Source code for mdevaluate.functions

import numpy as np


def kww(t, A, τ, β):
    return A * np.exp(-(t / τ)**β)


def kww_1e(A, τ, β):
    return τ * (-np.log(1 / (np.e * A)))**(1 / β)


def cole_davidson(w, A, b, t0):
    P = np.arctan(w * t0)
    return A * np.cos(P)**b * np.sin(b * P)


def cole_cole(w, A, b, t0):
    return A * (w * t0)**b * np.sin(np.pi * b / 2) / (1 + 2 * (w * t0)**b * np.cos(np.pi * b / 2) + (w * t0)**(2 * b))


def havriliak_negami(ω, A, β, α, τ):
    r"""
    Imaginary part of the Havriliak-Negami function.

    .. math::
       \chi_{HN}(\omega) = \Im\left(\frac{A}{(1 + (i\omega\tau)^\alpha)^\beta}\right)
    """
    return -(A / (1 + (1j * ω * τ)**α)**β).imag


# fits decay of correlation times, e.g. with distance to pore walls
def colen(d, X, t8, A):
    return t8 * np.exp(A*np.exp(-d/X))


# fits decay of the plateau height of the overlap function, e.g. with distance to pore walls
def colenQ(d, X, Qb, g):
    return (1-Qb)*np.exp(-(d/X)**g)+Qb