Nonlinear PDE's: Pattern Formation (ripples) and Dendritic Growth (snowflakes)

1998: not covered in 1999

• Fourier Methods for Partial Differential Equations
• The Fast Fourier Transform and the Diffusion Equation: Finding Gradients FAST.
• Linear Stability and Wavenumber Selection: Pattern Formation in the Swift-Hohenberg Equation
• Spiral Defect Chaos: Mean Flow and the Generalized Swift-Hohenberg Equation

The Movie (9MB).

• Assignment
• Solution
• The Swift Hohenberg Equation
• Solution Executable

This software was developed in collaboration with Eberhard Bodenschatz and Matthew Kuntz. It remains in draft form. You are welcome to try it out, or use it in educational settings: we retain copyright and will continue modifying the code without notice.

The Course

James P. Sethna, sethna@lassp.cornell.edu.

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).