deterministic fractals - shahid beheshti...
TRANSCRIPT
![Page 1: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/1.jpg)
Deterministic Fractals
1
Seyed Mohammad Sadegh Movahed !
Department of Physics-Shahid Beheshti University, Tehran IRAN Computational Cosmology Group (CCG-SBU)
School of Physics (IPM), Tehran IRAN www.smovahed.ir
http://faculties.sbu.ac.ir/~movahed !
![Page 2: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/2.jpg)
ObservationsTheoretical Models Measures
Simulations Mak
e ne
w stra
tegy
for
obse
rvat
ion
Data modelling
My road map Model - Observation & Experiments - Statistical analysis
Make new strategy for
theory
![Page 3: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/3.jpg)
Classification of processes
i
x(i
)
250 500 750 1000
-5
0
5
10
15
• Deterministic processes
• Chaotic processes
• Stochastic Processes1) Purely Random processes2) Dependent processes 3) Markov processes
r
Xn
0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
xn+1 = 4rxn (1− xn )x(t + Δt) = x(t) − γ x(t)Δt +η(t) Δt
![Page 4: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/4.jpg)
A brief History on Fractals!
~1700 A.D. Gottfried leibniz
~1872 A.D. Karl Weierstrass
~1904 A.D. Helge von Koch
~1915 A.D. Waclaw Seirpinski
~1951 A.D. H. E. Hurst
~1968 A.D. B. B. Mandelbrot
![Page 5: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/5.jpg)
![Page 6: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/6.jpg)
![Page 7: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/7.jpg)
![Page 8: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/8.jpg)
Cloud structure
http://www.brockmann-consult.de/
![Page 9: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/9.jpg)
Natural time seriesGeophysics time series: temperature, precipitation, water runoff, seismic events, climate dynamics and so on.
Medical and physiological time series: Heartbeat, blood pressure, glucose level, gene expression data and so on.
Astrophysical time series: X-ray and cosmic ray, sunspot, CMB (actually not time series),....
Social and technical time series: Traffic, internet, Finance, language characteristics, chemistry a petroleum, ....
Physics data: surface roughness, spectroscopy, ....
![Page 10: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/10.jpg)
Fractional Gaussian Noise
![Page 11: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/11.jpg)
Fractional Brownian Motion
![Page 12: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/12.jpg)
می خواهیم یاد بگیریم که چگونه می توان چنین اشکالی ترسیم کرد؟
![Page 13: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/13.jpg)
![Page 14: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/14.jpg)
![Page 15: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/15.jpg)
![Page 16: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/16.jpg)
![Page 17: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/17.jpg)
![Page 18: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/18.jpg)
![Page 19: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/19.jpg)
![Page 20: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/20.jpg)
![Page 21: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/21.jpg)
![Page 22: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/22.jpg)
See Computational Physics, Rubin H. Landau et. al., 2011
![Page 23: Deterministic Fractals - Shahid Beheshti Universityfaculties.sbu.ac.ir/.../deterministic_fractals.pdf · 2015-10-28 · Deterministic Fractals 1 Seyed Mohammad Sadegh Movahed!! Department](https://reader035.vdocuments.mx/reader035/viewer/2022080717/5f7826f8dfa39c7cee5f384d/html5/thumbnails/23.jpg)
با تشکر
برای اطالعات بیشتر می توانید به بخش Talk & Presentation یا!بخش course/computational physics منزلگاهم به آدرس:!
!http://faculties.sbu.ac.ir/~movahed مراجعه کنید