Cumulative radial distribution of particle centers

Hi, I have just started working with Matlab. Need some help to initiate my following task.

I want to find out the cumulative radial distribution of particle centers by drawing spheres of radius 'R'. Initially the value of radius 'R' will be zero and it will increment with a value 'delta R' in each step. In each step the program should calculate the number of particle centers falling inside the sphere and it will terminate when all the given particle centers covered. In the end I want the code to plot a graph between 'reduced radial distance from centers vs Included particles'

I have particle centers in 3D and also their radius as they are itself considered as spheres. The starting point for the sphere of radius 'R' is the geometric center of the system which I also need to calculate.

[Image Analyst]

Are the particles themselves spheres? So that you have a bunch of spheres of increasing radius? And you place each new sphere such that it does not overlap/intersect existing spheres, so that you need to keep getting/testing random locations until the new sphere would fit? And then you want to find how how many individual small spheres are in a bigger containing sphere of radius "R"?

[yu sh]

Yes the particles are spheres but their radii are fixed they are not increasing, they are located at different points I just know their center coordinate and individual radii. I will draw a sphere with geometric center of the system as its center and increment that particular sphere and check how many particle centers (existing spheres with fixed radii) are falling inside them until all of them included

Answer 1

[Image Analyst]

See if this simulation does what you want:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;

% Make 99,000 spheres in a cube 100 by 100 by 100
numParticles = 99000;
x = 100 * rand(1, numParticles);
y = 100 * rand(1, numParticles);
z = 100 * rand(1, numParticles);
% Find the center of all of these
xCentroid = mean(x);
yCentroid = mean(y);
zCentroid = mean(z);
% Find the distances of all the particles from the centroid
distances = sort(sqrt((x - xCentroid).^2+(y - yCentroid).^2+(z - zCentroid).^2));
% Get a distribution (count) of how many particles are at each distance
subplot(2, 1, 1);
histObj = histogram(distances)
grid on;
title('Histogram', 'FontSize', fontSize);
xlabel('Distance', 'FontSize', fontSize);
ylabel('Count', 'FontSize', fontSize);
% Compute the count within a radius by computing the CDF
cdf = cumsum(histObj.Values);
radius = histObj.BinEdges(1:end-1);
subplot(2, 1, 2);
plot(radius, cdf, 'b-', 'LineWidth', 2);
grid on;
title('CDF, Cumulative Distribution Function', 'FontSize', fontSize);
xlabel('Radius (Distance from centroid)', 'FontSize', fontSize);
ylabel('Number Within that Radius', 'FontSize', fontSize);

[yu sh]

Thanks a lot Image Analyst for your effort. Please tell me instead of generating random numbers how can I input my own center coordinates? I have an array available like this

centers = [0.000329057 0.000465808 0.000816233
0.000641021  0.000709396  0.000401706
0.000521363  0.000470082  0.000598286
0.000572645  0.000256408  0.000893155
0.000282049  0.000551278  0.000675208
]

where row is representing centerX,centerY, centerZ. How can I link up this data with your coding.

[Image Analyst]

x = centers(:, 1);
y = centers(:, 2);
z = centers(:, 3);

Then use my code.

[yu sh]

Thanks Image Analyst

[yu sh]

Sorry to bother you again Image Analyst. I actually want to understand what does this command is performing in the coding.

radius = histObj.BinEdges(1:end-1)

In my research, I want the radius value to be the 'minimum distance between the particle centers'. Initially the radius will have zero value and then it will increment with 'minimum distance between the particle centers' value. Kindly guide how to achieve this.

[Image Analyst]

That gives you a list of all the radii that are in the histogram. The distances (radii) for the expanding sphere are taken from the centroid of all the particles. If you want the sphere center to be from one specific particle, then you can do that.

[AB]

Hello,

This is a great post. I have a follow up question as I am trying to do something very similar.

If I have different data sets for my problem but all of them have different no. of spherical particles. How can I normalize them and plot them on the same graph? Can I use fraction of spherical particles in the CDF graph? If yes, how to do that? Any other suggestions will also be appreciated

Thanks!

[Fahad Obaid]

Hello,

I am working on finding the radial distribution function. My question is how I plot the code that written by (Image Analyst) as the curve shown in the link https://en.wikibooks.org/wiki/Molecular_Simulation/Radial_Distribution_Functions#/media/File:Simulated_Radial_Distribution_Functions_for_Solid,_Liquid,_and_Gaseous_Argon.svg

I need to plot the curve instead of the histogram I really appreciate your help.

Answer 2

[John D'Errico]

You are looking at this the wrong way. First, NEVER reinvent the wheel. Use existing, high quality code written by professionals before stepping in and writing your own, especially if you are a novice to programming. Otherwise, you will find yourself overwhelmed with the complexities of dealing with a poorly written, inefficient code.

You are looking for a histogram, or perhaps a cumulative histogram. There are tools for this already written.

Just compute the set of distances from the origin, then call the appropriate histogram tool. I honestly can't recall if there is a cumhist tool in MATLAB. I think so, but it is easily cobbled from hist itself anyway, and I won't have access to MATLAB for the next day or so. A google search for cumhist did show MATLAB code.

[yu sh]

Thanks John.