Lineal measures of clustering in overlapping particle systems

Journal Article · Tue Oct 01 04:00:00 EDT 1996 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.54.4027· OSTI ID:392010

Quintanilla, J; Torquato, S ^[1]

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1. Princeton Materials Institute and Department of Civil Engineering and Operations Research, Princeton, New Jersey 08544 (United States)

The lineal-path function {ital L}({ital z}) gives the probability of finding a line segment of length {ital z} entirely in one of the phases of a disordered multiphase medium. We develop an exact methodology to determine {ital L}({ital z}) for the particle phase of systems of overlapping particles, thus providing a measure of particle clustering in this prototypical model of continuum percolation. We describe this procedure for systems of overlapping disks and spheres with a polydispersivity of sizes and for randomly aligned equal-sized overlapping squares. We also study the effect of polydispersivity on the range of the lineal-path function. We note that the lineal-path function {ital L}({ital z}) is a rigorous lower bound on the two-point cluster function {ital C}{sub 2}({ital z}), which is not available analytically for overlapping particle models for spatial dimension {ital d}{ge}2. By evaluating the second derivative of {ital L}({ital z}), we then evaluate the chord-length distribution function for the particle phase. Computer simulations that we perform are in excellent agreement with our theoretical results. {copyright} {ital 1996 The American Physical Society.}

• DOE Contract Number: FG02-92ER14275
• OSTI ID: 392010
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 4 Vol. 54; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
AGGLOMERATION
EVALUATION
FLUID FLOW
MICROSTRUCTURE
OBSERVABLES
PERCOLATION CLUSTERS
POROUS MATERIALS