generating random particles in a cylinder

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hamed 2015-6-11

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https://ww2.mathworks.cn/matlabcentral/answers/223423-generating-random-particles-in-a-cylinder

评论： Denisse Campos Muñoz 2016-2-17

I am trying to generate random particles in a cylinder corresponds to a finite volume fraction. Therefore, each volume fraction results in different number of particles. But, as volume fraction increases, say number of particles increases, the simulation time increases dramatically. For example, for 1100 particles (about volume fraction equal to 0.3) it takes just a minute to generate them in a way that they maintain within the cylinder boundaries and also do not overlap. However, if I want 1400 particles corresponds to volume fraction 0.4 it took about 24 hours and still not finished. Any suggestion is appreciated. The code is as below;

    vol_frac=0.400831;
    lz=0.04;
    lx=lz;ly=lx;
    x(1)=(2*lz-2*R)*rand(1)-lz+R;
    y(1)=(2*sqrt(lz^2-x(1)^2)-2*R)*rand(1)-sqrt(lz^2-x(1)^2)+R;
    z(1)=(2*lz-2*R)*rand(1)-lz+R;
    %no. of particles
    Npart=round(6*0.08^3*vol_frac/4/0.006^3);
    %Npart=1100;
    for i=2:Npart;
    x(i)=(2*lz-2*R)*rand(1)-lz+R;
    y(i)=(2*sqrt(lz^2-x(i)^2)-2*R)*rand(1)-sqrt(lz^2-x(i)^2)+R;
    z(i)=(2*lz-2*R)*rand(1)-lz+R;
     k=i-1;
    while k>=1;
         c=((y(k)-y(i))^2+(x(k)-x(i))^2+(z(k)-z(i))^2)^0.5;
             if c<=2*R 
                 x(i)=(2*lz-2*R)*rand(1)-lz+R;
                 y(i)=(2*sqrt(lz^2-x(i)^2)-2*R)*rand(1)-sqrt(lz^2-x(i)^2)+R;
                 z(i)=(2*lz-2*R)*rand(1)-lz+R;
                 k=i-1;
             else
                 k=k-1;
             end
    end
    end

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hamed 2015-6-12

编辑：hamed 2015-6-12

Thanks for your comments. The axial direction of the cylinder is along the z-axis (lz). Polar coordinate has been assumed in x-y plane. According to generate the position of the particles within a circle in x-y plane, I firstly guess an x value then from this value I calculate the y value in a way with which fall within the boundary of the circle. A margin of R equal to radius of particles exclude from the min and max of random values for x,y and z to avoid overlapping with the boundaries. "While" loop is for checking the overlapping of the particles. In each iteration, "for" loop generate a random position (x, y and z) and the "while" loop check whether this value is overlapping with all previous positions. If so, it would be replaced with another x,y and z and again checked. Unfortunately, I forgot to preallocate a zero values for the x,y and z. However, I assume that it might not the cause root of main problem. Thanks again and if you need any further information just don't hesitate to ask.

hamed 2015-6-14

在 MATLAB Online 中打开

I'm still not getting appropriate answer. I think the problem is due to random number rejection by overlapping check which results in predictable random numbers. However, I have revised the previous code due to mapping like this and becomes faster;

%Initial random position of particles (Normal distribution)
    vol_frac=0.400831;
    %no. of particles
    rng shuffle
    % Npart=1100;
      R=0.003;
      Npart=round(6*0.08^3*vol_frac/4/0.006^3);
      x=zeros(1,Npart);y=zeros(1,Npart);z=zeros(1,Npart);
      lz=0.04;
      lx=lz;ly=lx;
      teta=2*pi*rand;
      ri=(lz-R)*sqrt(rand);
      x(1)=ri*cos(teta);
      y(1)=ri*sin(teta);
      z(1)=(2*lz-2*R)*rand-lz+R;
      for i=2:Npart;
          teta=2*pi*rand;
          ri=(lz-R)*sqrt(rand);
          x(i)=ri*cos(teta);
          y(i)=ri*sin(teta);
          z(i)=(2*lz-2*R)*rand-lz+R;
          k=i-1;
      while k>=1;
          c=((y(k)-y(i))^2+(x(k)-x(i))^2+(z(k)-z(i))^2)^0.5;
               if c<2*R
                   teta=2*pi*rand;
                   ri=(lz-R)*sqrt(rand);
                   x(i)=ri*cos(teta);
                   y(i)=ri*sin(teta);
                   z(i)=(2*lz-2*R)*rand-lz+R;
                   k=i-1;
               else
                   k=k-1;
               end
      end
      end

Denisse Campos Muñoz 2016-2-17

I used your code to generating particles in cylindrical coordinates and that these follow uniform distribution using random ('unif', ..., ...) and would like to know how to graph the particles.

How I can plot the distributed along the center of each particle?

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generating random particles in a cylinder

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generating random particles in a cylinder

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