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Motivation
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Classical
10-610-910-15
Quantum Nano/Micro Astro
Motivation
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NLD
10-610-910-15
?Inaccessibility
Astrophysical systems
Inaccessiblesystems
Motivation
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NLD
10-610-910-15
?Inaccessibility
Impossible Experiment
Aim: Dynamical aspects of solar activities
Inaccessiblesystems
Sun
Sunspots
Sunspots: dark spots on the surface of the Sun due to intense magnetic field activity. Durations: typically last for several days, although very large ones may live for several weeks. Sizes: around 200-80000KMFirst observation: 346 BC Gan De (China)
Bangladesh, 2004
Sunspot Number cycle
Source: Wikipedia; Nasa’s prediction
Sunspot Number cycle
http://sidc.oma.be/sunspot-data/
S.No . T N SSN1 1998.25 1665 542 1998.71 1314 693 1998.91 789 754 1999.11 1927 845 1999.41 2716 926 1999.73 1139 1047 1999.94 1404 1118 2000.15 3075 1179 2000.88 1580 11310 2001.40 1315 11011 2002.03 3329 11312 2002.41 3417 10713 2003.03 789 8114 2003.24 1840 7215 2003.90 2633 5416 2005.33 2541 3017 2006.45 2278 1618 2008.39 2108 3.5
Solar wind data
Solar Wind Ion Composition Spectrometer: ACE
Permutation Entropy
Time series: xi ,i =1,2,……,N
Embedded m-dimensional Space:Xi={xi,xi+1,……..,xi+(m-1)}
Arranged in ascending order:Xi={xi+k1,xi+k2,……..,xi+km}
kj=0,….,m-1m! permutation
Each Xi => (0,1,..m-1) symbolsPj: P1 P2 P3 …Pj ; j≤m!
Bandt & Pompe, PRL 88, 174101 (2002)
Permutation Entropy
)!ln(
)ln(!
1
m
PPS
m
j jj
Bandt & Pompe, PRL 88, 174101 (2002)
Application in known dynamical systems
Prasad et al. Pramana J. Phys. 64, 513 (2005)
Suyal, Prasad, Singh, Solar Phys. 276, 407 (2012)
Hysteresis in sloar activity
Suyal, Prasad, Singh, Solar Phys. 276, 407 (2012)
Sunspot Number cycle
Lypunov exponents,dimension,entropy,dynamical variability/correlation
Macek group, CS&F, 8,1601 (1997),9,221(1998)PRE, 62 6496 (2000).
Planet. Space Sci. 56, 550 (2008)Planet. Space Sci. 62, 55(2012)
Solar Phys. 276, 407 (2012)
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NLD
10-610-910-15
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Impossible ExperimentTechnological Limitations
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Nonlinear Dynamics at Micro/Nano scales
Fractal dimension in micro/nano scaleTape peeling
Persson et. al. Euro. Phys. Lett. 92, 46001 (2010)
Fractal Dimension: Nano scale - tape peeling
Persson et. al. Euro. Phys. Lett. 92, 46001 (2010)
df=2.3
AFM image of irradiated and etched PET (Poly ethylene terephthalate) film
Macro to micro/nano
Cell configuration
A & D-Compartments of cellB & C- Platinum electrodes
F- Porous PET film
Dynamics
Phys. Lett A 376, 1915 (2012), Solid State Electronics 225, 751 (2012)
I-V Measurements: Li-Mg
Li & Mg Polymer Gel Electrolyte (PGE)Conductivity: LiPGE > MgPGEpH: LiPGE = MgPGE
Bifurcation diagram
Dynamics
Rawat, Bernamala, Prasad & Chandra, Phys. Lett A 376, 1915 (2012), Solid State Electronics 225, 751 (2012)
Marcos G. E. da Luz and Celia AnteneodoPhil. Trans. R. Soc. A 369, 245 (2011).
Nonlinear dynamics in meso and nano scales
Summary
NLD: in all scalesbut promising in Micro/Nano scales systems because it can be reproduced in Laboratory for applications
Human brain
Onset of a temporal lobe epileptic seizureElectroencephalogram (EEG)
Neurons
Problem 1: Synchronization(Seizure)
Brain Dynamics: ChaoticL. Iasemidis, ASU, Tempe, USA
Prediction/charaterization
Prediction/charaterization
EEG
Thanks