Ginzburg-Landau
I spent most of last week looking for an idea for my nonlinear physics course project. We were given a few pointers to topics that could become potential projects: various kinds of pattern formation in Fluid Mechanics, Complex fluids, Biological systems, Chemical systems, Optics, Combustion and Hydrodynamics.
I came up with four topics (all four of them weren’t on the initial list of things suggested.) Somebody else in the class had exactly the same proposal as mine, including references, so that was out of the picture. One turned out to be computationally infeasible (couple of hours for a single step of a Finite Element Method), the other turned out to be extremely hard and outside the scope of the course.
I finally settled on “Global feedback methods for the subcritical Complex Ginzburg-Landau Equation.” If that didn’t make any sense, I’ve tried to explain what each word means in my proposal.
(picture courtesy of Shankar Venkataramani.)
April 9th, 2007 at 11:13 am
[...] On a similar note, I’m having doubts about a PDE solver that I’m writing for my course project. I’m implementing the Pseodo-Spectral Method for the space dynamics. The technique is quite simply a projection onto another basis that requires fewer coefficients in the series expansion. At each time step, I take the forward and backward fourier transform of the space variables. This might have made sense a few years back when the algorithmic complexity of the FFT beats a space convolution hands down, but the added code complexity is probably not worth it. The only reason I’m doing it now is because I’ve never done anything like this before and it’s pretty cool. [...]
July 23rd, 2007 at 3:18 am
[...] Giraffes for example. The model is based on Reaction-Diffusion systems, which I had studied in the Ginzburg-Landau equation. The Ginzburg-Landau equation also forms patterns when carbon monooxide diffuses and [...]