Introduction to the network approximation method for materials modeling:
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 ap...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2013
|
| Series: | Encyclopedia of mathematics and its applications
volume 148 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xiv, 243 pages) |
| ISBN: | 9781139235952 |
| DOI: | 10.1017/CBO9781139235952 |
Staff View
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| 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 | |
| 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 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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| 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 |
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| discipline | Mathematik |
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| id | DE-604.BV043940951 |
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| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9781139235952 |
| language | English |
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| spelling | Berlyand, Leonid 1957- Verfasser aut 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 Cambridge Cambridge University Press 2013 1 online resource (xiv, 243 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 148 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 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 Mathematisches Modell Composite materials / Mathematical models Graph theory Differential equations, Partial Duality theory (Mathematics) Verbundwerkstoff (DE-588)4062670-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Partielle Differentialgleichung (DE-588)4044779-0 s Verbundwerkstoff (DE-588)4062670-2 s Mathematisches Modell (DE-588)4114528-8 s 1\p DE-604 Kolpakov, A. G. Sonstige oth Novikov, A. Sonstige oth Erscheint auch als Druckausgabe 978-1-107-02823-4 https://doi.org/10.1017/CBO9781139235952 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Berlyand, Leonid 1957- Introduction to the network approximation method for materials modeling 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 Mathematisches Modell Composite materials / Mathematical models Graph theory Differential equations, Partial Duality theory (Mathematics) Verbundwerkstoff (DE-588)4062670-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4062670-2 (DE-588)4044779-0 (DE-588)4114528-8 (DE-588)4113782-6 |
| title | Introduction to the network approximation method for materials modeling |
| title_auth | Introduction to the network approximation method for materials modeling |
| title_exact_search | Introduction to the network approximation method for materials modeling |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | Introduction to the network approximation method for materials modeling |
| title_sort | introduction to the network approximation method for materials modeling |
| topic | Mathematisches Modell Composite materials / Mathematical models Graph theory Differential equations, Partial Duality theory (Mathematics) Verbundwerkstoff (DE-588)4062670-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Mathematisches Modell Composite materials / Mathematical models Graph theory Differential equations, Partial Duality theory (Mathematics) Verbundwerkstoff Partielle Differentialgleichung Graphentheorie |
| url | https://doi.org/10.1017/CBO9781139235952 |
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