Bussi

class hoomd.md.methods.thermostats.Bussi(kT, tau=0.0)

Bases: Thermostat

The Bussi-Donadio-Parrinello thermostat.

Parameters:

• kT (hoomd.variant.variant_like) – Temperature set point for the thermostat $[\mathrm{energy}]$.

• tau (float) – Thermostat time constant $[\mathrm{time}]$. Defaults to 0.

Bussi controls the system temperature by separately rescaling the velocity and angular momenta by the factor $\alpha$ sampled from the canonical distribution.

When tau is 0, the stochastic evolution of system is instantly thermalized and $\alpha$ is given by:

$$\alpha = \sqrt{\frac{g_N kT}{K}}$$

where $K$ is the instantaneous kinetic energy of the corresponding translational or rotational degrees of freedom, $N$ is the number of degrees of freedom, and $g_N$ is a random value sampled from the distribution $\mathrm{Gamma}(N, 1)$:

$$f_N(g) = \frac{1}{\Gamma(N)} g^{N-1} e^{-g}.$$

When tau is non-zero, the kinetic energies decay to equilibrium with the given characteristic time constant and $\alpha$ is given by:

$$\alpha = \sqrt{e^{-\delta t / \tau} + (1 - e^{-\delta t / \tau}) \frac{(2 g_{N-1} + n^2) kT}{2 K} + 2 n \sqrt{e^{-\delta t / \tau} (1-e^{-\delta t / \tau}) \frac{kT}{2 K}}}$$

where $\delta t$ is the step size and $n$ is a random value sampled from the normal distribution $\mathcal{N}(0, 1)$.

See also

Bussi et. al. 2007.

Example:

bussi = hoomd.md.methods.thermostats.Bussi(
    kT=1.5, tau=simulation.operations.integrator.dt * 20
)
simulation.operations.integrator.methods[0].thermostat = bussi

kT

Temperature set point for the thermostat $[\mathrm{energy}]$.

Examples:

bussi.kT = 1.0

bussi.kT = hoomd.variant.Ramp(A=1.0, B=2.0, t_start=0, t_ramp=1_000_000)

Type:

hoomd.variant.variant_like

tau

Thermostat time constant $[\mathrm{time}].$

Example:

bussi.tau = 0.0

Type:

float