hpmc.external.field

Overview

Harmonic

Restrain particle positions and orientations with harmonic springs.

Details

Apply external fields to HPMC simulations.

class hoomd.hpmc.external.field.Harmonic(reference_positions, reference_orientations, k_translational, k_rotational, symmetries)

Restrain particle positions and orientations with harmonic springs.

Parameters

• reference_positions ((N_particles, 3) numpy.ndarray of float) – the reference positions to which particles are restrained \([\mathrm{length}]\).

• reference_orientations ((N_particles, 4) numpy.ndarray of float) – the reference orientations to which particles are restrained \([\mathrm{dimensionless}]\).

• k_translational (hoomd.variant.Variant or float) – translational spring constant \([\mathrm{energy} \cdot \mathrm{length}^{-2}]\).

• k_rotational (hoomd.variant.Variant or float) – rotational spring constant \([\mathrm{energy}]\).

• symmetries ((N_symmetries, 4) numpy.ndarray of float) – the orientations that are equivalent through symmetry, i.e., the rotation quaternions that leave the particles unchanged. At a minimum, the identity quaternion ([1, 0, 0, 0]) must be included here \([\mathrm{dimensionless}]\).

Harmonic specifies that harmonic springs are used to restrain the position and orientation of every particle:

\[ \begin{align}\begin{aligned}\begin{split}V_\mathrm{translational} = \sum_i^{N_\mathrm{particles}} \frac{1}{2} k_{translational} \cdot (\vec{r}_i-\vec{r}_{0,i})^2 \\\end{split}\\V_\mathrm{rotational} = \sum_i^{N_\mathrm{particles}} \frac{1}{2} k_{rotational} \cdot \min_j \left[ (\mathbf{q}_i-\mathbf{q}_{0,i} \cdot \mathbf{q}_{\mathrm{symmetry},j})^2 \right]\end{aligned}\end{align} \]

where \(k_{translational}\) and \(k_{rotational}\) correspond to the parameters k_translational and k_rotational, respectively, \(\vec{r}_i\) and \(\mathbf{q}_i\) are the position and orientation of particle \(i\), the \(0\) subscripts denote the given reference quantities, and \(\mathbf{q}_{\mathrm{symmetry}}\) is the given set of symmetric orientations from the symmetries parameter.

Note

Harmonic does not support execution on GPUs.

k_translational

The translational spring constant \([\mathrm{energy} \cdot \mathrm{length}^{-2}]\).

Type

hoomd.variant.Variant

k_rotational

The rotational spring constant \([\mathrm{energy}]\).

Type

hoomd.variant.Variant

reference_positions

The reference positions to which particles are restrained \([\mathrm{length}]\).

Type

(N_particles, 3) numpy.ndarray of float

reference_orientations

The reference orientations to which particles are restrained \([\mathrm{dimensionless}]\).

Type

(N_particles, 4) numpy.ndarray of float

symmetries

The orientations that are equivalent through symmetry, i.e., the rotation quaternions that leave the particles unchanged \([\mathrm{dimensionless}]\).

Type

(N_symmetries, 4) numpy.ndarray of float

property energy

The total energy of the harmonic field [mathrm{energy}]`.

\(V_\mathrm{translational} + V_\mathrm{rotational}\)

(Loggable: category=”scalar”)

Type

float

property energy_rotational

The energy associated with rotational fluctuations \([\mathrm{energy}]\).

\(V_\mathrm{rotational}\)

(Loggable: category=”scalar”)

Type

float

property energy_translational

The energy associated with positional fluctuations \([\mathrm{energy}]\).

\(V_\mathrm{translational}\)

(Loggable: category=”scalar”)

Type

float