Variational Principles

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

Abstract

For random media of arbitrary microstructure, exact analytical solutions of the effective properties are unattainable, and so any rigorous statement about the effective properties must be in the form of rigorous bounds. To get variational bounds on effective properties, one must first express the effective parameter in terms of some functional and then formulate an appropriate variational (extremum) principle for the functional. We shall primarily deal with “energy” functionals. Once the variational principle is established, then specific bounds on the property of interest are obtained by constructing trial, or admissible, fields that conform with the variational principle. Specific bounds derived from trial fields are the subject of Chapter 21. In this chapter we will derive variational principles for the effective conductivity, effective elastic moduli, trapping constant, and fluid permeability.

Keywords

Variational Principle Effective Conductivity Energy Representation Stiffness Tensor Fluid Permeability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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