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Precise algorithms to compute surface correlation functions of two-phase heterogeneous media and their applications

Author(s): Ma, Zheng; Torquato, Salvatore

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Abstract: © 2018 American Physical Society. The quantitative characterization of the microstructure of random heterogeneous media in d-dimensional Euclidean space Rd via a variety of n-point correlation functions is of great importance, since the respective infinite set determines the effective physical properties of the media. In particular, surface-surface Fss and surface-void Fsv correlation functions (obtainable from radiation scattering experiments) contain crucial interfacial information that enables one to estimate transport properties of the media (e.g., the mean survival time and fluid permeability) and complements the information content of the conventional two-point correlation function. However, the current technical difficulty involved in sampling surface correlation functions has been a stumbling block in their widespread use. We first present a concise derivation of the small-r behaviors of these functions, which are linked to the mean curvature of the system. Then we demonstrate that one can reduce the computational complexity of the problem, without sacrificing accuracy, by extracting the necessary interfacial information from a cut of the d-dimensional statistically homogeneous and isotropic system with an infinitely long line. Accordingly, we devise algorithms based on this idea and test them for two-phase media in continuous and discrete spaces. Specifically for the exact benchmark model of overlapping spheres, we find excellent agreement between numerical and exact results. We compute surface correlation functions and corresponding local surface-area variances for a variety of other model microstructures, including hard spheres in equilibrium, decorated "stealthy" patterns, as well as snapshots of evolving pattern formation processes (e.g., spinodal decomposition). It is demonstrated that the precise determination of surface correlation functions provides a powerful means to characterize a wide class of complex multiphase microstructures.
Publication Date: 30-Jul-2018
Citation: Ma, Z., Torquato, S. (2018). Precise algorithms to compute surface correlation functions of two-phase heterogeneous media and their applications. Physical Review E, 98 (1), 10.1103/PhysRevE.98.013307
DOI: doi:10.1103/PhysRevE.98.013307
ISSN: 2470-0045
EISSN: 2470-0053
Pages: 98, 013307-1 - 013307-17
Type of Material: Journal Article
Journal/Proceeding Title: Physical Review E
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.
Notes: Volume 98, Issue 1, 30 July 2018, Article number 013307

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