atom/brownian_statistics.py

This example prints out various statistics about a prospective Brownian dynamics simulation. You can use the statistics to determine if the time step is likely to be sufficiently short given the forces and particle sizes involved.

## \example atom/brownian_statistics.py
# This example prints out various statistics about a prospective Brownian
# dynamics simulation. You can use the statistics to determine if the time
# step is likely to be sufficiently short given the forces and particle
# sizes involved.

from __future__ import print_function
from IMP.atom import *

# fs
time_step = 1000
# angstrom
minimum_particle_radius = 10
# kCal/mol/A
maximum_spring_constant = 1

maximum_diffusion_coefficient =\
    get_einstein_diffusion_coefficient(minimum_particle_radius)
expected_delta = get_diffusion_length(maximum_diffusion_coefficient,
                                      time_step)

expected_rotational_delta =\
    get_diffusion_angle(maximum_diffusion_coefficient,
                        time_step) * minimum_particle_radius

expected_spring_diffusion_length =\
    get_diffusion_length(maximum_diffusion_coefficient,
                         .5 * maximum_spring_constant *
                         4 * expected_delta ** 2,
                         time_step)

print("with a time step of", time_step, "fs")
print("an object of radius", minimum_particle_radius, "A will move",\
    expected_delta, "A and a point on its surface will move",\
    expected_rotational_delta, "A more")
print("the motion from fluctuations in the spring compression will be",\
    expected_spring_diffusion_length, "A")
print("and a compression of 10% of the radius will induce a motion of",\
    get_diffusion_length(maximum_diffusion_coefficient,
                         .5 * maximum_spring_constant *
                         (.1 * minimum_particle_radius) ** 2,
                         time_step), "A")