motion is subjected

to certain holonomic constraints. The motion of points is restricted to certain curves and

surfaces or hyper-surfaces. We illustrate the complicated behaviour of trajectories of these

systems using Poincaré cross sections. For some models we prove their non-integrability

analyzing properties of the differential Galois group of variational equations along certain

particular solutions of considered systems. Also some integrable cases are identified.

34

Quantum correlations in a two-atom system

R. Tanaś

Nonlinear Optics Division, Faculty of Physics, Adam Mickiewicz University,


Quantum correlations in systems composed of several subsystems are presently the subject

of intensive studies because of their crucial role in quantum information processing. It is

important to have reliable measures of quantum correlations to distinguish them from

classical correlations. Recently, various measures of quantum correlations have been

introduced and tested. Probably the most popular of them is quantum entanglement, but

there are other measures, such as quantum discord, geometric quantum discord,

measurement induced disturbance and others. We will shortly discuss some of them. The

simplest multipartite system is a bipartite system composed of two qubits, or two two-level

atoms. In case of two-level atoms interacting with the reservoir of electromagnetic field

modes in the vacuum, the evolution of the system can be described by the well known

Lehmberg-Agarwal master equation. The collective evolution of the two-atom system

depends on two collective parameters: collective damping and dipole-dipole interaction,

which both depend on the interatomic distance. Such a system is a good testing ground for

studying evolution of quantum correlations. Nice feature of the system is the fact that, if the

spontaneous emission is the only relaxation process and the system is not driven, the so

called X-form of the density matrix is preserved during the evolution. Examples of time

evolution of various measures of quantum correlations in the two-atom system for different

initial states of the system will be given to illustrate the similarities and differences between

the most popular measures of quantum correlations.

35

Optical properties of gold nanoparticles

A. Timoszyk, A. Mirończyk and J. J. Kozioł

Faculty of Biological Sciences, University of Zielona Góra,


Gold nanoparticles (GNPs) have been considered as an important area of research due to

their unique properties and their biomedical science including drug delivery, photothermal

therapy, chemical sensing, tissue/tumor imaging and immune-chromatographic

identification of pathogens [1-3]. Due to the recent increasing green chemistry, synthesis of

GNPs must be a nontoxic and environmentally friendly. Biological methods of GNPs

synthesis using plant extract or microorganisms have offered a reliable eco-friendly

alternative to chemical and physical methods [4]. Metal nanoparticles have unique physical

and chemical properties, which are strongly affected by particle size, size distribution,

shape and particle-to-particle interaction [5, 6]. When exited with an electromagnetic field,

GNPs produce an intense absorption attributed to the collective oscillation of electrons on

the particle surface, termed a plasmon resonance [7, 8]. The resonant frequency is high

dependent on particle size, shape and environment. For instance, the sphere geometry of

GNPs allows for control of optical properties in a highly predictive manner, making them a

new class of materials that are capable of tailoring radiation throughout the visible and

infrared wavelength regimes [9]. Because of the mentioned factors above the GNPs could

be characterized by UV-visible spectroscopy, fluorescence spectroscopy, Scanning Electron

Microscopy (SEM) and Different Light Scattering (DLS).

References

[1] L. Du, H. Jiang, X. Liu, E. Wang, Electrochem. Commmun. 9 (2007) 1165.

[2] X. Zhang, S. Yan, R.D. Tyagi, R.Y. Surampalli, Chemosphere 82 (2011) 489.

[3] C.G. Kumar, S.K. Mamidyala, Colloid Surf. B: Biointerfaces 84 (2011) 462.

[4] A.K. Suresh, D.A. Pelletier, W. Wang, M.L. Broich, J-W. Moon, B. Gu, D.P. Allison, D.C. Joy,

T.J. Phelps, M.J. Doktycz, Acta Biomater. 7(5) (2011) 2148.

[5] R. Sardar, A.M. Funston, P. Mulvaney, R.W. Murray, Langmuir 25(24) (2009) 13840.

[6] A. Sànchez-Iglesias, I. Pastoriza-Santos, J. Pérez-Juste, B. Rodríguez- González, F. Javier García

de Abajo, L.M. Liz-Marzán, Advanced Materials 18 (2006) 2529.

[7] T. Ahmad, I.A. Wani, J. Ahmed, O.A. Al-Hartomy, Appl. Nanosci.

DOI 10.1007/s13204-013-0224-y.

[8] W. Rechberger, A. Hohenau, A. Leitner, J.R. Krenn, B. Lamprecht, F.R. Aussenegg,

Optics Commun. 220 (2003) 137.

[9] G. Schatz, K. Shuford, Nanoscape 2(1) (2005) 27

36

Effect of the generalized uncertainty principle on

Galilean and Lorentz transformations

V. M. Tkachuk

Department for Theoretical Physics, Ivan Franko National University of Lviv,


Generalized Uncertainty Principle (GUP) was obtained in string theory and quantum

gravity and suggested the existence of a fundamental minimal length which, as was

established, can be obtained within the deformed Heisenberg algebra. We use the deformed

commutation relations or in classical case (studied in this paper) the deformed Poisson

brackets, which are invariant with respect to the translation in configurational space. We

have found the transformations relating coordinates and times of moving and rest frames of

reference in the space with GUP in the first order over parameter of deformation. For the

non- rclativistic case we find the deformed Galilean transformation which is similar to the

Lorentz one written for Euclidean space with signature (1,1,1,1). The role of the speed of

light here plays some velocity u related to the parameter of deformation, which as we

estimate is many order of magnitude large then the speed of light u 1.2 1022

c.

The coordinates of the rest and moving frames of reference for a relativistic particle in the

space with GUP satisfy the Lorentz transformation with some effective speed of light. We

estimate that the relative deviation of this effective speed of light from c

is ( — e)/c 3.5 10-45

. Finally, note that the influence of GUP on the motion of

particle and the Lorentz transformation in the first order over the parameter of deformation

is hidden in 1/c2 relativistic effects.

37

Two-dimensional models of auxetic foams

K. W. Wojciechowski

Institute of Molecular Physics, Polish Academy of Sciences,

M. Smoluchowskiego 17/19, 60-179 Poznań, Poland

Poisson’s ratio is defined as the negative ratio of the relative change in the transverse

dimension to the relative change in the longitudinal dimension when infinitesimal change

of the longitudinal stress is applied with other components kept fixed [1]. Foams of

negative Poisson’s ratio have been first manufactured by Lakes in 1987 [2]. Materials

exhibiting negative Poisson’s ratio were coined auxetics by Evans [3].

In this lecture, results of computer simulation studies of two simple models of auxetic

foams in two dimensions [4] will be discussed.

Acknowledgments

Part of the simulations was performed at Poznań Supercomputing and Networking Center (PCSS).

References

[1] L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Pergamon Press, London, 1986.

[2] R. S. Lakes, Science 235, 1038 (1987).

[3] K. E. Evans, Endeavour 15, 170 (1991).

[4] A. A. Poźniak, J. Smardzewski, and K. W. Wojciechowski, Smart Materials and

Structures 22, art. 084009 (2013).

38

Theoretical study of magnetic properties of

compounds containing transitional metals

M. Wojciechowski1, B. Brzostowski

1, G. Kamieniarz

2,

A. Bieńko3, J. Mroziński

3

1Institute of Physics, University of Zielona Góra,

ul. Prof. Szafrana 4a, 65-516 Zielona Góra

2Faculty of Physics, A. Mickiewicz University,

ul. Umultowska 85, 61-614 Poznań

3Faculty of Chemistry, University of Wrocław,

ul. F. Joliot-Curie 14, 50-383 Wrocław

Theoretical study of magnetic properties of compounds containing transitional metals

Based on first principles density functional theory (DFT) calculations, we present study of

magnetic compounds. These compounds are (mostly) pentamers containing such

transitional metals as iron, nickel, chromium and copper. Preliminary results for Cu3Cr2 and

Fe2Ni3 structures are presented and discussed. These include spin density maps and energy

values. The 'vanishing' of magnetic moment due to charge transfer between metallic ions is

observed. These results are qualitatively in agreement with empirical results. However full

quantitative explanation of the process requires further study. The computational problems

that arise in the research are also discussed, primarily long computational times which

result from large amount of atoms comprising the structure and methods to overcome them

are presented.

39

Relativistic effects in Penning trap

Yu. Yaremko1, M. Przybylska

2, A.J. Maciejewski

3

1Department for Theoretical Physics, Ivan Franko National University of Lviv,




3 Institute of Astronomy, University of Zielona Góra,

65-516 Zielona Góra, Poland

We are interested in the motion of a classical charge within a processing chamber of a

Penning trap. We examine the relativistic Lagrangian and Hamiltonian dynamics and show

that the radial and axial motions are coupled to each other whenever the special relativity is

taken into account. We demonstrate that for wz ≠ 0 the Hamiltonian system is not integrable

in the Liouville sense in the class of functions meromorphic in coordinates and momenta.

The nonintegrability proof is based on analysis of differential Galois group of variational

equations along a certain particular solution. Also some Poincare sections illustrating

dynamics for physically important values of parameters are shown. In a specific case of

oscillations along the axis of symmetry of quadruple potential the equations of motion are

solved. The solution is expressed in terms of Jacobi elliptic functions. The approximation of

high-energy radial oscillating mode and low-energy axial oscillating mode is analyzed. The

observable relativistic effects such as radiation friction and relativistic cyclotron resonance

are considered.

40

Synthesis of superparamagnetic iron oxide

nanoparticles (SPIONs) in mesoporous silica

materials

B. Zapotoczny1, M.R. Dudek

1, J.J. Kozioł

2, N. Guskos

3,4.



2 Faculty of Biological Sciences, University of Zielona Góra,


3 Department of Solid State Physics, University of Athens,

Panepistimiopolis 15 784, Greece

4 Institute of Physics, West Pomeranian University of Technology,

Al. Piastów 17, 70-310 Szczecin, Poland

Mesoporous silica materials are promising for drug delivery, e.g. [1-3]. Their high surface

areas, tunable pore sizes and volumes give opportunity to carry chemicals, including drugs.

Moreover, high chemical and mechanical stability of silica makes this material perfect as a

template for synthesis inside the pores.

The method of the synthesis of superparamagnetic iron oxide nanoparticles (SPIONS)

directly inside the pores of porous silica will be presented. It is a modification of the

Massart method [4]. According to the diameter of pores, different size of iron oxide

nanoparticles was obtained. The synthesized material has good magnetic properties

(saturation magnetizations 0,7 - 17 emu/g, where the highest saturation magnetizations for

pure iron oxides exhibit magnetite and maghemite: 90–95 emu/g and 60–80 emu/g,

respectively) [5]). Estimated size of gained SPIONs diameter varies from 0.5 to 6 nm.

Samples exhibit superparamagnetic properties in a wide temperature range, both at room

temperature and at 2K.

Porous silica with magnetic nanoparticles have also other advantages. One of them is that

magnetic silica can be controlled by external magnets; another that it can generate magnetic

hyperthermia. Both advantages can be used in drug delivery systems. The recent results on

the use of fabricated magnetic silica as drug delivery nanocapsules will also be mentioned.

Acknowledgements:

The author (B.Z.) is a scholar within Sub-measure 8.2.2 Regional Innovation Strategies, Measure 8.2 Transfer of

knowledge, Priority VIII Regional human resources for the economy Human Capital Operational Programme co-

financed by European Social Fund and state budget.

References

[1] A.B.D. Nandiyanto, S. Kim, F. Iskandar, K. Okuyama Synthesis of spherical mesoporous silica

nanoparticles with nanometer-size controllable pores and outer diameters, Microporous and

Mesoporous Materials 120 (2009) 447–453.

[2] M. Vallet-Regı, F. Balas, M. Colilla, M. Manzano Bioceramics and pharmaceuticals: A

remarkable synergy, Solid State Sciences 9 (2007) 768-776.

[3] A.B.D. Nandiyanto, K. Okuyama Progress in developing spray-drying methods for the production

of controlled morphology particles: From the nanometer to submicrometer size ranges, Advanced

Powder Technology 22 (2011) 1–19.

[4] R. Massart, IEEE T. Magn. 17 (1981) 1247.

[5] B.D. Cullity, C. Graham, Introduction to Magnetic Materials, J. Wiley & Sons, New York, 2008.

41

Critical Casimir forces along the iso-fields

M. Zubaszewska1, A. Maciołek

2,3,4, A. Drzewiński

1



2 Max-Planck-Institut für Intelligente Systeme,

Heisenbergstr. 3, D-70569 Stuttgart, Germany

3 IV Institut für Theoretische Physik, Universität Stuttgart,

Pfaffenwaldring 57, D-70569 Stuttgart, German0079

4 Institute of Physical Chemistry, Polish Academy of Sciences,

Kasprzaka 44/52, PL-01-224 Warsaw, Poland

The present study are related to recent experiments showing that plasma membranes are

near a critical point in the two-dimensional Ising class. Using the numerical density-matrix

renormalization-group technique and the Derjaguin approximation we determine the critical

Casimir force and its potential for two discs. To verify our numerical results we analytically

derive the asymptotic decay law.

The most interesting result of our calculation is a signicant increase in the value of the

critical Casimir force along the iso-elds which lie between the bulk coexistence and and the

capillary condensation line. It may have an important consequences for lipid membranes

with protein inclusions, because most probably the concentration of components of the

membrane is not exactly at its critical value.

Acknowledgements:

The author (M.Z.) is a scholar within Sub-measure 8.2.2 Regional Innovation Strategies, Measure 8.2 Transfer of

knowledge, Priority VIII Regional human resources for the economy Human Capital Operational Programme co-

financed by European Social Fund and state budget. Numerical calculations were performed in WCSS Wrocław

(Poland, grant 82).

42

A characteristic structures in entropy surfaces of

cardiovascular time series estimated by the Norm

Component Matrix Algorithm

S. Żurek

Institute of Physics, University of Zielona Góra, ul. Szafrana 4a, 65-516

Zielona Góra, Poland

Sample entropy (SampEn) is a popular complexity measure in HRV analysis. SampEn is

estimated by fixing the values of the embedding dimension "m" and distance threshold "r"

and traditionally SampEn is calculated with m = 2 and r = 0.2 times the standard deviation

of the series. Attempts to extend the estimates to different (m,r) pairs are hampered by the

high computational burden of the traditional algorithm. However, recently an extremely fast

Norm Component Matrix (NCM) algorithm was proposed for SampEn calculation [1]

which allows analyzing whole ranges of (m,r) values leading to entropy surfaces. This short

lecture presents the first attempts to calculate these surfaces by NCM and discusses their

properties for both synthetic and physiological time series.

References

[1] S. Żurek, P. Guzik, S. Pawlak, M. Kośmider, J. Piskorski, Physica A, 391 (2012) 6601

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