Useful Quantities#
Describes different physical quantities.
Forces#
Structural Features#
- jax_md.quantity.cosine_angles(dR)[source]#
Returns cosine of angles for all atom triplets.
- Parameters
dR (
Array) – Matrix of displacements;ndarray(shape=[num_atoms, num_neighbors, spatial_dim]).- Return type
Array- Returns
Tensor of cosine of angles;
ndarray(shape=[num_atoms, num_neighbors, num_neighbors]).
- jax_md.quantity.pair_correlation(displacement_or_metric, radii, sigma, species=None, eps=1e-07, compute_average=False)[source]#
Computes the pair correlation function at a mesh of distances.
The pair correlation function measures the number of particles at a given distance from a central particle. The pair correlation function is defined by
\[g(r) = <\sum_{i \neq j}\delta(r - |r_i - r_j|)>\]We make the approximation,
\[\delta(r) \approx {1 \over \sqrt{2\pi\sigma^2}e^{-r / (2\sigma^2)}}\]- Parameters
displacement_or_metric (
Union[Callable[[Array,Array],Array],Callable[[Array,Array],float]]) – A function that computes the displacement or distance between two points.radii (
Array) – An array of radii at which we would like to compute \(g(r)\).sigima – A float specifying the width of the approximating Gaussian.
species (
Optional[Array]) – An optional array specifying the species of each particle. If species is None then we compute a single \(g(r)\) for all particles, otherwise we compute one \(g(r)\) for each species.eps (
float) – A small additive constant used to ensure stability if the radius is zero.
- Returns
A function
g_fnthat computes the pair correlation function for a collection of particles.
\(g(r)\) is calculated separately for each particle. For species=None, the output of
g_fnis an array of shape (N, nr), where N is the number of particles passed tog_fnand nr is the size of radii (the number of points at which we calculate \(g(r)\). When species is specified, the output is a list of nspecies arrays, each of shape (N, nr), where nspecies is the number of unique species. Ifgofris the output ofg_fn, then gofr[si][i] gives the \(g(r)\) for particle i considering only pair particles of species si.Note: when species is specified, the returned list is in the order of the sorted unique species indices, not the order in which they appear.
- jax_md.quantity.pair_correlation_neighbor_list(displacement_or_metric, box_size, radii, sigma, species=None, dr_threshold=0.5, eps=1e-07, fractional_coordinates=False, format=NeighborListFormat.Dense, compute_average=False)[source]#
Computes the pair correlation function at a mesh of distances.
The pair correlation function measures the number of particles at a given distance from a central particle. The pair correlation function is defined by
\[g(r) = <\sum_{i \neq j}\delta(r - |r_i - r_j|)>\]We make the approximation,
\[\delta(r) \approx {1 \over \sqrt{2\pi\sigma^2}e^{-r / (2\sigma^2)}}\]This function uses neighbor lists to speed up the calculation.
- Parameters
displacement_or_metric (
Union[Callable[[Array,Array],Array],Callable[[Array,Array],float]]) – A function that computes the displacement or distance between two points.box_size (
Array) – The size of the box containing the particles.radii (
Array) – An array of radii at which we would like to compute \(g(r)\).sigima – A float specifying the width of the approximating Gaussian.
species (
Optional[Array]) – An optional array specifying the species of each particle. If species is None then we compute a single \(g(r)\) for all particles, otherwise we compute one \(g(r)\) for each species.dr_threshold (
float) – A float specifying the halo size of the neighbor list.eps (
float) – A small additive constant used to ensure stability if the radius is zero.fractional_coordinates (
bool) – Bool determining whether positions are stored in the unit cube or not.format (
NeighborListFormat) – The format of the neighbor lists. Must beDenseorSparse.
- Returns
neighbor_fnthat constructs a neighbor list (seeneighbor_listinpartition.pyfor details).g_fnthat computes the pair correlation function for a collection of particles given their position and a neighbor list.- Return type
A pair of functions
\(g(r)\) is calculated separately for each particle. For species=None, the output of
g_fnis an array of shape (N, nr), where N is the number of particles passed tog_fnand nr is the size of radii (the number of points at which we calculate \(g(r)\). When species is specified, the output is a list of nspecies arrays, each of shape (N, nr), where nspecies is the number of unique species. Ifgofris the output ofg_fn, then gofr[si][i] gives the \(g(r)\) for particle i considering only pair particles of species si.Note: when species is specified, the returned list is in the order of the sorted unique species indices, not the order in which they appear.
- jax_md.quantity.phop(displacement, window_size)[source]#
Computes the phop indicator of rearrangements.
phop is an indicator function that is effective at detecting when particles in a quiescent system have experienced a rearrangement. Qualitatively, phop measures when the average position of a particle has changed significantly.
Formally, given a window of size \(\Delta t\) we two averages before and after the current time,
\[E_A[f] = E_{t\in[t - \Delta t / 2, t]}[f(t)] E_B[f] = E_{t\in[t, t + \Delta t / 2]}[f(t)].\]In terms of these expectations, phop is given by,
\[phop = \sqrt{E_A[(R_i(t) - E_B[R_i(t)])^2]E_B[(R_i(t) - E_A[R_i(t)])^2]}\]phop was first introduced in Candelier et al. 1
- Parameters
- Return type
Tuple[Callable[[Array],PHopState],Callable[[PHopState,Array],PHopState]]- Returns
A pair of functions,
(init_fn, update_fn)that initialize the state of a phop measurement and update the state of a phop measurement to include new positions.
References
- 1
R. Candelier et al. “Spatiotemporal Hierarchy of Relaxation Events, Dynamical Heterogeneities, and Structural Reorganization in a Supercooled Liquid” Physical Review Letters 105, 135702 (2010).
Physical Properties#
- jax_md.quantity.kinetic_energy(*unused_args, momentum=None, velocity=None, mass=1.0)[source]#
Computes the kinetic energy of a system.
To avoid ambiguity, either momentum or velocity must be passed explicitly as a keyword argument.
- jax_md.quantity.temperature(*unused_args, momentum=None, velocity=None, mass=1.0)[source]#
Computes the temperature of a system.
To avoid ambiguity, either momentum or velocity must be passed explicitly as a keyword argument.
- Parameters
- Return type
- Returns
The temperature of the system in units of the Boltzmann constant.
- jax_md.quantity.pressure(energy_fn, position, box, kinetic_energy=0.0, **kwargs)[source]#
Computes the internal pressure of a system.
- Parameters
energy_fn (
Callable[…,Array]) – A function that computes the energy of the system. This function must take as an argumentperturbationwhich perturbs the box shape. Any energy function constructed usingsmapor inenergy.pywith a standard space will satisfy this property.position (
Array) – An array of particle positions.box (
Array) – A box specifying the shape of the simulation volume. Used to infer the volume of the unit cell.kinetic_energy (
float) – A float specifying the kinetic energy of the system.
- Return type
- Returns
A float specifying the pressure of the system.
- jax_md.quantity.stress(energy_fn, position, box, mass=1.0, velocity=None, **kwargs)[source]#
Computes the internal stress of a system.
- Parameters
energy_fn (
Callable[…,Array]) – A function that computes the energy of the system. This function must take as an argumentperturbationwhich perturbs the box shape. Any energy function constructed usingsmapor inenergy.pywith a standard space will satisfy this property.position (
Array) – An array of particle positions.box (
Array) – A box specifying the shape of the simulation volume. Used to infer the volume of the unit cell.mass (
Array) – The mass of the particles; only used to compute the kinetic contribution ifvelocityis notNone.velocity (
Optional[Array]) – An array of atomic velocities.
- Return type
Array- Returns
A float specifying the pressure of the system.