# How can I draw a histogram from Maxwell's distribution using C#?

• Engineering
Gold Member
Homework Statement:
I need to create a histogram of Maxwell-Boltzman's distribution.
Relevant Equations:
https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution#Distribution_for_the_speed
I have written the following source code:

Maxwell-Bolzman:
using System;

public class CommonDistributions
{
public static double Uniform(Random random)
{
return random.NextDouble();
}

static double Gaussian(Random random)
{
return Math.Sqrt(-2 * Math.Log(Uniform(random))) * Math.Cos(2 * Math.PI * Uniform(random));
}
public static double Gaussian(Random random, double mu, double sigma)
{
return sigma * Gaussian(random) + mu;
}
}

public class MaxwellBolzman
{
static double KB = 1.38064852e-23;

static double MaxwellVariance(double mass, double temperature)
{
return Math.Sqrt(KB * temperature / mass);
}

static double MaxwellComponent(Random random, double mass, double temperature)
{
double mu = 0.0;
double sigma = MaxwellVariance(mass, temperature);

return CommonDistributions.Gaussian(random, mu, sigma);
}
public static double Maxwell(Random random, double mass, double temperature)
{
double one = MaxwellComponent(random, mass, temperature);
double two = MaxwellComponent(random, mass, temperature);
double thr = MaxwellComponent(random, mass, temperature);

return Math.Sqrt(one * one + two * two + thr * thr);
}
}

public static class Normalization
{
public static int Normalize(double n_bins, double mu, double sigma, double gaussian)
{
var z = (gaussian - mu) / sigma;

if (z > 3 || z < -3)
{
return -1;
}
else
{
return (int)((z + 3) * n_bins / 6d);
}
}
}

class Program
{
static void Main(string[] args)
{
const double N = 1000000;
int time = (int)N;
int binsCount = 51;

Random rand = new Random();
int[] bins = new int[binsCount];

double mass = 14 * 1.67e-27;
double T = 300;

for (int i = 0; i < time; i++)
{
double gauss = MaxwellBolzman.Next(rand, mass, T);

int index = Normalization.Normalize(binsCount, mass, T, gauss);

if (index >= 0)
{
bins[index]++;
}
}

PointPairList list = new PointPairList();
for (int i = 0; i < bins.Length; i++)
{
}

PlotForm form = new PlotForm("Maxwell-Bolzman");
form.AxisChange();
form.ShowDialog();
}
}

It gives the following output:

But, according to this link, the graph should look like the following:

## Answers and Replies

berkeman
Mentor
I didn't go through the code/algorithm in detail, but this line would seem to be the reason that the program cuts off there, no? Where did the number come from? Did you expect the distribution to be done by then? Also, are you wanting to plot all 4 distributions from the graph you posted? Sorry if it's obvious, but I didn't really go through your code and assumptions in much detail yet.

int binsCount = 51;