Pattern Formation in Spatially Extended Systems

Newton Institute - August, 2005

Michael Cross

Slides

These are the slides used in the lecture (pdf format).

Demonstrations

These are some simple java demonstrations that illustrate aspects of my lectures. If you want to modify the demonstrations here are some documentation, a zip file of the executable and the various HTML files, and the java source files.

Lecture 1

Lecture 2

These demonstrations show the variety of planforms that are obtained from the Swift-Hohenberg equation and some generalizations, as well as the complicated transient dynamics.

Lecture 3

Complex Ginzburg Landau equation.
A reaction-diffusion system due to Bar and Eiswirth.

Lecture 4

Chaos in the Lorenz model.
Chaos in a coupled map lattice.

Notes

These notes explore the more technical aspects of the theoretical methods described in the lectures.

Lecture 1

Derivation of the amplitude equation using the method of multiple scales

Lecture 2

Derivation of the phase equation

Lecture 3

Review article on the "the world of the complex Ginzburg-Landau equation" by Igor Aranson and Lorenz Kramer [Reviews of Modern Physics 74, 99 (2002)]

References

A selected set of useful references for you to explore more of the issues