Unified Approach to Characterize Microstructure

  • Salvatore Torquato
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 16)


A unified and general formalism has been developed by Torquato (1986c) to characterize statistically the microstructure of heterogeneous materials composed of d-dimensional spherical inclusions distributed throughout a matrix phase. He accomplished this by introducing a general n-point correlation function H n and by deriving two different series representations for it in terms of the probability density functions that characterize the particle configurations (quantities that are known, in principle). This methodology provides a means of calculating any of the various types of microstructural correlation functions that have arisen in rigorous expressions for the transport, electromagnetic, and transport properties (see Chapter 2 and Part II) for such nontrivial models of two-phase disordered media as well as generalizations of these correlation functions. For this reason, H n is referred to as the canonical n-point correlation function.).


Correlation Function Test Particle Series Representation Spherical Inclusion Identical Sphere 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Salvatore Torquato
    • 1
  1. 1.Department of Chemistry and Princeton Materials InstitutePrinceton UniversityPrincetonUSA

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