The OrnsteinZernike Module

A generic solver package for Ornstein-Zernike equations from liquid state theory

EwaldSplitting(α) <: CoulombSplitting

Splits the Coulomb potential into short-range and long-range parts using the Ewald splitting parameter α. Fields:

• α::Float64 : Ewald splitting (inverse length scale)

The short-range part is given by: ushortrange(r) = (zi * zj * ℓB / r) * erfc(α * r) The long-range part is given by: ulongrange(r) = (zi * zj * ℓB / r) * erf(α * r)

NoSplitting <: CoulombSplitting

No splitting of the Coulomb potential; the entire Coulomb potential is treated as long range.

OZSolution

Holds the solution of an Ornstein Zernike problem.

Fields:

• r: vector of distances
• k: vector of wave numbers
• gr: radial distribution function
• Sk: static structure factor
• ck: direct correlation function in k space
• cr: direct correlation function in real space
• gamma_r: indirect correlation function in real space
• gamma_k: indirect correlation function in k space

if the system was a single-component system, gr, Sk, etc, are vectors. If instead the system was a multicomponent one, they are three dimensional vectors, where the first dimension contains the values along r, and the second and third dimension contain the data for the species.

compute_compressibility(sol::OZSolution, system::SimpleFluid)

Computes the isothermal compressibility χ of the system

uses the formula 1/ρkBTχ = 1 - ρ ĉ(k=0) for single component systems and 1/ρkBTχ = 1 - ρ Σᵢⱼ ĉᵢⱼ(k=0) for mixtures. Eq. (3.6.16) in Hansen and McDonald

compute_excess_energy(sol::OZSolution,  system::SimpleUnchargedSystem)

Computes the excess energy per particle Eₓ, such that E = (dims/2kBT + Eₓ)N.

uses the formula Eₓ = 1/2 ρ ∫dr g(r) u(r) for single component systems and Eₓ = 1/2 ρ Σᵢⱼ xᵢxⱼ ∫dr gᵢⱼ(r) uᵢⱼ(r) for mixtures. Here x is the concentration fraction xᵢ=ρᵢ/sum(ρ).

compute_virial_pressure(sol::OZSolution,  system::SimpleUnchargedSystem)

Computes the pressure via the virial route

uses the formula p = kBTρ - 1/(2d) ρ^2 ∫dr r g(r) u'(r) for single component systems and p = kBT Σᵢρᵢ - 1/(2d) Σᵢⱼ ρᵢρⱼ ∫dr r gᵢⱼ(r) u'ᵢⱼ(r) for mixtures.

It handles discontinuities in the interaction potential analytically if discontinuities(potential) is defined. For additional speed/accuracy define a method of evaluate_potential_derivative(potential, r::Number) that analytically computes du/dr. By default this is done using finite differences.

dispersion_tail(potential::Potential, kBT, r, βu)

Return the dispersion long-range contribution associated with potential. The default implementation returns zero, signalling that no tail is provided.

solve(system::System, closure::Closure, method::Method)

Solves the system system using the closure closure with method method.

solve(system::System, closure::Closure)

Solves the system system using the closure closure with the default method NgIteration().