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MATLAB Stochastic Simulations

MATLAB Stochastic Simulations. Wednesday, 9/13/2002. Diffusion. nPart = 400; %number of particles sizeRandomStep = .02; %temperature related parameter rMax = 10; %initial particles x = rand(nPart,1)-0.5; y = rand(nPart,1)-0.5; h = plot(x,y,'.'); %plot particles as dots hold on

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MATLAB Stochastic Simulations

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  1. MATLAB Stochastic Simulations Wednesday, 9/13/2002

  2. Diffusion

  3. nPart = 400; %number of particles • sizeRandomStep = .02; %temperature related parameter • rMax = 10; • %initial particles • x = rand(nPart,1)-0.5; • y = rand(nPart,1)-0.5; • h = plot(x,y,'.'); %plot particles as dots • hold on • axis([-20 20 -20 20]) • axis square • grid off • set(h,'EraseMode','xor','MarkerSize',18) • % draw the circle the diffusion will finally reach to • theta = linspace( 0, pi*2, 50 ); • plot(rMax*cos(theta),rMax*sin(theta),'r-'); • nStep = 0; • while ( max(sqrt(x.^2+y.^2)) < rMax ) • drawnow • x = x + sizeRandomStep * randn(nPart,1); • y = y + sizeRandomStep * randn(nPart,1); • nStep = nStep + 1; • set(h,'XData',x,'YData',y) • End • nStep % display how many steps cost to reach to the circle DiffusionSimulation

  4. Erase Mode for Animation

  5. Brownian Motion in a Closed Box

  6. Boundary Treatment Reflection for the random movement with tendency to go outside.

  7. Pressure Momentum change for particle hit on the boundary surface with random movement of distance s and hit angle q is mass = 1 unit mass timestep = 1 unit time

  8. Extension of particles from one room to two rooms

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