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Simulation of 3D Diffusion Using the Monte Carlo Method

​
time
1
range
2
Using a Monte Carlo method, this Demonstration simulates the diffusion process in three dimensions, which obeys the equation
∂
t
u(x,y,z,t)=
∂
x,x
u(x,y,z,t)+
∂
y,y
u(x,y,z,t)+
∂
z,z
u(x,y,z,t)
.
At time
t=1
, the square of points at the bottom of the box represents the initial condition. At each time step, these points will diffuse by a random walk (Monte Carlo simulation) in three dimensions
x
,
y
, and
z
. Each dimension can have a different diffusion coefficient, but in this Demonstration the three diffusion coefficients are assumed equal. You can also change the range of the initial square.
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