hwk8 - Phys. 7268 Assignment 8 Due: 3/31/11 You are highly...

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 8 Due: 3/31/11 You are highly encouraged to use Maple or Mathematica to do these problems. You are welcome (and encouraged) to use and modify the Maple program(s) posted on the class homepage. Problem 1 Quintic nonlinearity. Consider a variation of the Swift-Hohenberg equation with a quintic nonlinearity t u = ru- (1 + 2 ) 2 u- u 5 , where u ( x,y,t ) is a real field in a two-dimensional space. (a) Conduct the linear stability analysis and determine the type of the primary instability. (b) The next several questions consider base patterns with wave numbers equal to the critical one, q = q c . Find the nonlinear saturated stripe solution. You will need to determine which harmonics will be present in the Galerkin expansion and find the coefficients of the three leading terms. (c) Find the nonlinear saturated square solution. You may stop after you find the leading order term in the Galerkin expansion. (d) Find the nonlinear saturated hexagon solution. You may stop after you find the leading order term in the Galerkin expansion. (e) Determine the linear stability of the stripe state with respect to a cross-roll instability where the new set of stripes can have arbitrary orientation and wave number.stripes can have arbitrary orientation and wave number....
View Full Document

This note was uploaded on 08/25/2011 for the course PHYS 7268 taught by Professor Staff during the Spring '11 term at Georgia Institute of Technology.

Page1 / 2

hwk8 - Phys. 7268 Assignment 8 Due: 3/31/11 You are highly...

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