Introduction to the Network Approximation Method for Materials Modeling

Leonid Berlyand (Pennsylvania State University), Alexander G. Kolpakov, Alexei Novikov (Pennsylvania State University)

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English

Cambridge University Press
13 December 2012

Mathematics & Sciences; Applied mathematics; Mathematical modelling; Mathematical physics; Materials science; Mechanics of solids; Mechanics of fluids

Series: Encyclopedia of Mathematics and its Applications

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.

By: Leonid Berlyand (Pennsylvania State University), Alexander G. Kolpakov, Alexei Novikov (Pennsylvania State University)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 148
Dimensions: Height: 241mm, Width: 161mm, Spine: 19mm
Weight: 540g
ISBN: 9781107028234
ISBN 10: 110702823X
Series: Encyclopedia of Mathematics and its Applications
Pages: 255
Publication Date: 13 December 2012
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

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