Motivation

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Motivation
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Classical
Astro
Nano/Micro
Quantum
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Motivation
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NLD
Inaccessibility
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Astrophysical systems
Inaccessible systems
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Motivation
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NLD
Inaccessibility
Impossible Experiment
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Aim Dynamical aspects of solar activities
Inaccessible systems
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Sun
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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 200-80000KM First
observation 346 BC Gan De (China)
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Bangladesh, 2004
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Sunspot Number cycle
Source Wikipedia Nasas prediction
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Sunspot Number cycle
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http//sidc.oma.be/sunspot-data/
S.No . T N SSN 1
1998.25 1665 54 2 1998.71 1314 69 3
1998.91 789 75 4 1999.11 1927 84 5
1999.41 2716 92 6 1999.73 1139 104 7
1999.94 1404 111 8 2000.15 3075 117 9
2000.88 1580 113 10 2001.40 1315 110 11
2002.03 3329 113 12 2002.41 3417
107 13 2003.03 789 81 14 2003.24 1840
72 15 2003.90 2633 54 16 2005.33 2541
30 17 2006.45 2278 16 18 2008.39 2108
3.5
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Solar wind data
Solar Wind Ion Composition Spectrometer ACE
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Permutation Entropy
Time series xi ,i 1,2,,N
Embedded m-dimensional Space Xixi,xi1,..,xi
(m-1)

• Arranged in ascending order
• Xixik1,xik2,..,xikm
• kj0,.,m-1
• m! permutation
• Each Xi gt (0,1,..m-1) symbols
• Pj P1 P2 P3 Pj jm!

Bandt Pompe, PRL 88, 174101 (2002)
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Permutation Entropy
Bandt Pompe, PRL 88, 174101 (2002)
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Application in known dynamical systems
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Prasad et al. Pramana J. Phys. 64, 513 (2005)
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Suyal, Prasad, Singh, Solar Phys. 276, 407 (2012)
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Hysteresis in sloar activity
Suyal, Prasad, Singh, Solar Phys. 276, 407 (2012)
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Sunspot Number cycle
Lypunov exponents,dimension,entropy, dynamical
variability/correlation Macek group, CSF, 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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Nonlinear Dynamics at Micro/Nano scales
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NLD
Inaccessibility
Technological Limitations
Impossible Experiment
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Fractal dimension in micro/nano scaleTape peeling
Persson et. al. Euro. Phys. Lett. 92, 46001 (2010)
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Fractal Dimension Nano scale - tape peeling
df2.3
Persson et. al. Euro. Phys. Lett. 92, 46001 (2010)
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AFM image of irradiated and etched PET (Poly
ethylene terephthalate) film
Macro to micro/nano
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Cell configuration
A D-Compartments of cell B C- Platinum
electrodes F- Porous PET film
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Dynamics
Phys. Lett A 376, 1915 (2012), Solid State
Electronics 225, 751 (2012)
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I-V Measurements Li-Mg
Li Mg Polymer Gel Electrolyte
(PGE) Conductivity LiPGE gt MgPGE pH LiPGE
MgPGE
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Bifurcation diagram
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Dynamics
Rawat, Bernamala, Prasad Chandra, Phys. Lett A
376, 1915 (2012), Solid State Electronics 225,
751 (2012)
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Nonlinear dynamics in meso and nano scales
Marcos G. E. da Luz and Celia Anteneodo Phil.
Trans. R. Soc. A 369, 245 (2011).
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Summary
NLD in all scales but promising in Micro/Nano
scales systems because it can be reproduced in
Laboratory for applications
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Human brain
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Onset of a temporal lobe epileptic
seizureElectroencephalogram (EEG)
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Neurons
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Problem 1 Synchronization(Seizure)
Brain Dynamics Chaotic L. Iasemidis, ASU, Tempe,
USA
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Prediction/charaterization
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Prediction/charaterization
EEG
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Thanks