Professor Leonid Berlyand, Professor Alexander G. Kolpakov, Dr Alexei NovikovCambridge University Press, 12/13/2012EAN 9781107028234, ISBN10: 110702823XHardcover, 255 pages, 24.1 x 16.1 x 1.9 cmLanguage: EnglishIn 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.Preface1. Review of mathematical notions used in the analysis of transport problems in dense-packed composite materials2. Background and motivation for introduction of network models3. Network approximation for boundary-value problems with discontinuous coefficients and a finite number of inclusions4. Numerics for percolation and polydispersity via network models5. The network approximation theorem for an infinite number of bodies6. Network method for nonlinear composites7. Network approximation for potentials of disks8. Application of complex variables methodBibliographyIndex.
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