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Introduction to the Network Approximation Method for Materials Modeling

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: December 2012
  • availability: In stock
  • format: Hardback
  • isbn: 9781107028234

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  • 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 network approximation for PDE 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.

    • Provides a unified approach for solving a wide variety of applied problems
    • Explains basic concepts through real-world examples
    • Includes results previously available only in journal publications
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    Product details

    • Date Published: December 2012
    • format: Hardback
    • isbn: 9781107028234
    • length: 255 pages
    • dimensions: 241 x 161 x 19 mm
    • weight: 0.54kg
    • contains: 65 b/w illus.
    • availability: In stock
  • Table of Contents

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

  • Authors

    Leonid Berlyand, Pennsylvania State University
    Leonid Berlyand is Professor of Mathematics and a member of the Materials Research Institute at Pennsylvania State University.

    Alexander G. Kolpakov, Università degli Studi di Cassino e del Lazio Meridionale
    Alexander G. Kolpakov holds a long term Senior Marie Curie Fellow position at the University of Cassino, Italy. He is also a Professor at the Siberian State University of Telecommunications and Informatics, Novosibirsk, Russia.

    Alexei Novikov, Pennsylvania State University
    A. Novikov is Associate Professor of Mathematics at Pennsylvania State University.

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