Evaluation of Bounds

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


Although some improved bounds have been in existence for nearly four decades, they have, until the recent past, lain dormant and untested because of the difficulty associated with ascertaining the various types of correlation functions involved, even for simple models (e.g., random arrays of spherical particles). Advances in the quantitative characterization of the microstructure, described in Part I of this book, have paved the way for the computation of improved bounds on the effective conductivity, effective elastic moduli, trapping constant, and fluid permeability of nontrivial models of two-phase random heterogeneous materials.


Fiber Volume Fraction Particle Volume Fraction Effective Conductivity Random Array 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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