1. Physics 313: Lecture 17 Wednesday, 10/22/08

2. Announcements ● Please make an appointment to see me, to choose a project by Friday, October 24. ● Please experiment with the Game of Life program mentioned in today's lecture.

3. Cellular Automata Models: Discrete Time, Discrete Space, Discrete Values ● Widely used and studied in computer science. Computers are, in fact, CAs since memory composed of bits and time advances in discrete clock values. ● CA simulations easy to code, easy to parallelize. ● CAs with complex enough rules can carry out any computation that a digital computer can (Alan Turing's notion of universal computation).

4. Drawback of Cellular Automata: No Continuous Variables or Parameters ● Difficult to characterize dynamics or dependence of dynamics on rules since everything changes discontinuously.

5. One-Dimensional Cellular Automata

6. Rules for Conway's “Game of Life” Time t Time t+1 Loneliness: cell with less than two neighbors dies. Overcrowding: cell with more than 3 neighbors dies. Reproduction: empty cell with at least 3 neighbors becomes alive. Stasis: cell with exactly two neighbors stays the same

7. Simple Starting States for Game of Life

8. Playing With the Game of Life: Lucid Life on Linux Systems

9. For Discussion: Is Nature a Cellular Automaton? ● How to test if time, space, and observables are discrete? ● Feynman's question: does a finite volume of space contain a finite or infinite amount of information? ● Are animal brains more powerful than digital computers because they are (possibly) not discreteTuring machines? Book “Emperor's New Mind” by Roger Penrose if you want to learn more...

10. The Swift-Hohenberg Ecology of Models ● How to relate to experiments ● Properties: potential versus non-potential dynamics. ● Generalized models: no inversion symmetry, non-potential, mean flow, achiral dynamics

11. How To Compare Swift-Hohenberg With Experiments

12. Stability Balloons for Swift-Hohenberg Versus Infinite-Prandtl-Number Convection

13. Simulations of the Swift-Hohenberg Equation: Small Domains

14. Simulations of the Swift-Hohenberg Model

15. Repulsive and Attractive Gliding of Dislocations

16. Linear Instability of Swift-Hohenberg

17. Simulations of 2d Swift-Hohenberg

18. Simulation Versus Experiment

19. Swift-Hohenberg in Large Periodic Domain: Understand Coarsening Size of domains scales empirically as t 1/5 for both potential and nonpotential models, not understood theoretically.

20. Selected Wave Number q d By Coarsening

21. Generalized Swift-Hohenberg Models ● Non-symmetric ● Non-potential ● Mean flow: use stability balloon to tune parameters! ● Chiral symmetry (rotation)