Introduction to the network approximation method for materials modeling / Leonid Berlyand, Pennsylvania State University, Alexander G. Kolpakov, Università degli Studi di Cassino e del Lazio Meridionale, Alexei Novikov, Pennsylvania State University.

Berlyand, Leonid, 1957-

Call Number	620.1/18015115
Author	Berlyand, Leonid, 1957- author.
Title	Introduction to the network approximation method for materials modeling / Leonid Berlyand, Pennsylvania State University, Alexander G. Kolpakov, Università degli Studi di Cassino e del Lazio Meridionale, Alexei Novikov, Pennsylvania State University.
Physical Description	1 online resource (xiv, 243 pages) : digital, PDF file(s).
Series	Encyclopedia of mathematics and its applications ; volume 148
Notes	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Contents	Machine generated contents note: 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.
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 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.
Added Author	Kolpakov, A. G., author. Novikov, A. author.
Subject	Composite materials Mathematical models. GRAPH THEORY. DIFFERENTIAL EQUATIONS, PARTIAL. DUALITY THEORY (MATHEMATICS)
Multimedia	https://doi.org/10.1017/CBO9781139235952

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$a 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.

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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 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.
Notes	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Contents	Machine generated contents note: 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.
Subject	Composite materials Mathematical models. GRAPH THEORY. DIFFERENTIAL EQUATIONS, PARTIAL. DUALITY THEORY (MATHEMATICS)
Multimedia	https://doi.org/10.1017/CBO9781139235952