Physics 313: Lecture 4
Wednesday, 9/3/08
Comments to the Class
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You should be reading Chapter 2 of Cross-Greenside
(linear stability).
Do not start homework one day before due date, that
will not give you enough time.
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Lecture next Tuesday on chaos in the brain.
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Topics:
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Linear stability of spatially uniform fixed points: a first
step toward understanding spatially extended driven
dissipative systems.
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How to estimate critical parameter, critical wave
number, critical frequency in an experiment.
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Type I, II, and III instabilities.
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Role of symmetry in linear stability analysis
Discussion Question
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From your homework problem related to Reynolds
number, does fluid instability play a role in the
randomness of a coin toss? Does chaos play a role?
Any questions from class?
Big Picture of Where We are Heading
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Linear stability of uniform fixed points
Application to chemical systems,
Turing's discovery and morphogenesis.
What do the linearly unstable states turn
into? Saturated nonlinear states and
their linear stability (stability balloons).
How to invent or obtain mathematical
models of pattern formation
Amplitude equations
Linear Instability Analysis of
Time-Independent Spatially Uniform States