22222222 - walk steps (time). Describe the significance of...

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BIM 107 Winter 2011 Problem Set 2 (Stochastic Systems: Master Equation) Due 2/3/11. 1. Random walk diffusion has been heavily used to study diffusion and transport in biological systems. Recent applications include mathematical modeling of receptor diffusion during cell-cell interactions and trafficking of immune cells in lymph nodes. The following problem considers (unbiased) random walk problem in one dimension. (a) Master equation for a simple random walk on one dimension (for discrete space and time) is given by P n,N denotes the probability of finding the random walker at site n after N random
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Unformatted text preview: walk steps (time). Describe the significance of the two terms on the right hand side of the above equation. (b) Calculate the characteristic function G(s,N) for the probability function P(n,N) G ( s , N ) = P ( n , N )exp( ins ) !" " # Assume the particle is at the origin n=0 at N=0. (c) Calculate the average and variance of the random walk using the expression of G(s,N) obtained in part (b). [Interested students can also try the following: Solve the master equation for a simple random walk to obtain an analytical expression for P n,N .] P n , N + 1 = 1 2 P n + 1, N + 1 2 P n ! 1, N...
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