def compute_energy(particles, box_length, cut_off, constants, forcefield):
r"""Calculates the total energy of the simulation.
Parameters
----------
particles: util.particle_dt, array_like
Information about the particles.
box_length: float
Length of a single dimension of the simulation square, in Angstrom.
cut_off: float
The distance greater than which the energies between particles is
taken as zero.
constants: float, array_like (optional)
The constants associated with the particular forcefield used, e.g. for
the function forcefields.lennard_jones, theses are [A, B]
forcefield: function (optional)
The particular forcefield to be used to find the energy and forces.
Returns
-------
util.particle_dt, array_like
Information about particles, with updated accelerations and forces.
float, array_like
Current distances between pairs of particles in the simulation.
float, array_like
Current energies between pairs of particles in the simulation.
"""
pairs = int((particles["xacceleration"].size - 1) *
particles["xacceleration"].size / 2)
distances = np.zeros(pairs)
energies = np.zeros(pairs)
distances, dx, dy = heavy.dist(particles["xposition"],
particles["yposition"], box_length)
energies = forcefield(distances, constants, force=False)
energies[np.where(distances > cut_off)] = 0.0
return distances, energies
def test_dist(self):
xpos = np.array([0, 1])
ypos = np.array([0, 1])
box_length = 5.
dr, dx, dy = comp.dist(xpos, ypos, box_length)
assert_almost_equal(dr, [np.sqrt(2)])
assert_almost_equal(dx, [-1])
assert_almost_equal(dy, [-1])
def compute_force(particles, box_length, cut_off, constants, forcefield, mass):
r"""Calculates the forces and therefore the accelerations on each of the
particles in the simulation.
Parameters
----------
particles: util.particle_dt, array_like
Information about the particles.
box_length: float
Length of a single dimension of the simulation square, in Angstrom.
cut_off: float
The distance greater than which the forces between particles is taken
as zero.
constants: float, array_like (optional)
The constants associated with the particular forcefield used, e.g. for
the function forcefields.lennard_jones, theses are [A, B]
forcefield: function (optional)
The particular forcefield to be used to find the energy and forces.
mass: float (optional)
The mass of the particle being simulated (units of atomic mass units).
Returns
-------
util.particle_dt, array_like
Information about particles, with updated accelerations and forces.
float, array_like
Current distances between pairs of particles in the simulation.
float, array_like
Current forces between pairs of particles in the simulation.
float, array_like
Current energies between pairs of particles in the simulation.
"""
particles["xacceleration"] = np.zeros(particles["xacceleration"].size)
particles["yacceleration"] = np.zeros(particles["yacceleration"].size)
pairs = int((particles["xacceleration"].size - 1) *
particles["xacceleration"].size / 2)
forces = np.zeros(pairs)
distances = np.zeros(pairs)
energies = np.zeros(pairs)
atomic_mass_unit = 1.660539e-27 # kilograms
mass_amu = mass # amu
mass_kg = mass_amu * atomic_mass_unit # kilograms
distances, dx, dy = heavy.dist(particles["xposition"],
particles["yposition"], box_length)
forces = forcefield(distances, constants, force=True)
energies = forcefield(distances, constants, force=False)
forces[np.where(distances > cut_off)] = 0.0
energies[np.where(distances > cut_off)] = 0.0
particles = update_accelerations(particles, forces, mass_kg, dx, dy,
distances)
return particles, distances, forces, energies
def calculate_pressure(particles, box_length, temperature, cut_off, constants,
forcefield):
r"""Calculates the instantaneous pressure of the simulation cell, found
with the following relationship:
.. math::
p = \langle \rho k_b T \rangle + \bigg\langle \frac{1}{3V}\sum_{i}
\sum_{j<i} \mathbf{r}_{ij}\mathbf{f}_{ij} \bigg\rangle
Parameters
----------
particles: util.particle_dt, array_like
Information about the particles.
box_length: float
Length of a single dimension of the simulation square, in Angstrom.
temperature: float
Instantaneous temperature of the simulation.
cut_off: float
The distance greater than which the forces between particles is taken
as zero.
constants: float, array_like (optional)
The constants associated with the particular forcefield used, e.g. for
the function forcefields.lennard_jones, theses are [A, B]
forcefield: function (optional)
The particular forcefield to be used to find the energy and forces.
Returns
-------
float:
Instantaneous pressure of the simulation.
"""
distances, dx, dy = heavy.dist(particles["xposition"],
particles["yposition"], box_length)
forces = forcefield(distances, constants, force=True)
forces[np.where(distances > cut_off)] = 0.0
pres = np.sum(forces * distances)
boltzmann_constant = 1.3806e-23 # joules / kelvin
pres = 1.0 / (2 * box_length * box_length) * pres + (
particles["xposition"].size /
(box_length * box_length) * boltzmann_constant * temperature)
return pres