1. Motivation …10 7 …....10 -4 … Classical 10 -6 10 -9 10 -15 Quantum Nano/Micro Astro

2. Motivation …10 7 …....10 -4 … NLD 10 -6 10 -9 10 -15 ? Inaccessibility

3. Astrophysical systems Inaccessible systems

4. Motivation …10 7 …....10 -4 … NLD 10 -6 10 -9 10 -15 ? Inaccessibility Impossible Experiment

5. Aim: Dynamical aspects of solar activities Inaccessible systems

6. Sun

7. 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)

8. Bangladesh, 2004

9. Sunspot Number cycle Source: Wikipedia; Nasa’s prediction

10. Sunspot Number cycle

11. 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

12. Solar wind data Solar Wind Ion Composition Spectrometer: ACE

13. Permutation Entropy Time series: x i,i =1,2,……,N Embedded m-dimensional Space: X i ={x i,x i+1,……..,x i+(m-1) } Arranged in ascending order: X i ={x i+k1,x i+k2,……..,x i+km } k j =0,….,m-1  m! permutation Each X i => (0,1,..m-1) symbols P j : P 1 P 2 P 3 …P j ; j≤m! Bandt & Pompe, PRL 88, 174101 (2002)

14. Permutation Entropy Bandt & Pompe, PRL 88, 174101 (2002)

15. Application in known dynamical systems

16. Prasad et al. Pramana J. Phys. 64, 513 (2005)

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

18. Hysteresis in sloar activity Suyal, Prasad, Singh, Solar Phys. 276, 407 (2012)

19. 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)

20. …10 7 …....10 -4 … NLD 10 -6 10 -9 10 -15 ? Inaccessibility Impossible Experiment Technological Limitations ? Nonlinear Dynamics at Micro/Nano scales

21. Fractal dimension in micro/nano scale Tape peeling Persson et. al. Euro. Phys. Lett. 92, 46001 (2010)

22. Fractal Dimension: Nano scale - tape peeling Persson et. al. Euro. Phys. Lett. 92, 46001 (2010) d f =2.3

23. AFM image of irradiated and etched PET (Poly ethylene terephthalate) film Macro to micro/nano

24. Cell configuration A & D-Compartments of cell B & C- Platinum electrodes F- Porous PET film

25. Dynamics Phys. Lett A 376, 1915 (2012), Solid State Electronics 225, 751 (2012)

26. I-V Measurements: Li-Mg Li & Mg Polymer Gel Electrolyte (PGE) Conductivity: LiPGE > MgPGE pH: LiPGE = MgPGE

27. Bifurcation diagram

28. Dynamics Rawat, Bernamala, Prasad & Chandra, Phys. Lett A 376, 1915 (2012), Solid State Electronics 225, 751 (2012)

29. Marcos G. E. da Luz and Celia Anteneodo Phil. Trans. R. Soc. A 369, 245 (2011). Nonlinear dynamics in meso and nano scales

30. Summary NLD: in all scales but promising in Micro/Nano scales systems because it can be reproduced in Laboratory for applications

31. Human brain

32. Onset of a temporal lobe epileptic seizure Electroencephalogram (EEG)

33. Neurons

34. Problem 1: Synchronization (Seizure) Brain Dynamics: Chaotic L. Iasemidis, ASU, Tempe, USA

35. Prediction/charaterization

36. EEG

37. Thanks