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Motivation. ...10 -4 …. …10 7 …. 10 -15. 10 -9. 10 -6. Classical. Astro. Nano/Micro. Quantum. Motivation. 10 -9. 10 -6. ...10 -4 …. …10 7 …. 10 -15. ?. NLD. Inaccessibility. Astrophysical systems. Inaccessible systems. Motivation. 10 -9. 10 -6. ...10 -4 …. …10 7 ….

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Motivation
Motivation

...10-4…

…107….

10-15

10-9

10-6

Classical

Astro

Nano/Micro

Quantum


Motivation1
Motivation

10-9

10-6

...10-4…

…107….

10-15

?

NLD

Inaccessibility


Astrophysical systems
Astrophysical systems

Inaccessible

systems


Motivation2
Motivation

10-9

10-6

...10-4…

…107….

10-15

?

NLD

Inaccessibility

Impossible Experiment




Sunspots
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)



Sunspot number cycle
Sunspot Number cycle

Source: Wikipedia; Nasa’s prediction



Http sidc oma be sunspot data
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


Solar wind data
Solar wind data

Solar Wind Ion Composition Spectrometer: ACE


Permutation entropy
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-1

  • m! permutation

  • Each Xi => (0,1,..m-1) symbols

  • Pj: P1 P2 P3 …Pj ; j≤m!

Bandt & Pompe, PRL 88, 174101 (2002)


Permutation entropy1
Permutation Entropy

Bandt & Pompe, PRL 88, 174101 (2002)





Hysteresis in sloar activity
Hysteresis in sloar activity

Suyal, Prasad, Singh, Solar Phys. 276, 407 (2012)


Sunspot number cycle2
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)


Nonlinear dynamics at micro nano scales
Nonlinear Dynamics at Micro/Nano scales

10-9

10-6

...10-4…

…107….

10-15

?

?

NLD

Inaccessibility

Technological Limitations

Impossible Experiment


Fractal dimension in micro nano scale tape peeling
Fractal dimension in micro/nano scaleTape peeling

Persson et. al. Euro. Phys. Lett. 92, 46001 (2010)


Fractal dimension nano scale tape peeling

Fractal Dimension: Nano scale - tape peeling

df=2.3

Persson et. al. Euro. Phys. Lett. 92, 46001 (2010)


Afm image of irradiated and etched pet poly ethylene terephthalate film
AFM image of irradiated and etched PET (Poly ethylene terephthalate) film

Macro to micro/nano


Cell configuration
Cell configuration

A & D-Compartments of cell

B & C- Platinum electrodes

F- Porous PET film


Dynamics
Dynamics

Phys. Lett A 376, 1915 (2012),

Solid State Electronics 225, 751 (2012)


I v measurements li mg
I-V Measurements: Li-Mg

Li & Mg Polymer Gel Electrolyte (PGE)

Conductivity: LiPGE > MgPGE

pH: LiPGE = MgPGE



Dynamics1
Dynamics

Rawat, Bernamala, Prasad & Chandra, Phys. Lett A 376, 1915 (2012),

Solid State Electronics 225, 751 (2012)


Nonlinear dynamics in meso and nano scales

Marcos G. E. da Luz and Celia Anteneodo

Phil. Trans. R. Soc. A 369, 245 (2011).


Summary
Summary

NLD: in all scales

but promising in Micro/Nano scales systems because it can be reproduced in Laboratory for applications





Problem 1 synchronization seizure
Problem 1: Synchronization(Seizure)

Brain Dynamics: Chaotic

L. Iasemidis, ASU, Tempe, USA





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