33333333 - your simulation to compute< r>< r 2> and...

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BIM 107 Winter 2011 Problem set 3 (Monte Carlo Simulation) Due: 2/14/11 1 (a) Use Monte Carlo method (on MATLAB) to simulate the random walk of a single random walker on a one-dimensional integer lattice. This random walker is allowed only two moves, move to the any of the two nearest neighbor sites with probability 0.5. The variable r denotes the displacement from the initial point r = 0 at t = 0. Compute < r > (mean displacement) and < r 2 > (mean square displacement) from this simulation as described below after part (b). Also estimate the probability distribution P(r) for a set of time of points (at least three). (b) Now include another move so that your random walker now has three choices of moves to choose from: move to the right, move to the left and stay at the same position. Each of these moves is sampled with equal probability 1/3. Again, use
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Unformatted text preview: your simulation to compute < r > , < r 2 >, and P(r). How do < r > and < r 2 > compare for parts (a) and (b)? Does this make sense to you? Why or why not? (c) What happens to < r > and < r 2 > if those three Monte Carlo moves in part (b) are performed with unequal probabilities? Run each simulation for 1000 time steps all with infinite large lattices (therefore there are no boundary conditions to worry about) and report (and plot) the values for < r > and < r 2 > that you found and answer the questions given above. Note: You need to average over many runs (~ 100) to generate your plots. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Your MatLab code should be commented using ʻ % ʼ to explain to someone who has never seen your code what you are doing at each step. If you do not comment your code, I cannot tell what is going on, and you cannot get points....
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This note was uploaded on 04/03/2011 for the course BIM 107 taught by Professor Raychaudhari during the Winter '11 term at UC Davis.

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