MATLAB Stochastic Simulations

Wednesday, 9/13/2002

Diffusion

DiffusionSimulation

nPart = 400; %number of particlessizeRandomStep = .02; %temperature related parameterrMax = 10;

%initial particlesx = rand(nPart,1)-0.5;y = rand(nPart,1)-0.5;

h = plot(x,y,'.'); %plot particles as dotshold onaxis([-20 20 -20 20])axis squaregrid offset(h,'EraseMode','xor','MarkerSize',18)

% draw the circle the diffusion will finally reach totheta = 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)EndnStep % display how many steps cost to reach to the circle

Erase Mode for Animation

This tells the MATLAB graphics system not to redraw theentire plot when the coordinates of one point are changed,but to restore the background color in the vicinity of thepoint using an “exclusive or” operation.

set(h,'EraseMode','xor','MarkerSize',18)

Brownian Motion in a Closed Box

Boundary Treatment

Reflection for the random movement with tendency to go outside.

Pressure

Momentum change for particle hit on the boundary surface with random movement of distance s and hit angle is

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mass⋅s⋅sinθtimestep

mass = 1 unit masstimestep = 1 unit time

Extension of particles from one room to two rooms