Welcome to Physics 313 Professor Henry Greenside Department of Physics

Physics 313: Lecture 1 Monday 8/25/08 ● Introduction of students ● Key information to know. ● Outline of some topics discussed ● Class discussion: highlights of intro nonlinear dynamics course ● Canonical example of a pattern-forming nonequilibrium system ● Discussion of examples: natural and artificial (man-made) patterns.

Who is in the Class? ● Name, Department, interests, skills (experiment, analytics, simulation?). ● I'll go first.

Key Information to Know ● Course website: ● Login and password for copyrighted files: 313/?????? ● Start reading Chapter 1 of Cross-Greenside for Wednesday's class. ● Download first homework assignment from this website. Question 1 for first homework assignment is due this Wednesday, rest due next week.

Outline of Course Topics ● 60-70% of course: follow Cross-Greenside text on pattern formation. Key question is how does spatial structure play a role in temporal dynamics? ● 40-30% of course: depends on class interests (Problem 1 of Homework 1). More of Cross- Greenside, networks, special topics in nonlinear dynamics (control, numerical methods), fluid dynamics?

More Details of Outline ● Linear instability of uniform and periodic spatial stationary structures with applications to chemistry and biology. (Turing instability) ● Nonlinear saturated stationary states: periodic states, stability balloons, deviations from ideal periodicity (defects). ● How to derive and analyze mathematical models of spatiotemporal dynamics. ● Amplitude equations: powerful formalism for studying slowly varying deviations from ideal periodic patterns. ● Miscellaneous topics: defects and fronts, spatiotemporal chaos, how to quantify high-dimensional systems, excitable media. ● Finish course with material on structure and dynamics of networks: properties of real networks, applications to Internet, biology (brain and genomes), immunization strategies.

Class Discussion: Highlights of Nonlinear Dynamics ● In one sentence, what is the single most useful insight from an introductory nonlinear dynamics course? ● What are some key concepts, techniques that you learned? ● What are some unsolved problems in nonlinear dynamics? ● What did you personally find interesting or useful in your intro nonlinear course?

Compare with “Phase Diagram” For Logistic Map

Relation of This Course to Intro Course

Conditions for Thermal Equilibrium ● All transients have decayed, all macroscopic motions time independent (but see next bullet). ● No relative macroscopic motion: system must be translating rigidly or rotating rigidly. ● Temperature T constant in time and uniform in space. ● Pressure p the same everywhere in absence of external field. ● Chemical potential constant everywhere in presence of external field (gravitational, electrical). Reference: L. Landau and E. Lifshitz, Statistical Physics, Part 1, Third Edition, Chapter 2, Sections 9, 10, 12, 25, 26.

Rayleigh-Benard Convection: Canonical Pattern-Forming System

Buoyancy Force Versus Dissipation From Viscosity and Thermal Conduction

Convection Patterns