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Introduction to the Network Approximation Method for Materials Modeling

Leonid Berlyand, Alexander G. Kolpakov, Alexei Novikov
Format
Book
Published
Cambridge : Cambridge University Press, 2013.
Language
English
Series
Encyclopedia of Mathematics and Its Applications
ISBN
9781107028234 (hardback), 110702823X (hardback)
Related Resources
Cover image
Summary
"In recent years the traditional subject of continuum mechanics has grown rapidly and many new techniques have emerged. This text provides a rigorous, yet accessible introduction to the basic concepts of the network approximation method and provides a unified approach for solving a wide variety of applied problems. As a unifying theme, the authors discuss in detail the transport problem in a system of bodies. They solve the problem of closely placed bodies using the new method of the network approximation for partial differential equations with discontinuous coefficients, developed in the 2000s by applied mathematicians in the USA and Russia. Intended for graduate students in applied mathematics and related fields such as physics, chemistry and engineering, the book is also a useful overview of the topic for researchers in these areas.In recent years the traditional subject of continuum mechanics has grown rapidly and many new techniques have emerged. This text provides a rigorous, yet accessible introduction to the basic concepts of the network approximation method and provides a unified approach for solving a wide variety of applied problems. As a unifying theme, the authors discuss in detail the transport problem in a system of bodies. They solve the problem of closely placed bodies using the new method of the network approximation for partial differential equations with discontinuous coefficients, developed in the 2000s by applied mathematicians in the USA and Russia. Intended for graduate students in applied mathematics and related fields such as physics, chemistry and engineering, the book is also a useful overview of the topic for researchers in these areas"--
Contents
  • Ch. 1. Review of mathematical notions used in the analysis of transport problems in dense-packed composite materials
  • ch. 2. Background and motivation for introduction of network models
  • ch. 3. Network approximation for boundary-value problems with discontinuous coefficients and a finite number of inclusions
  • ch. 4. Numerics for percolation and polydispersity via network models
  • ch. 5. The network approximation theorem for an infinite number of bodies
  • ch. 6. Network method for nonlinear composites
  • ch. 7. Network approximation for potentials of disks
  • ch. 8. Application of complex variables method
  • Bibliography
  • Index.
Description
xiv, 243 pages : illustrations ; 24 cm.
Notes
Includes bibliographical references and index.
Series Statement
Encyclopedia of mathematics and its applications ; 148
Technical Details
  • Access in Virgo Classic
  • Staff View

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    a| Includes bibliographical references and index.
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    a| Ch. 1. Review of mathematical notions used in the analysis of transport problems in dense-packed composite materials -- ch. 2. Background and motivation for introduction of network models -- ch. 3. Network approximation for boundary-value problems with discontinuous coefficients and a finite number of inclusions -- ch. 4. Numerics for percolation and polydispersity via network models -- ch. 5. The network approximation theorem for an infinite number of bodies -- ch. 6. Network method for nonlinear composites -- ch. 7. Network approximation for potentials of disks -- ch. 8. Application of complex variables method -- Bibliography -- Index.
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