Cluster Expansions

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


Heterogeneous materials composed of well-defined inclusions (e.g., spheres, cylinders, ellipsoids) distributed randomly throughout a matrix material have served as excellent starting points for modeling the complex field interactions in random composites. The celebrated formulas of Maxwell (1873) and Einstein (1906) for the effective conductivity and effective viscosity of dispersions of spheres, respectively, assume that the particles do not interact with another and therefore are valid through first order in the sphere volume fraction ø 2. Similar formulas for the trapping constant of dilute distributions of traps or the fluid permeability of dilute beds of spheres can easily be obtained from the classical results of Smoluchowski (1917) and Stokes (1851), respectively, given in Chapter 17.


Effective Conductivity Cluster Expansion Ellipsoidal Inclusion Identical Sphere Effective Shear Modulus 
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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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