Langevin¶

class hoomd.md.methods.Langevin(filter, kT, tally_reservoir_energy=False, default_gamma=1.0, default_gamma_r=(1.0, 1.0, 1.0))¶

Bases: Method

Langevin dynamics.

Parameters:

filter (hoomd.filter.filter_like) – Subset of particles to apply this method to.
kT (hoomd.variant.variant_like) – Temperature of the simulation \([\mathrm{energy}]\).
tally_reservoir_energy (bool) – When True, track the energy exchange between the thermal reservoir and the particles. Defaults to False \([\mathrm{energy}]\).
default_gamma (float) – Default drag coefficient for all particle types \([\mathrm{mass} \cdot \mathrm{time}^{-1}]\).
default_gamma_r ([float, float, float]) – Default rotational drag coefficient tensor for all particles \([\mathrm{mass} \cdot \mathrm{length}^{2} \cdot \mathrm{time}^{-1}]\).

Langevin integrates particles forward in time according to the Langevin equations of motion, modelling a canonical ensemble (NVT).

The translational degrees of freedom follow:

\[ \begin{align}\begin{aligned}m \frac{d\vec{v}}{dt} &= \vec{F}_\mathrm{C} - \gamma \cdot \vec{v} + \vec{F}_\mathrm{R}\\\langle \vec{F}_\mathrm{R} \rangle &= 0\\\langle |\vec{F}_\mathrm{R}|^2 \rangle &= 2 d kT \gamma / \delta t\end{aligned}\end{align} \]

where \(\vec{F}_\mathrm{C}\) is the force on the particle from all potentials and constraint forces, \(\gamma\) is the drag coefficient, \(\vec{v}\) is the particle’s velocity, \(\vec{F}_\mathrm{R}\) is a uniform random force, and \(d\) is the dimensionality of the system (2 or 3). The magnitude of the random force is chosen via the fluctuation-dissipation theorem to be consistent with the specified drag and temperature, \(kT\).

About axes where \(I^i > 0\), the rotational degrees of freedom follow:

\[ \begin{align}\begin{aligned}I \frac{d\vec{\omega}}{dt} &= \vec{\tau}_\mathrm{C} - \gamma_r \cdot \vec{\omega} + \vec{\tau}_\mathrm{R}\\\langle \vec{\tau}_\mathrm{R} \rangle &= 0,\\\langle \tau_\mathrm{R}^i \cdot \tau_\mathrm{R}^i \rangle &= 2 k T \gamma_r^i / \delta t,\end{aligned}\end{align} \]

where \(\vec{\tau}_\mathrm{C} = \vec{\tau}_\mathrm{net}\), \(\gamma_r^i\) is the i-th component of the rotational drag coefficient (gamma_r), \(\tau_\mathrm{R}^i\) is a component of the uniform random torque, \(\vec{\omega}\) is the particle’s angular velocity and \(I\) is the the particle’s moment of inertia. The magnitude of the random torque is chosen via the fluctuation-dissipation theorem to be consistent with the specified drag and temperature, \(kT\).

Langevin numerically integrates the translational degrees of freedom using Velocity-Verlet and the rotational degrees of freedom with a scheme based on Kamberaj 2005.

The attributes gamma and gamma_r set the translational and rotational damping coefficients, respectively, by particle type.

Example:

langevin = hoomd.md.methods.Langevin(filter=hoomd.filter.All(), kT=1.5)
simulation.operations.integrator.methods = [langevin]

Members inherited from AutotunedObject:

property kernel_parameters¶: Kernel parameters. Read more...

property is_tuning_complete¶: Check if kernel parameter tuning is complete. Read more...

tune_kernel_parameters()¶: Start tuning kernel parameters. Read more...

Members defined in Langevin:

filter¶

Subset of particles to apply this method to.

Type:: hoomd.filter.filter_like

kT¶

Temperature of the simulation \([\mathrm{energy}]\).

Examples:

langevin.kT = 1.0

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

Type:: hoomd.variant.Variant

tally_reservoir_energy¶

When True, track the energy exchange between the thermal reservoir and the particles.

Example:

langevin.tally_reservoir_energy = True

Type:: bool

gamma¶

The drag coefficient for each particle type \([\mathrm{mass} \cdot \mathrm{time}^{-1}]\).

Example:

langevin.gamma["A"] = 0.5

Type:: TypeParameter[ particle type, float ]

gamma_r¶

The rotational drag coefficient tensor for each particle type \([\mathrm{mass} \cdot \mathrm{length}^{2} \cdot \mathrm{time}^{-1}]\).

Example:

langevin.gamma_r["A"] = [1.0, 2.0, 3.0]

Type:: TypeParameter[particle type,[float, float , float]]

property reservoir_energy¶

Energy absorbed by the reservoir \([\mathrm{energy}]\).

Set tally_reservoir_energy to True to track the reservoir energy.

Example:

langevin.tally_reservoir_energy = True
logger.add(obj=langevin, quantities=["reservoir_energy"])

Warning

When continuing a simulation, the energy of the reservoir will be reset to zero.

(Loggable: category=”scalar”)