Introduction to the Network Approximation Method for Materials Modeling

Erscheinungsjahr 2012
ISBN: 978-1-107-02823-4
Verlag: Cambridge University Press

Buch, Englisch, Band 148, 255 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 602 g

Reihe: 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.

Autoren/Hrsg.

Berlyand, Leonid

Kolpakov, Alexander G.

Novikov, Alexei

Fachgebiete

• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Werkstoffkunde, Materialwissenschaft: Forschungsmethoden

Inhaltsverzeichnis

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.

Über Autor(innen)

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

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

Kolpakov, Alexander G.
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.

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.