Stochastic (re)constructions of non-stationary material structures: Using ensemble averaged correlation functions and non-uniform phase distributions

Abstract

Depending on the spatial distribution of mass or phases within the studied materials, they can be classified into two distinct property types: stationary and non-stationary. Stochastic reconstruction with simulated annealing and correlation functions is a powerful technique to produce material structural images from limited input data, but they usually deal with statistically homogeneous images only. In this work we show that the alteration of the initial phase distributions before starting annealing can produce non-stationary structures. The degree of such non-stationarity depends on numerous parameters of the annealing, including maximum correlation length, the choice of correlation function weights, annealing cooling schedule, in a convoluted manner—this makes it impossible to segregate the influence of each parameter. In general, we have shown that it is possible to choose such parameters in order to suppress the inhomogeneity of the resulting replicas. The degree of stationarity of the stochastic reconstructions had a significant influence on the physical properties of the reconstructed binary structures—computed full permeability tensors showed different degree of anisotropy and off-diagonal terms values depending on the reconstruction parameters. The proposed approach to produce non-stationary structures from ensemble averaged set of correlation functions opens numerous ways to attack theoretical and practical problems with natural and artificial materials with statistically inhomogeneous structure.