1. Physics 313: Lecture 5 Monday, 9/8/08

2. Comments to the Class
You should be reading Chapter 3 of Cross-Greenside.
Lecture tomorrow on chaos in the brain.
Topics:
Two examples of linear stability analysis: 1d Swift- Hohenberg and reaction-diffusion with one chemical.
How to estimate critical parameter, critical wave number, critical frequency in an experiment or complicated simulation.
Type I, II, and III instabilities, each 's' or 'o': six categories in all.
Chapter 3: Turing-instability of two interacting chemicals.

3. Graded Assignment 1
Grades are on inside of homeworks, point score and rough grade.
Points per problem: about 4 for simple calculation, for more complex calculations.
Please include Mathematica or Matlab code used to obtain answers.
Detailed answer sheet by later in the week, a few comments now...

4. Effect of Cell Geometry on Convection Rolls

5. Discussion Questions Any questions from class? In class calculations:
linearize to lowest order
when is non-zero fixed state of 1d Swift-Hohenberg linearly stable?

6. Growth Rate For Swift-Hohenberg State u=0
Range of wave numbers for nonlinear states?

7. Linear Instability of Single-Reagent Reaction-Diffusion System
Study linear stability of fixed point f(c*)=0 for concentration c(t,x).
How does analysis change if we allow two extended coordinates, c=c(x,y,t)?