vn2.py

#!/usr/bin/env python3

"""
Calculate v2{2} for an isotropic emission law (zero flow).  Will converge
to zero as the number of particles -> infinity.
"""

import itertools
import sys

import numpy as np
import numpy.random as rnd


def main():
    try:
        npart = int(sys.argv[1])
    except (IndexError, ValueError):
        print('usage: ' + sys.argv[0] + ' number_particles')
        exit(1)

    phi = 2*np.pi*rnd.rand(npart)
    deltaphi = np.array(
        [phi1-phi2 for (phi1, phi2) in itertools.combinations(phi, 2)]
    )

    v2_2x = np.cos(2.*deltaphi).mean()
    v2_2y = np.sin(2.*deltaphi).mean()

    v2_2 = (v2_2x*v2_2x + v2_2y*v2_2y)**.5

    print(v2_2)


if __name__ == "__main__":
    main()