Boltzmann distribution

This module initialises particle velocities from a Boltzmann distribution.

The velocity distribution per degree of freedom is a Gaussian with mean \(\mu_{v} = 0\) and width \(\sigma_{v} = \sqrt{\frac{kT}{m}}\),

\[f\left(v\right) = \sqrt{\frac{m}{2\pi kT}} \exp\left(\frac{-mv^2}{2 kT}\right)\]

To account for the finite size of the system, the velocities are shifted,

\[\vec{v}_\text{shifted} \equiv \vec{v} - \vec{V}_\text{cm}\]

to yield a centre of mass velocity of zero.

class halmd.mdsim.velocities.boltzmann(args)

Construct boltzmann module.

Parameters:

• args (table) – keyword arguments

• args.particle – instance of halmd.mdsim.particle

• args.temperature (number) – temperature of distribution

set()

Initialise particle velocities from Boltzmann distribution.

temperature

Temperature of the distribution in reduced units. The value can be changed by assignment.