Complex Systems and Emergent Structures: Understanding the Dynamics and Patterns

1. CSSS Experimental Labs Alfred Hubler and Jiajun Xu Center for Complex Systems Research University of Illinois at Urbana-Champaign server17.how-why.com/blog a-hubler@illinois.edu J. Jun & A. Hubler, Proceedings of the National Academy of Sciences 102, 536 (2005) Supported by the National Science Foundation PHY-01-40179 and DMR-9976550 (MCC)

2. Complex system: • Large Throughput of Matter, Electrical Current, Chemicals, Energy, Information, Force, .... Through a Well Designed Boundary • Many Parts That Form Emergent Structures Examples for emergent patterns: turbulent flows, volcanic eruptions, star formation & galaxies, oscillating chemical reactions, explosions, earth quakes, traffic congestions, computer crashes, learning, formation and dissolution of interaction networks (www, social, rivers, roots, neural, genetic, chemical, …), Mathematical Tools: Fractals, Chaos, NNs, GAs, CAs) To make a system complex, we increase the throughput until the systems forms patterns or starts to oscillate.

3. What is a thought?

4. What is a thought? Completing a connection.

5. Why do complex systems have natural tendency to harvest energy from the environment? State of least resistance = Stationary state of many open dissipative many particle system (related to: limiting state = state with minimum entropy production, Ilya Prigogine, Nobel Prize 1976) M. Dueweke, U. Dierker, A. Hubler, Self-assembling Electrical Connections Based on the Principle of Minimum Resistance, Phys.Rev.E 54, 496-506 (1996). M. Sperl, A Chang, N. Weber, A. Hubler, Hebbian Learning in the Agglomeration of Conducting Particles, Phys.Rev.E. 59, 3165-3168 (1999).D. Smyth, A. Hubler, A Conductivity-Dependent Phase Transition from Closed-Loop to Open-Loop Dendritic Networks, Complexity 9, 56-60(2003). Joseph K. Jun and Alfred W. Hubler, Formation and structure of ramified charge transportation networks in an electromechanical system, PNAS 102, 536–540 (2005). Assume there is an obstacle to an energy flow (= resistor) inside the system. The obstacle creates a drop in the energy density (= pressure drop). The pressure drop creates a force which pushes the obstacle out of the way.=> The resistance is minimized. The system forms minimum resistance structures (electrical wires, optimal river networks, optimal force flow networks, …)

6. 13 Laboratory experiments: (1) Arbortrons Conducting particles in castor oil subject to an electrical current. Conclusions: • Self-assembling wire networks maximize their access to external energy sources • Fractal neural nets can be trained like pets, where a small amount of energy is offered as a reward for “good” behavior • Arbortrons minimize their resistance (min/max entropy production) • M. Dueweke, U. Dierker, A. Hubler, Self-assembling Electrical Connections Based on the Principle of Minimum Resistance, Phys.Rev.E 54, 496-506 (1996). • M. Sperl, A Chang, N. Weber, A. Hubler, Hebbian Learning in the Agglomeration of Conducting Particles, Phys.Rev.E. 59, 3165-3168 (1999).D. Smyth, A. Hubler, A Conductivity-Dependent Phase Transition from Closed-Loop to Open-Loop Dendritic Networks, Complexity 9, 56-60(2003). • Joseph K. Jun and Alfred W. Hubler, Formation and structure of ramified charge transportation networks in an electromechanical system, PNAS 102, 536–540 (2005).

7. 13 Laboratory experiments: (2) Chaotic Water Wheel If xn < xc => static friction largest force, bucket overflows: xn+1 = xn (stationary state) If xn > xc => Newton’s second law => water wheel equation xn+1 = (xn + 2 / sin(xn)) mod (2π / number-of-bins) + noise - Deterministic but incomputable for small static friction - Thousands of exp. data required to see a pattern in the return map - Chaotic - Limiting state depends on number system (decimals, irrational) • If noise > static friction use irrational numbers • If noise < static friction use decimals (http://www.how-why.com/cgi-bin/cyberprof/os.exe?home=&document=http://www.how-why.com/phys194/Notes/MapDynamicsActivity.html, user: guest, password: guest)

8. 13 Laboratory experiments: (3) Mixing and segregation in open dissipative systems Two types of particles in a rotated drum: • Filling level < 50% => moon pattern • Filling level >50% => sun pattern • Square container => infinity pattern Conclusions: • The particles always segregate. • The complexity of the segregation pattern depends on the complexity of the boundary condition.

9. 13 Laboratory experiments: (4) Chaos of a bouncing ball Soft objects have internal degrees of freedom => Averaging over internal degrees of freedom leads to maps NOT ODEs. Conclusion: Time discrete models can be more accurate than time continuous models. Hubler and A. Gerig, Are Discrete Models more Accurate? Complexity 16(2), 5-7(2010)

10. 13 Laboratory experiments:(5) Adaptation to the Edge of Chaos Self-adjusting systems avoid chaos: Dynamical variable: xn+1=f(xn,an) Parameter:an+1 = an + εF(xn, xn-1, …),ε small Low-Pass Feedback: F(xn, xn-1, …), such as F=xn – xn-32 Wave chaos in vibrated Water droplet disappears Parameter versus time Number of occurrences versus parameter

11. 13 Laboratory experiments:(5) Adaptation to the Edge of Chaos Self-adjustment competing with external control Dynamical variable: xn+1=f(xn,an) Parameter:an+1 = an + εF(xn, xn-1, …) + c (An – an) Target: An = A0 + Δ n P. Melby, J. Kaidel, N. Weber, A. Hubler, Adaptation to the Edge of Chaos in the Self-Adjusting Logistic Map, Phys.Rev.Lett 84 5991-5993 (2000).P. Melby, N. Weber, A. Hubler, Robustness of Adaptation in Controlled Self-adjusting Chaotic Systems, Phys. Fluctuation and Noise Lett. 2, L285-L292 (2002). P. Melby, N. Weber, A. Hubler, Dynamics of Self-Adjusting System with Noise, CHAOS 15, 33902 (2005).

12. 13 Laboratory experiments: (6) Oscillating Chemical Reactions: Belousov–Zhabotinsky reaction Chemical chaos is rare: - side reactions suppress chaos eventually - no negative concentrations Conclusion: Chemical chaos is rich and beautiful.

13. 13 Laboratory experiments: (7) Exploring Mixed Reality States and out-of-body experiences -A real pendulum and a virtual pendulum with bi-directional instantaneous interaction. - Out of body experience … Conclusion: If the real system and the virtual system are close they Synchronize. V. Gintautas and A. Hubler Experimental evidence for mixed reality states in an interreality system. Phys. Rev. E 75, 057201 (2007).

14. 13 Laboratory experiments: (8) Thermo-acoustic resonator A sound wave in the resonator can extinguish the flame which powers the sound wave. The shape of the container, i.e. the largest scale structure influences determines if the flame is blown out or not. Conclusion: This experiments illustrates: Whole > sum of parts

15. 13 Laboratory experiments:(8) Thermo-acoustic resonatorThe whole is more than the sum of the parts, i.e. the size and shape of the container matters When the Top-Down and the Bottom-Up Sequences of Symmetry Breakings Match the Must Stable Structures Emerge A.Hubler, Predicting Complex Systems with a Holistic Approach, Complexity 10,11-16 (2005).

16. 12 Laboratory experiments: (9) Hardware implementation of an 2-dimensional CA Patterns of information and energy travel along a digital wire. => Future power grid and internet? Conclusion: Compartmentalized complex systems are more manageable.

17. 12 Laboratory experiments: (10) Video Feedback A video camera points at a screen = 2-dimensional nonlinear mapping function Conclusion: Complexity is beautiful.

18. 13 Laboratory experiments: (11) Quantization in dissipative wave particle systems. A particle on a vibrated string has preferred locations. Conclusion: The formalism of quantum mechanics applies to dissipative wave particle phenomena. D. Sivil, A. Hubler, Quantized motion of a particle pushed around by waves, Complexity 15(2), 10-12(2009)

19. 13 Laboratory experiments: • Synthetic atoms: High energy density and record power density Synthetic atom - A. Hubler and D. Lyon, Gap Size Dependence of the Dielectric Strength in Nano Vacuum Gaps, accepted by IEEE Transactions on Dielectrics and Electrical Insulation (2013) - E. Shinn, A. Hubler, D. Lyon, M. Grosse-Perdekamp, A. Bezryadin, and A. Belkin, Nuclear Energy Conversion with Stacks of Graphene Nano-capacitors, Complexity 18(3), 24–27(2013)

20. 13 Laboratory experiments: • Synthetic atoms: High energy density and record power density (a) Arcing in a capacitor occurs at an electric field of about 25kV / cm = 2 million V/m (b) If the voltage on a 4nm aluminum oxide layer of aluminum foils is greater than 12V electric breakdown occurs, i.e. the maximum electric field is 4V / 4nm = 1 billion V/m Energy release time = 4nm / speed of light = 4nm / 3108 m/s = 1.3  10-17s Alfred Hubler, Synthetic Atoms: Large energy density and record power density, Complexity 18(4), 12-14(2013)

21. Creation of mass: High-energy cosmic rays produce minute quantities of matter and antimatter, such as an electron – positron pair. • - Soliton machine model: Small regular waves represent heat, light, X-rays. Full left twist (solitons) represents matter. Full right twist (antisoliton) represents antimatter. 13 Laboratory experiments: (13) Solitons: Nonlinear waves Conclusion: A description of complex wave phenomena in terms of agents (solitons) and their interaction s (attractive and repulsive forces between them) is useful. Solition machine illustrates the creation of matter. Here an antisoliton passes through a soliton.

22. 13 Laboratory experiments • Chaotic water wheel: deterministic, but incomputable, many data required • Mixing and Segregation: mixing never occurs • Fractal networks: seek energy sources • Chaos of a bouncing ball: discrete models are better • Vibrated droplets: adapt to the edge of chaos • Oscillating chemical reactions: rich and beautiful • Mixed reality states: occur if the virtual world mirrors real world • Thermo-acoustic resonator: whole > sum of parts • Solitons: creating particles • Elementary CAs: packages and modules make complex systems manageable • Video feedback: can create beautiful patterns • Dissipative wave-particle systems have preferred states, like QM systems • Synthetic atoms: High energy density and record power density Thank you. Please sign up for the labs on the CSSS Wiki.