Physics 313: Lecture 5
Monday, 9/8/08
Comments to the Class
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You should be reading Chapter 3 of Cross-Greenside.
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Lecture tomorrow on chaos in the brain.
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Topics:
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Two examples of linear stability analysis: 1d SwiftHohenberg and reaction-diffusion with one chemical.
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How to estimate critical parameter, critical wave
number, critical frequency in an experiment or
complicated simulation.
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Type I, II, and III instabilities, each 's' or 'o': six
categories in all.
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Chapter 3: Turing-instability of two interacting
chemicals.
Graded Assignment 1
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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
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Any questions from class?
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In class calculations:
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linearize to lowest order
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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
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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)?