Complex Systems - a Physics Perspective

1. Complex Systems- a Physics Perspective Alfred Hübler Center for Complex Systems Research Department of Physics University of Illinois at Urbana-Champaign

2. Complex systems: • A system with a large throughput of • a fluid = turbulence, river networks • chemicals = flames & explosion • tension = fracture • electrical current = lightning, dielectric breakthrough • information = internet, social networks • The throughput is large means “sudden appearance of a pattern or dynamics (self-organization)” • This self-organization causes emergent properties.

3. Example of Emergence:Experimental Study of Structural Changes in Materials due to High-voltage Currents needle electrode sprays charge over oil surface 20 kV air gap between needle electrode and oil surface approx. 5 cm ring electrode forms boundary of dish has a radius of 12 cm oil height is approximately 3 mm, enough to cover the particles castor oil is used: high viscosity, low ohmic heating, biodegradable particles are non-magnetic stainless steel, diameter D=1.6 mm particles sit on the bottom of the dish J. Jun, A. Hubler, PNAS 102, 536 (2005)

4. Self-organization { 12 cm stage I: strand formation t=0s 10s 5m 13s 14m 7s { 14m 14s 14m 41s 15m 28s 77m 27s stage II: boundary connection stage III: geometric expansion stationary state

5. Emergent properties: Adjacency defines topological species Termini = particles touching only one other particle Branching points = particles touching three or more other particles Trunks = particles touching only two other particles Particles become termini or three-fold branch points in stage III. In addition there are a few loners (less than 1%). Loners are not connected to any other particle. There are no closed loops in stage III.

6. Emergent property: Relative number of each species is robust Graphs show how the number of termini, T, and branching points, B, scale with the total number of particles in the tree. J. Jun, A. Hubler, PNAS 102, 536 (2005)

7. Emergence (Y. Bar-Yam): • substructure (stem, branch, sub-branch, …) • the relationship of component to collective behavior • (termini, branching points, trunks) • the relationship of internal behavior to external influence (minimum resistance, open loop, dimension, minimum spanning tree predictor) • multiscale structure and dynamics (fractal dimension = 1.67)

8. The number of trees is not an emergent property J. Jun, A. Hubler, PNAS 102, 536 (2005)

9. Overall electrical resistance of system We estimate the resistance, as K = height of oil  conductivity of oil I0= total current

10. Hebbian Learning in a three-electrode system M. Sperl, A Chang, N. Weber, A. Hubler, Hebbian Learning in the Agglomeration of Conducting Particles, Phys.Rev.E. 59, 3165 (1999)

11. The limiting state has minimum resistance. • - conducting particle, submerged in low-conductance liquid, can move along x-axis • resistance between electrodes is minimal of the particle is in the center • resistance causes drop in energy density = force on resistor =>resistor moves away • limiting state = minimum resistance state Entropy created = Heat / Temperature Heat = Power = Current2 * Resistance = Voltage2 / Resistance Temperature = kept constant Case 1: Constant Current Battery Power = Current2 * Resistance = minimal Entropy production rate = minimized (Prigogine NP) Case 2: Constant Voltage Battery Power = Voltage2 / Resistance = maximized Entropy production rate = maximized Variation principles lead to the emergence of order.

12. Experimental demonstrations of some Complex Systems Paradigms • Stationary State has Minimum Resistance • Fractal Particle Networks Convection Cells • Adaptation to the edge of chaos • Vibrated Water Droplet Segregation • Discretisation Paradigm • Bouncing ball Water wheel Video Feedback

13. - Quantization Phenomena in Dissipative Wave-particle Systems • Vibrated Beam, Soliton Machine • The Whole > Sum of the Parts • Thermo-acoustic Resonator • -Resonances: Dynamical key & Synchronization • Mixed Reality Video Feedback

14. Synchronization: Out-of-body experiences with video feedback - Subject sees video image of itself with 3D goggles - Two sticks, one strokes person's chest for two minutes, second stick moves just under the camera lenses, as if it were touching the virtual body. - Synchronous stroking => people reported the sense of being outside their own bodies, looking at themselves from a distance where the camera is located. - While people were experiencing the illusion, the experimenter pretended to smash the virtual body by waving a hammer just below the cameras. Immediately, the subjects registered a threat response as measured by sensors on their skin. They sweated and their pulses raced. Real system & similar virtual system & bi-directional instant. coupling = mixed reality Blanke O et al.Linking OBEs and self processing to mental own body imagery at the temporo-parietal junction. J Neurosci 25:550-55 (2006).

15. Synchronization: Experimental evidence for mixed reality states in physical systems Objective: Understand synchronization between virtual and real systems. Approach: - Couple a real dynamical system to its virtual counterpart with an instantaneous bi-direction coupling (so far: non-linear pendulum, future: network). - Measure an order parameter of the real and the virtual systems and then detect synchronization.

16. Synchronization:Mixed reality states in physical systems, why are they important? - Virtual systems match their real counter parts with ever-increasing accuracy, such as graph theoretical network predictors. - New hardware for instantaneous bi-directional coupling, such as video feedback. - In mixed reality states there is no clear boundary between the real and the virtual system. Mixed reality states can be used to analyze and control real systems with high precision. And then there is the possibility for time travel … by the virtual system. Publication: The paper "Experimental evidence for mixed reality states in an inter-reality system" by Vadas Gintautas and Alfred Hubler, in Phys. Rev. E 75, 057201 (2007), was selected for the APS tip sheet: http://www.aps.org/about/tipsheets/tip68.cfm Photo: A. Hubler and V. Gintautas at the inter-reality system

17. Experimental demonstrations of some Complex Systems Paradigms • Stationary State has Minimum Resistance • Fractal Particle Networks Convection Cells • Adaptation to the edge of chaos • Vibrated Water Droplet Segregation • Discretisation Paradigm • Bouncing ball Water wheel Video Feedback

18. - Quantization Phenomena in Dissipative Wave-particle Systems • Vibrated Beam, Soliton Machine • The Whole > Sum of the Parts • Thermo-acoustic Resonator • -Resonances: Dynamical key & Synchronization • Mixed Reality Video Feedback • - Other cool experiments: BZ, Cellular Automata

19. - Quantization Phenomena in dissipative wave-particle systems • Vibrated Beam, Soliton Machine • The whole > sum of the parts • Thermo-acoustic Resonator • -Resonances: dynamical key & synchronization • Mixed Reality Video Feedback • - Other cool experiments: BZ, Cellular Automata