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

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Presentation transcript:

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

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.

Graded Assignment 1 Grades are on inside of homeworks, point score and rough grade. Points per problem: about 4 for simple calculation, 10-30 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...

Effect of Cell Geometry on Convection Rolls

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?

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

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)?