One D spheres.py

From Werner KRAUTH

Revision as of 12:53, 8 October 2018 Werner (Talk | contribs) ← Previous diff		Current revision Werner (Talk | contribs)
Line 3:		Line 3:
	import pylab		import pylab
-		+
	def binomialCoeff(n, k):		def binomialCoeff(n, k):
	result = 1		result = 1
Line 9:		Line 9:
	result = result * (n-i+1) / i		result = result * (n-i+1) / i
	return result		return result
-		+
	def Z(N, L, sigma):		def Z(N, L, sigma):
	freespace = L - 2.0 * N * sigma		freespace = L - 2.0 * N * sigma
Line 17:		Line 17:
	result = 0.0		result = 0.0
	return result		return result
-		+
	def pi(x, N, L, sigma):		def pi(x, N, L, sigma):
	tot = 0.0		tot = 0.0
Line 26:		Line 26:
	Ztotal = Z(N, L, sigma)		Ztotal = Z(N, L, sigma)
	return tot / Ztotal		return tot / Ztotal
-		+
	L = 105.0		L = 105.0
	N = 100		N = 100

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Current revision

Here is the program discussed in Lecture 05, for computing the probability to have a particle at position $x$

import pylab

def binomialCoeff(n, k):
    result = 1
    for i in range(1, k+1):
        result = result * (n-i+1) / i
    return result

def Z(N, L, sigma):
    freespace = L - 2.0 * N * sigma
    if freespace > 0.0:
        result = freespace ** N
    else:
        result = 0.0
    return result

def pi(x, N, L, sigma):
    tot = 0.0
    for k in range(0, N):
        Z1 = Z(k, x - sigma, sigma)
        Z2 = Z(N - k - 1, L - x - sigma, sigma)
        tot += binomialCoeff( N - 1, k) * Z1 * Z2
    Ztotal = Z(N, L, sigma)
    return tot / Ztotal

L = 105.0
N = 100
sigma = .50
xr = pylab.linspace(0.0, L, 2001)
yr = [pi(x, N, L, sigma)  for x in xr]
pylab.plot(xr, yr, 'red', linewidth=2.0)
pylab.title('One-dimensional hard-sphere density, $L$ = ' + str(L) + ' $N$ = '
+ str(N) )
pylab.xlabel('$x$ (position)')
pylab.ylabel('$\pi(x)$ (probability for a particle to be at $x$)' )
pylab.show()