Rigorous Bounds

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


Since it is generally impossible to determine exactly the effective properties of random heterogeneous media, any rigorous statements about effective properties must take the form of bounds. In Chapter 14 we formulated variational (extremum) principles for the effective properties that are given in terms of trial fields. Here we will derive specific existing bounds on the effective conductivity, effective elastic moduli, trapping constant, and fluid permeability by constructing specific trial fields that conform with the variational principles.


Effective Conductivity Pade Approximant Effective Shear Modulus Effective Bulk Modulus Anisotropic Composite 
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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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