Motivation
10-15
Quantum
10-9
10-6
Nano/Micro
...10-4…
Classical
…107….
Astro
Motivation
10-15
10-9
10-6
...10-4…
NLD
…107….
?
Inaccessibility
Astrophysical systems
Inaccessible
systems
Motivation
10-15
10-9
10-6
...10-4…
NLD
…107….
?
Inaccessibility
Impossible Experiment
Aim: Dynamical aspects of solar activities
Inaccessible
systems
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 200-80000KM
First 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 .
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
T
1998.25
1998.71
1998.91
1999.11
1999.41
1999.73
1999.94
2000.15
2000.88
2001.40
2002.03
2002.41
2003.03
2003.24
2003.90
2005.33
2006.45
2008.39
N
1665
1314
789
1927
2716
1139
1404
3075
1580
1315
3329
3417
789
1840
2633
2541
2278
2108
SSN
54
69
75
84
92
104
111
117
113
110
113
107
81
72
54
30
16
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-1
m! permutation
Each Xi => (0,1,..m-1) symbols
Pj: P1 P2 P3 …Pj ; j≤m!
Bandt & Pompe, PRL 88, 174101 (2002)
Permutation Entropy

S 
m!
P
ln(
P
)
j
j
j 1
ln(m!)
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)
Nonlinear Dynamics at Micro/Nano scales
10-15
10-9
10-6
?
...10-4…
NLD
…107….
?
Inaccessibility
Technological Limitations
Impossible Experiment
Fractal dimension in micro/nano scale
Tape peeling
Persson et. al. Euro. Phys. Lett. 92, 46001 (2010)
Fractal Dimension: Nano scale - tape peeling
df=2.3
Persson et. al. Euro. Phys. Lett. 92, 46001 (2010)
Macro to micro/nano
AFM image of irradiated and etched
PET (Poly ethylene terephthalate) film
Cell configuration
A & D-Compartments of cell
B & 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 > MgPGE
pH: LiPGE = MgPGE
Bifurcation diagram
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
NLD: in all scales
but promising in Micro/Nano scales systems because
it can be reproduced in Laboratory for applications
Human brain
Onset of a temporal lobe epileptic seizure
Electroencephalogram (EEG)
Neurons
Problem 1: Synchronization
(Seizure)
Brain Dynamics: Chaotic
L. Iasemidis, ASU, Tempe, USA
Prediction/charaterization
Prediction/charaterization
EEG
Thanks