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

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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