hwk6 - Phys. 7268 Assignment 6 Due: 3/10/11 Problem 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Phys. 7268 Assignment 6 Due: 3/10/11 Problem 1 Nonlinear saturation in the Swift-Hohenberg equation. Consider the Swift-Hohenberg equation t u = ru- (1 + 2 x ) 2 u- u 3 (1) (a) Repeat the calculation for the nonlinear saturated stripe state using Galerkin expansion truncated to one mode for a general wave vector, i.e., calculate a q in the expression u = a q cos qx + (Note: it is helpful to understand how large q- q c is compared to r .) (b) Repeat the calculation for the nonlinear saturated stripe state using Galerkin expansion truncated to three modes for the critical wave vector q = q c = 1, i.e., calculate a 1 , a 3 and a 5 in the expression u = a 1 cos x + a 3 cos3 x + a 5 cos5 x + In principle we could immediately substitute this expansion into the Swift-Hohenberg equation with t u = 0. Setting the coefficients of three lowest order harmonics to zero would then provide the equations that can be solved for a 1 through a 5 . However, analytical solution of this system is difficult due to the unknown relative....
View Full Document

Page1 / 2

hwk6 - Phys. 7268 Assignment 6 Due: 3/10/11 Problem 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online