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

Abstract

The quantitative characterization of the microstructure of random heterogeneous media in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ 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 $F_{ss}$ and surface-void $F_{sv}$ 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 \textit{mean curvature} of the system. Then we demonstrate that one can reduce the computational complexity of the problem by extracting the necessary interfacial information from a cut of the 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.

References in corpus (16)

• Is Random Close Packing of Spheres Well Defined?
• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Reconstruction of three-dimensional porous media using generative adversarial neural networks
• Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles
• A Superior Descriptor of Random Textures and Its Predictive Capacity
• Modeling Heterogeneous Materials via Two-Point Correlation Functions: II. Algorithmic Details and Applications
• Hyperuniformity in point patterns and two-phase random heterogeneous media
• Hyperuniformity and its Generalizations
• Inferring low-dimensional microstructure representations using convolutional neural networks
• Precise Algorithm to Generate Random Sequential Addition of Hard Hyperspheres at Saturation
• Transport, Geometrical and Topological Properties of Stealthy Disordered Hyperuniform Two-Phase Systems
• Random Scalar Fields and Hyperuniformity
• Exactly Solvable Disordered Sphere-Packing Model in Arbitrary-Dimension Euclidean Spaces
• Disordered Hyperuniform Heterogeneous Materials
• Improved reconstructions of random media using dilation and erosion processes
• Characterization of Maximally Random Jammed Sphere Packings: II. Correlation Functions and Density Fluctuations

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• Adaptive phase-retrieval stochastic reconstruction with correlation functions: 3D images from 2D cuts
• Generation and Structural Characterization of Debye Random Media
• Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media
• Information Content of Hierarchical n-Point Polytope Functions for Quantifying and Reconstructing Disordered Systems
• A New Framework for Interfacial Statistics: Exact n-Point Correlations of Gaussian Level Sets
• Understanding Degeneracy of Two-Point Correlation Functions via Debye Random Media