hwk10 - Phys. 7268 Assignment 10 Due: 4/14/11 Problem 1...

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Unformatted text preview: Phys. 7268 Assignment 10 Due: 4/14/11 Problem 1 Exact solution for a moving front. Compute analytically the shape and speed of the moving front connecting the saturated stripe solution with the uniform state for the (complex) type-I s amplitude equation. Hint: Use the fact that f ( x ) = tanh( x ) is a solution of the differential equation: f 00 + 2 f- 2 f 3 = 0 (1) Give the answer in dimensional (unscaled) form. Problem 2 Pulled Fronts in the Swift-Hohenberg Equation. (a) Show that for the Swift-Hohenberg equation ∂ t u ( x,t ) = ru- ( ∂ 2 x + 1) 2 u- u 3 (2) the velocity c of a pulled front and the stationary-phase wave number q s are given by c = 4 3 √ 3 ( 2 + √ 1 + 6 r ) (- 1 + √ 1 + 6 r ) 1 / 2 (3) and q s = 1 2 ( 3 + √ 1 + 6 r ) 1 / 2 + i 2 √ 3 (- 1 + √ 1 + 6 r ) 1 / 2 (4) (b) For small r verify that these results agree with the results expected from the amplitude equation approach....
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This note was uploaded on 08/25/2011 for the course PHYS 7268 taught by Professor Staff during the Spring '11 term at Georgia Tech.

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hwk10 - Phys. 7268 Assignment 10 Due: 4/14/11 Problem 1...

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