This package is a collection of correlation functions described in Salvatore Torquato's book "Random Heterogeneous Materials" ISBN 978-1-4757-6357-7. These functions can be calculated for one-, two- or three-dimensional multiphase systems using closed walls (CW) or periodic boundary conditions (PBC) along multiple directions.

CorrelationFunctions.jl incorporates correlation functions based on two- and three-point statistics. The list of supported functions includes:

  • Two point statistics:
    • Two point $S_2$ function
    • Cluster $C_2$ function
    • Surface-surface $F_{ss}$ function
    • Surface-void $F_{sv}$ function
  • Three-point statistics:
    • Three point $S_3$ function
    • Cluster $C_3$ function
    • Surface-surface-surface $F_{sss}$ function
    • Surface-surface-void $F_{ssv}$ function
    • Surface-void-void $F_{svv}$ function
  • Other functions:
    • Pore size $P$ function
    • Chord length $p$ function
    • Lineal-path $L_2$ function

Correlation functions based on two-point statistics can be calculated using two slightly different ways. The first way is to calculate them across several predefined directions (e.g. axial directions of an array). Another way is to build a correlation map, in other words to calculate a correlation function in all possible directions in a given array. The first way is implemented in CorrelationFunctions.Directional module and the second is implemented in CorrelationFunctions.Map module. Correlation functions based on three-point statistics are in the first module and are calculated in a selected set of points or using a right triangle pattern.

Here is a documentation for each of those modules and some helper functions.