Monte Carlo method for Smoluchowski equation

[Feynman]

Hi every body,
i've a simple question in the programation for a certain methode called Monte Carlo method for Smoluchowski equation:
i programe this method in maple but the problem is that the positions of particules z[l]is not changing ( it most be changed ): can anyone tell me where is the problem?
this is the method:

//calculate natural random numbers
test:=proc(N)
local a,i,L;
L:=[];
a:=rand(1..N):
for i from 1 to N do L:=[op(L),a()] od;
L;
end:
\\z is the position of particules
z:=test(10);

pi:=test(10);
\\ calculate uniform random numbers U[0,1]

r:=stats[random, uniform](10):for i from 1 to 10
do
printf("r[%d]=%f\n",i,r);
od;

\\ position of particules at time t+dt=t+1/20

for i from 1 to 10
do
if
r>1/(20*z) or r=1/(20*z)
then
z(t+dt)=z:
end if;
if
r<1/(20*z)
then
z(t+dt)=z+z[pi]:
end if;
od:
thankx verry much

 

[techwonder]

I guess that r>1/(20*z) is "always" true. Then you have z[t+dt](i)=z[t] explicitly in your code.

 

[tacman]

Hi there,

I am not familiar with the specific programming language or method you are using, but I can provide some general insights on the Monte Carlo method for Smoluchowski equation.

The Monte Carlo method is a simulation technique used to solve complex mathematical problems by generating random numbers and using them to approximate the solution. In the context of the Smoluchowski equation, this method is used to simulate the motion of particles in a fluid.

From the code provided, it seems like you are generating random numbers to represent the positions (z) and velocities (pi) of the particles. However, the problem you are facing is that the positions of the particles (z) are not changing.

One possible reason for this could be that your code is not properly updating the positions of the particles. In the for loop, you are only checking for certain conditions and setting the position of the particle at the next time step (t+dt) to be equal to its current position (z). This may not accurately simulate the movement of particles as they should be changing positions over time.

I suggest reviewing your code and making sure that the positions of the particles are being properly updated at each time step. You may also want to consider using a different method or checking for any errors in your code.

I hope this helps and good luck with your programming!