# md.methods

Overview

 Method Base class integration method. Brownian Brownian dynamics. DisplacementCapped Newtonian dynamics with a cap on the maximum displacement per time step. Langevin Langevin dynamics. NPH Constant pressure, constant enthalpy dynamics. NPT Constant pressure, constant temperature dynamics. NVE Constant volume, constant energy dynamics. NVT Constant volume, constant temperature dynamics. OverdampedViscous Overdamped viscous dynamics.

Details

Integration methods for molecular dynamics.

Integration methods work with hoomd.md.Integrator to define the equations of motion for the system. Each individual method applies the given equations of motion to a subset of particles.

Integration methods with constraints

For methods that constrain motion to a manifold see hoomd.md.methods.rattle

class hoomd.md.methods.Brownian(filter, kT, alpha=None)

Bases: Method

Brownian dynamics.

Parameters
• filter (hoomd.filter.filter_like) – Subset of particles to apply this method to.

• kT (hoomd.variant.variant_like) – Temperature of the simulation $$[\mathrm{energy}]$$.

• alpha (float) – When set, use $$\alpha d_i$$ for the drag coefficient where $$d_i$$ is particle diameter $$[\mathrm{mass} \cdot \mathrm{length}^{-1} \cdot \mathrm{time}^{-1}]$$. Defaults to None

Brownian integrates particles forward in time according to the overdamped Langevin equations of motion, sometimes called Brownian dynamics or the diffusive limit. It integrates both the translational and rotational degrees of freedom.

The translational degrees of freedom follow:

\begin{align}\begin{aligned}\frac{d\vec{r}}{dt} &= \frac{\vec{F}_\mathrm{C} + \vec{F}_\mathrm{R}}{\gamma},\\\langle \vec{F}_\mathrm{R} \rangle &= 0,\\\langle |\vec{F}_\mathrm{R}|^2 \rangle &= 2 d k T \gamma / \delta t,\\\langle \vec{v}(t) \rangle &= 0,\\\langle |\vec{v}(t)|^2 \rangle &= d k T / m,\end{aligned}\end{align}

where $$\vec{F}_\mathrm{C} = \vec{F}_\mathrm{net}$$ is the net force on the particle from all forces (hoomd.md.Integrator.forces) and constraints (hoomd.md.Integrator.constraints), $$\gamma$$ is the translational drag coefficient (gamma), $$\vec{F}_\mathrm{R}$$ is a uniform random force, $$\vec{v}$$ is the particle’s velocity, and $$d$$ is the dimensionality of the system. The magnitude of the random force is chosen via the fluctuation-dissipation theorem to be consistent with the specified drag and temperature, $$T$$.

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

\begin{align}\begin{aligned}\frac{d\mathbf{q}}{dt} &= \frac{\vec{\tau}_\mathrm{C} + \vec{\tau}_\mathrm{R}}{\gamma_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,\\\langle \vec{L}(t) \rangle &= 0,\\\langle L^i(t) \cdot L^i(t) \rangle &= k T \cdot I^i,\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 the torque, $$L^i$$ is the i-th component of the particle’s angular momentum and $$I^i$$ is the i-th component of 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, $$T$$.

Brownian uses the numerical integration method from I. Snook 2007, The Langevin and Generalised Langevin Approach to the Dynamics of Atomic, Polymeric and Colloidal Systems, section 6.2.5, with the exception that $$\vec{F}_\mathrm{R}$$ is drawn from a uniform random number distribution.

In Brownian dynamics, particle velocities and angular momenta are completely decoupled from positions. At each time step, Brownian draws a new velocity distribution consistent with the current set temperature so that hoomd.md.compute.ThermodynamicQuantities will report appropriate temperatures and pressures when logged or used by other methods.

Brownian dynamics neglects the acceleration term in the Langevin equation. This assumption is valid when overdamped: $$\frac{m}{\gamma} \ll \delta t$$. Use Langevin if your system is not overdamped.

You can set $$\gamma$$ in two ways:

1. Specify $$\alpha$$ which scales the particle diameter to $$\gamma = \alpha d_i$$.

2. After the method object is created, specify the attribute gamma and gamma_r for rotational damping or random torque to assign them directly, with independent values for each particle type in the system.

Examples:

brownian = hoomd.md.methods.Brownian(filter=hoomd.filter.All(), kT=0.2,
alpha=1.0)
integrator = hoomd.md.Integrator(dt=0.001, methods=[brownian],
forces=[lj])


Examples of using gamma and gamma_r:

brownian = hoomd.md.methods.Brownian(filter=hoomd.filter.All(), kT=0.2)
brownian.gamma.default = 2.0
brownian.gamma_r.default = [1.0, 2.0, 3.0]

filter

Subset of particles to apply this method to.

Type

hoomd.filter.filter_like

kT

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

Type

hoomd.variant.Variant

alpha

When set, use $$\alpha d_i$$ for the drag coefficient where $$d_i$$ is particle diameter $$[\mathrm{mass} \cdot \mathrm{length}^{-1} \cdot \mathrm{time}^{-1}]$$.

Type

float

gamma

The drag coefficient can be directly set instead of the ratio of particle diameter ($$\gamma = \alpha d_i$$). The type of gamma parameter is either positive float or zero $$[\mathrm{mass} \cdot \mathrm{time}^{-1}]$$.

Type

TypeParameter[ particle type, float ]

gamma_r

The rotational drag coefficient can be set. The type of gamma_r parameter is a tuple of three float. The type of each element of tuple is either positive float or zero $$[\mathrm{force} \cdot \mathrm{length} \cdot \mathrm{radian}^{-1} \cdot \mathrm{time}^{-1}]$$.

Type

TypeParameter[particle type, [float, float, float]]

class hoomd.md.methods.DisplacementCapped(filter, maximum_displacement: )

Bases: NVE

Newtonian dynamics with a cap on the maximum displacement per time step.

The method employs a maximum displacement allowed each time step. This method can be helpful to relax a system with too much overlaps without “blowing up” the system.

Warning

This method does not conserve energy or momentum.

Parameters

DisplacementCapped integrates integrates translational and rotational degrees of freedom using modified microcanoncial dynamics. See NVE for the basis of the algorithm.

Examples:

relaxer = hoomd.md.methods.DisplacementCapped(
filter=hoomd.filter.All(), maximum_displacement=1e-3)
integrator = hoomd.md.Integrator(
dt=0.005, methods=[relaxer], forces=[lj])

filter

Subset of particles on which to apply this method.

Type

hoomd.filter.filter_like

maximum_displacement

The maximum displacement allowed for a particular timestep $$[\mathrm{length}]$$.

Type

hoomd.variant.variant_like

class hoomd.md.methods.Langevin(filter, kT, alpha=None, tally_reservoir_energy=False)

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 $$[\mathrm{energy}]$$.

• alpha (float) – When set, use $$\alpha d_i$$ for the drag coefficient where $$d_i$$ is particle diameter $$[\mathrm{mass} \cdot \mathrm{length}^{-1} \cdot \mathrm{time}^{-1}]$$. Defaults to None.

• tally_reservoir_energy (bool) – If true, the energy exchange between the thermal reservoir and the particles is tracked. Total energy conservation can then be monitored by adding langevin_reservoir_energy_groupname to the logged quantities. Defaults to False $$[\mathrm{energy}]$$.

Langevin integrates particles forward in time according to the Langevin equations of motion.

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, $$T$$.

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

\begin{align}\begin{aligned}I \frac{d\vec{L}}{dt} &= \vec{\tau}_\mathrm{C} - \gamma_r \cdot \vec{L} + \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 the torque, $$\vec{L}$$ is the particle’s angular momentum 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, $$T$$.

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

Langevin dynamics includes the acceleration term in the Langevin equation. This assumption is valid when underdamped: $$\frac{m}{\gamma} \gg \delta t$$. Use Brownian if your system is not underdamped.

You can set $$\gamma$$ in two ways:

1. Specify $$\alpha$$ which scales the particle diameter to $$\gamma = \alpha d_i$$.

2. After the method object is created, specify the attribute gamma and gamma_r for rotational damping or random torque to assign them directly, with independent values for each particle type in the system.

Examples:

langevin = hoomd.md.methods.Langevin(filter=hoomd.filter.All(), kT=0.2,
alpha=1.0)
integrator = hoomd.md.Integrator(dt=0.001, methods=[langevin],
forces=[lj])


Examples of using gamma and gamma_r:

langevin = hoomd.md.methods.Langevin(filter=hoomd.filter.All(), kT=0.2)
langevin.gamma.default = 2.0
langevin.gamma_r.default = [1.0,2.0,3.0]


Warning

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

filter

Subset of particles to apply this method to.

Type

hoomd.filter.filter_like

kT

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

Type

hoomd.variant.Variant

alpha

When set, use $$\alpha d_i$$ for the drag coefficient where $$d_i$$ is particle diameter $$[\mathrm{mass} \cdot \mathrm{length}^{-1} \cdot \mathrm{time}^{-1}]$$. Defaults to None.

Type

float

gamma

The drag coefficient can be directly set instead of the ratio of particle diameter ($$\gamma = \alpha d_i$$). The type of gamma parameter is either positive float or zero $$[\mathrm{mass} \cdot \mathrm{time}^{-1}]$$.

Type

TypeParameter[ particle type, float ]

gamma_r

The rotational drag coefficient can be set. The type of gamma_r parameter is a tuple of three float. The type of each element of tuple is either positive float or zero $$[\mathrm{mass} \cdot \mathrm{time}^{-1}]$$.

Type

TypeParameter[particle type,[float, float , float]]

class hoomd.md.methods.Method

Base class integration method.

Provides common methods for all subclasses.

Note

Users should use the subclasses and not instantiate Method directly.

class hoomd.md.methods.NPH(filter, S, tauS, couple, box_dof=(True, True, True, False, False, False), rescale_all=False, gamma=0.0)

Bases: Method

Constant pressure, constant enthalpy dynamics.

Parameters
• filter (hoomd.filter.filter_like) – Subset of particles on which to apply this method.

• Stress components set point for the barostat.

In Voigt notation: $$[S_{xx}, S_{yy}, S_{zz}, S_{yz}, S_{xz}, S_{xy}]$$ $$[\mathrm{pressure}]$$. In case of isotropic pressure P ($$[p, p, p, 0, 0, 0]$$), use S = p.

• tauS (float) – Coupling constant for the barostat $$[\mathrm{time}]$$.

• couple (str) – Couplings of diagonal elements of the stress tensor, can be “none”, “xy”, “xz”,”yz”, or “all”, default to “all”.

• box_dof (tuple [ bool ]) – Box degrees of freedom with six boolean elements corresponding to x, y, z, xy, xz, yz, each. Default to [True,True,True,False,False,False]). If turned on to True, rescale corresponding lengths or tilt factors and components of particle coordinates and velocities.

• rescale_all (bool) – if True, rescale all particles, not only those in the group, Default to False.

• gamma (float) – Dimensionless damping factor for the box degrees of freedom, Default to 0.

NPH integrates translational and rotational degrees of freedom forward in time in the Isoenthalpic-isobaric ensemble. The barostat is introduced as additional degrees of freedom in the Hamiltonian that couple with the box parameters.

The barostat tensor is $$\nu_{\mathrm{ij}}$$. Access these quantities barostat_dof.

Except for the thermostat, NPH shares parameters with NPT. See NPT for descriptions of the coupling and other barostat parameters.

Examples:

dt = 0.005
tauS = 1000 * dt
nph = hoomd.md.methods.NPH(filter=hoomd.filter.All(), tauS=tauS, S=2.0)
# orthorhombic symmetry
nph = hoomd.md.methods.NPH(filter=hoomd.filter.All(), tauS=tauS, S=2.0,
couple="none")
# tetragonal symmetry
nph = hoomd.md.methods.NPH(filter=hoomd.filter.All(), tauS=tauS, S=2.0,
couple="xy")
# triclinic symmetry
nph = hoomd.md.methods.NPH(filter=hoomd.filter.All(), tauS=tauS, S=2.0,
couple="none", rescale_all=True)
integrator = hoomd.md.Integrator(dt=dt, methods=[nph], forces=[lj])

filter

Subset of particles on which to apply this method.

Type

hoomd.filter.filter_like

S

Stress components set point for the barostat totalling 6 components. In Voigt notation, $$[S_{xx}, S_{yy}, S_{zz}, S_{yz}, S_{xz}, S_{xy}]$$ $$[\mathrm{pressure}]$$. Stress can be reset after method object is created. For example, an isotopic pressure can be set by nph.S = 4.

Type
tauS

Coupling constant for the barostat $$[\mathrm{time}]$$.

Type

float

couple

Couplings of diagonal elements of the stress tensor, can be “none”, “xy”, “xz”,”yz”, or “all”.

Type

str

box_dof

Box degrees of freedom with six boolean elements corresponding to x, y, z, xy, xz, yz, each.

Type
rescale_all

if True, rescale all particles, not only those in the group.

Type

bool

gamma

Dimensionless damping factor for the box degrees of freedom.

Type

float

barostat_dof

Additional degrees of freedom for the barostat ($$\nu_{xx}$$, $$\nu_{xy}$$, $$\nu_{xz}$$, $$\nu_{yy}$$, $$\nu_{yz}$$, $$\nu_{zz}$$)

Type
property barostat_energy

Energy the barostat contributes to the Hamiltonian $$[\mathrm{energy}]$$.

(Loggable: category=”scalar”)

thermalize_barostat_dof()

Set the barostat momentum to random values.

thermalize_barostat_dof sets a random value for the barostat $$\nu_{\mathrm{ij}}$$. Call thermalize_barostat_dof to set a new random state for the barostat.

Important

You must call Simulation.run before thermalize_barostat_dof. Call run(steps=0) to prepare a newly created hoomd.Simulation.

class hoomd.md.methods.NPT(filter, kT, tau, S, tauS, couple, box_dof=[True, True, True, False, False, False], rescale_all=False, gamma=0.0)

Bases: Method

Constant pressure, constant temperature dynamics.

Parameters
• filter (hoomd.filter.filter_like) – Subset of particles on which to apply this method.

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

• tau (float) – Coupling constant for the thermostat $$[\mathrm{time}]$$.

• Stress components set point for the barostat.

In Voigt notation: $$[S_{xx}, S_{yy}, S_{zz}, S_{yz}, S_{xz}, S_{xy}]$$ $$[\mathrm{pressure}]$$. In case of isotropic pressure P ($$[p, p, p, 0, 0, 0]$$), use S = p.

• tauS (float) – Coupling constant for the barostat $$[\mathrm{time}]$$.

• couple (str) – Couplings of diagonal elements of the stress tensor, can be “none”, “xy”, “xz”,”yz”, or “xyz”.

• box_dof (list [ bool ]) – Box degrees of freedom with six boolean elements corresponding to x, y, z, xy, xz, yz, each. Default to [True,True,True,False,False,False]). If turned on to True, rescale corresponding lengths or tilt factors and components of particle coordinates and velocities.

• rescale_all (bool) – if True, rescale all particles, not only those in the group, Default to False.

• gamma (float) – Dimensionless damping factor for the box degrees of freedom, Default to 0.

NPT integrates integrates translational and rotational degrees of freedom in the Isothermal-isobaric ensemble. The thermostat and barostat are introduced as additional degrees of freedom in the Hamiltonian that couple with the particle velocities and angular momenta and the box parameters.

The translational thermostat has a momentum $$\xi$$ and position $$\eta$$. The rotational thermostat has momentum $$\xi_{\mathrm{rot}}$$ and position $$\eta_\mathrm{rot}$$. The barostat tensor is $$\nu_{\mathrm{ij}}$$. Access these quantities using translational_thermostat_dof, rotational_thermostat_dof, and barostat_dof.

By default, NPT performs integration in a cubic box under hydrostatic pressure by simultaneously rescaling the lengths Lx, Ly and Lz of the simulation box. Set the integration mode to change this default.

The integration mode is defined by a set of couplings and by specifying the box degrees of freedom that are put under barostat control. Couplings define which diagonal elements of the pressure tensor $$P_{\alpha,\beta}$$ should be averaged over, so that the corresponding box lengths are rescaled by the same amount.

Valid couplings are:

• 'none' (all box lengths are updated independently)

• 'xy' (Lx and Ly are coupled)

• 'xz' (Lx and Lz are coupled)

• 'yz' (Ly and Lz are coupled)

• 'xyz' (Lx, Ly, and Lz are coupled)

Degrees of freedom of the box specify which lengths and tilt factors of the box should be updated, and how particle coordinates and velocities should be rescaled. The box_dof tuple controls the way the box is rescaled and updated. The first three elements box_dof[:3] controls whether the x, y, and z box lengths are rescaled and updated, respectively. The last three entries box_dof[3:] control the rescaling or the tilt factors xy, xz, and yz. All options also appropriately rescale particle coordinates and velocities.

By default, the x, y, and z degrees of freedom are updated. [True,True,True,False,False,False]

Note

If any of the diagonal x, y, z degrees of freedom is not being integrated, pressure tensor components along that direction are not considered for the remaining degrees of freedom.

For example:

• Specifying all couplings and x, y, and z degrees of freedom amounts to cubic symmetry (default)

• Specifying xy couplings and x, y, and z degrees of freedom amounts to tetragonal symmetry.

• Specifying no couplings and all degrees of freedom amounts to a fully deformable triclinic unit cell

NPT numerically integrates the equations of motion using the symplectic Martyna-Tobias-Klein equations of motion for NPT. For optimal stability, the update equations leave the phase-space measure invariant and are manifestly time-reversible.

Note

The coupling constant tau should be set within a reasonable range to avoid abrupt fluctuations in the kinetic temperature and to avoid long time to equilibration. The recommended value for most systems is $$\tau = 100 \delta t$$.

Note

The barostat coupling constant tauS should be set within a reasonable range to avoid abrupt fluctuations in the box volume and to avoid long time to equilibration. The recommend value for most systems is $$\tau_S = 1000 \delta t$$.

Important

Ensure that your initial condition includes non-zero particle velocities and angular momenta (when appropriate). The coupling between the thermostat and the velocities and angular momenta occurs via multiplication, so NPT cannot convert a zero velocity into a non-zero one except through particle collisions.

Examples:

npt = hoomd.md.methods.NPT(filter=hoomd.filter.All(), tau=1.0, kT=0.65,
tauS = 1.2, S=2.0, couple="xyz")
# orthorhombic symmetry
npt = hoomd.md.methods.NPT(filter=hoomd.filter.All(), tau=1.0, kT=0.65,
tauS = 1.2, S=2.0, couple="none")
# tetragonal symmetry
npt = hoomd.md.methods.NPT(filter=hoomd.filter.All(), tau=1.0, kT=0.65,
tauS = 1.2, S=2.0, couple="xy")
# triclinic symmetry
npt = hoomd.md.methods.NPT(filter=hoomd.filter.All(), tau=1.0, kT=0.65,
tauS = 1.2, S=2.0, couple="none", rescale_all=True)
integrator = hoomd.md.Integrator(dt=0.005, methods=[npt], forces=[lj])

filter

Subset of particles on which to apply this method.

Type

hoomd.filter.filter_like

kT

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

Type

hoomd.variant.Variant

tau

Coupling constant for the thermostat $$[\mathrm{time}]$$.

Type

float

S

Stress components set point for the barostat. In Voigt notation, $$[S_{xx}, S_{yy}, S_{zz}, S_{yz}, S_{xz}, S_{xy}]$$ $$[\mathrm{pressure}]$$. Stress can be reset after the method object is created. For example, an isotropic pressure can be set by npt.S = 4.

Type
tauS

Coupling constant for the barostat $$[\mathrm{time}]$$.

Type

float

couple

Couplings of diagonal elements of the stress tensor, can be “none”, “xy”, “xz”,”yz”, or “xyz”.

Type

str

box_dof

Box degrees of freedom with six boolean elements corresponding to x, y, z, xy, xz, yz, each.

Type

list[bool]

rescale_all

if True, rescale all particles, not only those in the group.

Type

bool

gamma

Dimensionless damping factor for the box degrees of freedom.

Type

float

translational_thermostat_dof

Additional degrees of freedom for the translational thermostat ($$\xi$$, $$\eta$$)

Type
rotational_thermostat_dof

Additional degrees of freedom for the rotational thermostat ($$\xi_\mathrm{rot}$$, $$\eta_\mathrm{rot}$$)

Type
barostat_dof

Additional degrees of freedom for the barostat ($$\nu_{xx}$$, $$\nu_{xy}$$, $$\nu_{xz}$$, $$\nu_{yy}$$, $$\nu_{yz}$$, $$\nu_{zz}$$)

Type
property barostat_energy

Energy the barostat contributes to the Hamiltonian $$[\mathrm{energy}]$$.

(Loggable: category=”scalar”)

thermalize_thermostat_and_barostat_dof()

Set the thermostat and barostat momenta to random values.

thermalize_thermostat_and_barostat_dof sets a random value for the momentum $$\xi$$ and the barostat $$\nu_{\mathrm{ij}}$$. When Integrator.integrate_rotational_dof is True, it also sets a random value for the rotational thermostat momentum $$\xi_{\mathrm{rot}}$$. Call thermalize_thermostat_and_barostat_dof to set a new random state for the thermostat and barostat.

Important

You must call Simulation.run before thermalize_thermostat_and_barostat_dof. Call run(steps=0) to prepare a newly created hoomd.Simulation.

property thermostat_energy

Energy the thermostat contributes to the Hamiltonian $$[\mathrm{energy}]$$.

(Loggable: category=”scalar”)

class hoomd.md.methods.NVE(filter)

Bases: Method

Constant volume, constant energy dynamics.

Parameters

filter (hoomd.filter.filter_like) – Subset of particles on which to apply this method.

NVE integrates integrates translational and rotational degrees of freedom in the microcanonical ensemble. The equations of motion are derived from the hamiltonian:

$H = U + K_\mathrm{translational} + K_\mathrm{rotational}$

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

Examples:

nve = hoomd.md.methods.NVE(filter=hoomd.filter.All())
integrator = hoomd.md.Integrator(dt=0.005, methods=[nve], forces=[lj])

filter

Subset of particles on which to apply this method.

Type

hoomd.filter.filter_like

class hoomd.md.methods.NVT(filter, kT, tau)

Bases: Method

Constant volume, constant temperature dynamics.

Parameters
• filter (hoomd.filter.filter_like) – Subset of particles on which to apply this method.

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

• tau (float) – Coupling constant for the Nosé-Hoover thermostat $$[\mathrm{time}]$$.

NVT integrates integrates translational and rotational degrees of freedom in the canonical ensemble using the Nosé-Hoover thermostat. The thermostat is introduced as additional degrees of freedom in the Hamiltonian that couple with the velocities and angular momenta of the particles.

The translational thermostat has a momentum $$\xi$$ and position $$\eta$$. The rotational thermostat has momentum $$\xi_{\mathrm{rot}}$$ and position $$\eta_\mathrm{rot}$$. Access these quantities using translational_thermostat_dof and rotational_thermostat_dof.

NVT numerically integrates the equations of motion using the symplectic Martyna-Tobias-Klein formalism described refs. G. J. Martyna, D. J. Tobias, M. L. Klein 1994 and J. Cao, G. J. Martyna 1996.

Note

The coupling constant tau should be set within a reasonable range to avoid abrupt fluctuations in the kinetic temperature and to avoid long time to equilibration. The recommended value for most systems is $$\tau = 100 \delta t$$.

Important

Ensure that your initial condition includes non-zero particle velocities and angular momenta (when appropriate). The coupling between the thermostat and the velocities and angular momenta occurs via multiplication, so NVT cannot convert a zero velocity into a non-zero one except through particle collisions.

Examples:

nvt=hoomd.md.methods.NVT(filter=hoomd.filter.All(), kT=1.0, tau=0.5)
integrator = hoomd.md.Integrator(dt=0.005, methods=[nvt], forces=[lj])

filter

Subset of particles on which to apply this method.

Type

hoomd.filter.filter_like

kT

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

Type

hoomd.variant.Variant

tau

Coupling constant for the Nosé-Hoover thermostat $$[\mathrm{time}]$$.

Type

float

translational_thermostat_dof

Additional degrees of freedom for the translational thermostat ($$\xi$$, $$\eta$$)

Type
rotational_thermostat_dof

Additional degrees of freedom for the rotational thermostat ($$\xi_\mathrm{rot}$$, $$\eta_\mathrm{rot}$$)

Type
thermalize_thermostat_dof()

Set the thermostat momenta to random values.

thermalize_thermostat_dof sets a random value for the momentum $$\xi$$. When Integrator.integrate_rotational_dof is True, it also sets a random value for the rotational thermostat momentum $$\xi_{\mathrm{rot}}$$. Call thermalize_thermostat_dof to set a new random state for the thermostat.

Important

You must call Simulation.run before thermalize_thermostat_dof. Call run(steps=0) to prepare a newly created hoomd.Simulation.

property thermostat_energy

Energy the thermostat contributes to the Hamiltonian $$[\mathrm{energy}]$$.

(Loggable: category=”scalar”)

class hoomd.md.methods.OverdampedViscous(filter, alpha=None)

Bases: Method

Overdamped viscous dynamics.

Parameters
• filter (hoomd.filter.filter_like) – Subset of particles to apply this method to.

• alpha (float) – When set, use $$\alpha d_i$$ for the drag coefficient where $$d_i$$ is particle diameter $$[\mathrm{mass} \cdot \mathrm{length}^{-1} \cdot \mathrm{time}^{-1}]$$. Defaults to None

OverdampedViscous integrates particles forward in time following Newtonian dynamics in the overdamped limit where there is no inertial term. (in the limit that the mass $$m$$ and moment of inertia $$I$$ go to 0):

\begin{align}\begin{aligned}\frac{d\vec{r}}{dt} &= \vec{v}\\\vec{v(t)} &= \frac{\vec{F}_\mathrm{C}}{\gamma}\\\frac{d\mathbf{q}}{dt} &= \vec{\tau}\\\tau^i &= \frac{\tau_\mathrm{C}^i}{\gamma_r^i}\end{aligned}\end{align}

where $$\vec{F}_\mathrm{C} = \vec{F}_\mathrm{net}$$ is the net force on the particle from all forces (hoomd.md.Integrator.forces) and constraints (hoomd.md.Integrator.constraints), $$\gamma$$ is the translational drag coefficient (gamma) $$\vec{v}$$ is the particle’s velocity, $$d$$ is the dimensionality of the system, $$\tau_\mathrm{C}^i$$ is the i-th component of the net torque from all forces and constraints, and $$\gamma_r^i$$ is the i-th component of the rotational drag coefficient (gamma_r).

You can set $$\gamma$$ in two ways:

1. Specify $$\alpha$$ which scales the particle diameter to $$\gamma = \alpha d_i$$.

2. After the method object is created, specify the attribute gamma and gamma_r for rotational damping or random torque to assign them directly, with independent values for each particle type in the system.

Tip

OverdampedViscous can be used to simulate systems of athermal active matter, such as athermal Active Brownian Particles.

Note

Even though OverdampedViscous models systems in the limit that $$m$$ and moment of inertia $$I$$ go to 0, you must still set non-zero moments of inertia to enable the integration of rotational degrees of freedom.

Examples:

odv = hoomd.md.methods.OverdampedViscous(filter=hoomd.filter.All())
odv.gamma.default = 2.0
odv.gamma_r.default = [1.0, 2.0, 3.0]

filter

Subset of particles to apply this method to.

Type

hoomd.filter.filter_like

alpha

When set, use $$\alpha d_i$$ for the drag coefficient where $$d_i$$ is particle diameter $$[\mathrm{mass} \cdot \mathrm{length}^{-1} \cdot \mathrm{time}^{-1}]$$.

Type

float

gamma

The drag coefficient can be directly set instead of the ratio of particle diameter ($$\gamma = \alpha d_i$$). The type of gamma parameter is either positive float or zero $$[\mathrm{mass} \cdot \mathrm{time}^{-1}]$$.

Type

TypeParameter[ particle type, float ]

gamma_r

The rotational drag coefficient can be set. The type of gamma_r parameter is a tuple of three float. The type of each element of tuple is either positive float or zero $$[\mathrm{force} \cdot \mathrm{length} \cdot \mathrm{radian}^{-1} \cdot \mathrm{time}^{-1}]$$.

Type

TypeParameter[particle type, [float, float, float]]

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