How do get the particles to bounce properly?

Hi i am trying to model gas particles when they collide with each other and a wall using elastic collision trying to keep it simple. But once they have collide they only change direction for 1 loop the go back to the original direction and collide again and so on.

Here is my code

clear all
figure(1)

%Constants
r = 0.5;
C = 0;
n = 5; %Number of Moles

 N = n; % Number of molecules
 x = 10*rand(N,1)-10;
 y = 10*rand(N,1)-10;

    velocityx =  15*rand(N,1)-5; %realsqrt((3*K*T)/MaO)
    velocityy =  15*rand(N,1)-5; %realsqrt((3*K*T)/MaO)

 dt = 0.1;

 for t = 1:1:60

    for i=1:1:N

     x(i) = x(i)+velocityx(i)*dt;
     y(i) = y(i)+velocityy(i)*dt;

 %Collisions
   for i=1:1:N
        for j=(i+1):1:N

           dx = x(i)-x(j);
           dy = y(i)-y(j);

           if sqrt((dx*dx)+(dy*dy)) <= 2*r   %Collision with other particle
             C = C+1;

               x(i) = x(i)-velocityx(i)*dt;
               y(i) = y(i)-velocityy(i)*dt; 
                for i=1:1:N;
                   x(i) = x(i)-velocityx(i)*dt;
                   y(i) = y(i)-velocityy(i)*dt; 
                end

           end 
        end

           %Collisions with the Y-axis bounds

           if  20 <= x(i)+r %Collision with chamber wall
                  C= C+1;

                 x(i) = x(i)-velocityx(i)*dt;
                 y(i) = y(i)-velocityy(i)*dt;
                 for i=1:1:N
                     x(i) = x(i)-velocityx(i)*dt;
                     y(i) = y(i)+velocityy(i)*dt;
                  end
           end

           if -20 >= x(i)-r %Collision with chamber wall
                  C = C+1;

                  x(i) = x(i)-velocityx(i)*dt;
                  y(i) = y(i)-velocityy(i)*dt;
                  for i=1:1:N
                     x(i) = x(i)-velocityx(i)*dt;
                     y(i) = y(i)+velocityy(i)*dt;
                 end
           end

            % Collisions with the X-axis bounds

           if 20 <= y(i)+r %Collision with chamber wall
                  C= C+1;

                  x(i) = x(i)-velocityx(i)*dt;
                  y(i) = y(i)-velocityy(i)*dt;
                   for i=1:1:N
                     x(i) = x(i)+velocityx(i)*dt;
                     y(i) = y(i)-velocityy(i)*dt;
                 end
           end

           if -20 >= y(i)-r %Collision with chamber wall
                  C = C+1;

                  x(i) = x(i)-velocityx(i)*dt;
                  y(i) = y(i)-velocityy(i)*dt;                                                           
                 for i=1:1:N
                     x(i) = x(i)+velocityx(i)*dt;
                     y(i) = y(i)-velocityy(i)*dt;
                 end

            end
    end

    end 

    plot(x,y,'o','markersize',11);
    axis([-20,20,-20,20]);
    hold on
    pause(dt);
    hold off

 end
display(C)

Any suggestions Thank you

Answer 1

[James Tursa]

You have multiple nested loops that use i for the index variable. These are going to clash and will not work. Change those inner loops to some other variable, e.g. k.

I would have expected the velocity to change when collisions occur, but I don't see that. I.e., I don't see anywhere in your code lines that begin with velocityx(i) = etc or velocityy(i) = etc. And once you do code this, I would expect the change in velocity to depend on the impact angles involved. I.e., don't just negate the velocities involved, but go through the geometry of the impact to see how things will bounce off of each other.

EDIT #1:

I still don't see the changes I suggested, so let's start with the simplest collision with the +x direction wall and agree that for this 1st cut we are only going to do the simplest result:

             if  20 <= x(i)+r %Collision with chamber wall
                    C= C+1;
                   x(i) = x(i)-velocityx(i)*dt;
                   y(i) = y(i)-velocityy(i)*dt;
                   for i=1:1:N
                       x(i) = x(i)-velocityx(i)*dt;
                       y(i) = y(i)+velocityy(i)*dt;
                    end
             end

The only thing that should change as a result of this collision is the velocity of the particle that had the collision, velocityx(i) and velocityy(i). None of the other particles should change anything as a result of this (so no inner loop should be used here), and none of the positions of any particle should change including the particle that had the collision, so you shouldn't be altering any x and y values. So this is how to code this collision:

             if  20 <= x(i)+r %Collision with chamber wall
                   C= C+1;
                   velocityx(i) = -velocityx(i);
             end

The only thing that happens is the x velocity of this particle reverses sign. No other particle has any changes. No particles have any position changes. And the y velocity of this particle does not change.

The other wall collisions are similar:

             if -20 >= x(i)-r %Collision with chamber wall
                    C = C+1;
                    velocityx(i) = -velocityx(i);
             end

             if 20 <= y(i)+r %Collision with chamber wall
                    C= C+1;
                    velocityy(i) = -velocityy(i);
             end

             if -20 >= y(i)-r %Collision with chamber wall
                    C = C + 1;
                    velocityy(i) = -velocityy(i);
             end

For your particle-to-particle collisions, the only things that change are the velocities of the two particles (again we are ignoring the geometry of the collision for this 1st simple cut). E.g.,

           if sqrt((dx*dx)+(dy*dy)) <= 2*r   %Collision with other particle
               C = C+1;
               velocityx(i) = -velocityx(i);
               velocityy(i) = -velocityy(i);
               velocityx(j) = -velocityx(j);
               velocityx(j) = -velocityy(j);
           end

Also, I think you want to end your loop of position updates before entering the collision code. E.g.,

      for i=1:1:N

       x(i) = x(i)+velocityx(i)*dt;
       y(i) = y(i)+velocityy(i)*dt;
      end % <-- ADDED THIS LINE

   %Collisions
     for i=1:1:N

[Alastair Martin]

Hi yea once i have a simplified version i will update it to factor in angle and change of speed.

i have made the changes above which you have suggested and now when the particles fits one of the collision statements all the particles all jump to the same x position but different y positions?

Thank you,

[Alastair Martin]

Thank you for the clear explanation, i understand what you mean and its improved my simulation. As i am someone new to matlab i am grateful for your help.

[Salike Anuraag]

Hi I would be glad if you can send me the modified code, I am working on the same particle-particle collision but here we are using superquadric structures which are complex in nature. I can go through your program as a reference, My email address is [e-mail]. Thanks in advance

[Animesh Biswas]

Could you please post the modified version of the code. I have similar problem doing the collision simularion.

Thank you