hw3 - Department of Chemical Engineering University of...

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Unformatted text preview: Department of Chemical Engineering University of California, Santa Barbara ChE 210C Spring 2008 Instructor: Glenn Fredrickson Homework #3 Homework Due: Friday, May 30, 2008 1. Repeat the derivation of the Kramers rate expression obtained in class in the high friction limit , but start your analysis with a Fokker-Planck equation ap- propriate for the high friction limit. 2. Consider a continuous-time, activated hopping process in which a particle makes nearest-neighbor jumps between sites on a simple cubic lattice in three-dimensions. Suppose that the hopping rate between neighboring sites is anisotropic, so that W x W y W z , where W is the hopping rate in direction . (a) Set up a master equation for this jump process and obtain its fundamental solution. (b) Analyze the behavior of your solution at both short and long times. Com- pute the mean-squared displacement matrix h x ( t ) x ( t ) i and identify a matrix of diffusion coefficients from the expression: h x ( t ) x...
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This note was uploaded on 12/29/2011 for the course CHE 210c taught by Professor Ceweb during the Fall '09 term at UCSB.

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