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DOE OSTI · 2999173

Multipoint Correlations in Poisson Media

Shelley, Alec [Stanford Univ., CA (United States)] (ORCID:0009000982222363)·Olson, Aaron Jeffrey [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)] (ORCID:0000000250362515)·Geraci, Gianluca [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)]·Tartakovsky, Daniel M. [Stanford Univ., CA (United States)] (ORCID:0000000190198935)
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Abstract

Multipoint correlations in randomly heterogeneous composite media are determined by the probability that a set of points belong to specific phases. They determine a wide range of macroscopic transport properties such as conductivity, dielectric constant, diffusion coefficient, and transmittance. The Poisson model—a random tesselation of space by hyperplanes—provides realistic descriptions of heterogeneous media in, e.g., radiation-transport applications; yet, until now, it has lacked closed-form expressions for its multipoint correlations. We resolve this problem by presenting an exact solution for the multipoint correlations in the Poisson model. By comparing it to Monte Carlo simulations of four-point correlations in three dimensions, we demonstrate the accuracy of our solution. In conclusion, we visualize the multipoint correlations and discuss their features.

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Amorphous materialsComplex mediaContinuum mechanics

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Shelley, Alec [Stanford Univ., CA (United States)] (ORCID:0009000982222363), Olson, Aaron Jeffrey [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)] (ORCID:0000000250362515), Geraci, Gianluca [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)], Tartakovsky, Daniel M. [Stanford Univ., CA (United States)] (ORCID:0000000190198935). 2025-10-09. Multipoint Correlations in Poisson Media. https://doi.org/10.1103/325k-g4dr

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