Percolation for a model of statistically inhomogeneous random media

J. Quintanilla, Salvatore Torquato

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

We study clustering and percolation phenomena for a model of statistically inhomogeneous two-phase random media, including functionally graded materials. This model consists of inhomogeneous fully penetrable (Poisson distributed) disks and can be constructed for any specified variation of volume fraction. We quantify the transition zone in the model, defined by the frontier of the cluster of disks which are connected to the disk-covered portion of the model, by defining the coastline function and correlation functions for the coastline. We find that the behavior of these functions becomes largely independent of the specific choice of grade in volume fraction as the separation of length scales becomes large. We also show that the correlation function behaves in a manner similar to that of fractal Brownian motion. Finally, we study fractal characteristics of the frontier itself and compare to similar properties for two-dimensional percolation on a lattice. In particular, we show that the average location of the frontier appears to be related to the percolation threshold for homogeneous fully penetrable disks.

Original languageEnglish (US)
Pages (from-to)5947-5954
Number of pages8
JournalJournal of Chemical Physics
Volume111
Issue number13
DOIs
StatePublished - Oct 1 1999

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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