Harmonic

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

Bases: External

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

• k_rotational (hoomd.variant.variant_like) – 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 computes harmonic spring energies between the particle positions/orientations and given reference positions/orientations:

\[\begin{split}U_{\mathrm{external},i} & = U_{\mathrm{translational},i} + U_{\mathrm{rotational},i} \\ U_{\mathrm{translational},i} & = \frac{1}{2} k_{translational} \cdot (\vec{r}_i-\vec{r}_{0,i})^2 \\ U_{\mathrm{rotational},i} & = \frac{1}{2} k_{rotational} \cdot \min_j \left[ (\mathbf{q}_i-\mathbf{q}_{0,i} \cdot \mathbf{q}_{\mathrm{symmetry},j})^2 \right]\end{split}\]

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.

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Members inherited from External:

property energy

Potential energy contributed by this potential \([\mathrm{energy}]\). Read more...

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Members defined in Harmonic:

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