sarkas.potentials.moliere#

Module for handling Moliere Potential.

Potential#

The Moliere Potential is defined as

\[U(r) = \frac{q_i q_j}{4 \pi \epsilon_0} \frac{1}{r} \sum_{\alpha} C_{\alpha} e^{- b_{\alpha} r}.\]

For more details see [Wilson et al., 1977]. Note that the parameters \(b\) are not normalized by the Bohr radius. They should be passed with the correct units [m] if mks or [cm] if cgs.

Force Error#

The force error is calculated from the Yukawa’s formula with the smallest screening length.

\[\Delta F = \frac{q^2}{4 \pi \epsilon_0} \sqrt{2 \pi n b_{\textrm min} }e^{-b_{\textrm min} r_c},\]

This overestimates it, but it doesn’t matter.

Potential Attributes#

The elements of the sarkas.potentials.core.Potential.matrix are:

pot_matrix[0] = q_iq_je^2/(4 pi eps_0) Force factor between two particles.
pot_matrix[1] = C_1
pot_matrix[2] = C_2
pot_matrix[3] = C_3
pot_matrix[4] = b_1
pot_matrix[5] = b_2
pot_matrix[6] = b_3

Functions

calc_force_error_quad(a, rc, pot_matrix)

Calculate the force error by integrating the square modulus of the force over the neglected volume.n The force error is calculated from

force_error_integrand(r, pot_matrix)

Auxiliary function to be used in scipy.integrate.quad to calculate the integrand.

moliere_force(r, pot_matrix)

Numba'd function to calculate the PP force between particles using the Moliere Potential.

potential_derivatives(r, pot_matrix)

Calculate the first and second derivative of the potential.

update_params(potential)

Assign potential dependent simulation's parameters.