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

2. Diffusion

3. Diffusion Simulation 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

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 is mass = 1 unit mass timestep = 1 unit time

8. Extension of particles from one room to two rooms