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Unformatted text preview: Phys 7268 Midterm exam Due: 3/10/11 Problem 1 Generalizations of SwiftHohenberg equation. The form of the SwiftHohenberg equation is determined by the symmetries of the system, such as translational and rotational symmetries. For instance, breaking the parity symmetry leads to an extra term s x u with s an arbitrary constant: t u = ru + s x u (1 + 2 x ) 2 u u 3 . (a) Compute the growth rate and determine the type of instability (i.e., I s , III o , etc.) of the trivial solution u = 0 which arises for different values of parameter s . Furthermore, determine the coherence length c , the characteristic timescale and, if the instability is oscillatory, the characteristic frequency c . (b) By substituting the growth rate into the linear solution determine the meaning of the new term. Can you show that by a suitable change of variables the above equation can be reduced to a standard SwiftHohenberg equation?...
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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 Institute of Technology.
 Spring '11
 Staff

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