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020 a| 9781107028234 (hardback);

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084 a| MAT0000002| bisacsh;

100 1 a| Berlyand, Leonid,d| 1957-=| ^A1169842;

245 10 a| Introduction to the network approximation method for materials modelingh| [electronic resource] /c| Leonid Berlyand, Pennsylvania State University, Alexander G. Kolpakov, Università degli Studi di Cassino e del Lazio Meridionale, Alexei Novikov, Pennsylvania State University.;

260 a| Cambridge, UK :b| Cambridge University Press,c| 2013.;

300 a| xiv, 243 pages :b| illustrations ;c| 24 cm.;

490 0 a| Encyclopedia of mathematics and its applications ;v| 148;

504 a| Includes bibliographical references (pages 228-241) and index.;

505 8 a| 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.;

506 a| Available only to authorized users.;

520 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 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Composite materialsx| Mathematical models.=| ^A51796;

650 0 a| Graph theory.=| ^A31040;

650 0 a| Differential equations, Partial.=| ^A20205;

650 0 a| Duality theory (Mathematics)=| ^A65736;

650 7 a| MATHEMATICS / General.2| bisacsh;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Kolpakov, A. G.=| ^A812816;

700 1 a| Novikov, A.q| (Alexei)=| ^A1169841;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=1057535;

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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.

Author/creator	Berlyand, Leonid, 1957-
Other author	Kolpakov, A. G.
Other author	Novikov, A. (Alexei)
Format	Electronic
Publication Info	Cambridge, UK : Cambridge University Press, 2013.
Description	xiv, 243 pages : illustrations ; 24 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Composite materials--Mathematical models. Graph theory. Differential equations, Partial. Duality theory (Mathematics)

Series	Encyclopedia of mathematics and its applications ; 148
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.
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 228-241) and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2012029156
ISBN	9781107028234 (hardback)
ISBN	110702823X (hardback)

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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.

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