The Study Of Random Heterogeneous Materials Is An Exciting And Rapidly Growing Multidisciplinary Endeavor. This Field Demands A Unified Rigorous Means Of Characterizing The Microstructures And Macroscopic Properties Of The Widely Diverse Types Of Heterogeneous Materials That Abound In Nature And Synthetic Products. This Book Is The First Of Its Kind To Provide Such An Approach. Emphasis Is Placed On Foundational Theoretical Methods That Can Simultaneously Yield Results Of Practical Utility. The First Part Of The Book Deals With The Quantitive Characterization Of The Microstructure Of Heterogeneous Materials. The Second Part Of The Book Treats A Wide Variety Of Macroscopic Transport, Electromagnetic, Mechanical, And Chemical Properties Of Heterogeneous Materials And Describes How They Are Linked To The Microstructure Of Model And Real Materials. Contemporary Topics Covered Include The Statistical Mechanics Of Many-partical Systems, The Canonical N-point Correlation Function, Percolation Theory, Computer-simulation Methods, Image Analyses And Reconstructions Of Real Materials, Homogenization Theory, Exact Property Predictions, Variational Bounds, Expansion Techniques, And Cross Property Relations. This Clear And Authoritative Volume Will Be Of Particular Interest To Graduate Students And Researchers In Applied Mathematics, Physics, Chemistry, Material Sciences, Engineering, Geophysics, And Biology. Moreover, The Book Is Self-contained And Approachable By Nonspecialist. Salvatore Torquato Is A Professor In The Department Of Chemistry And In The Materials Institute At Princeton University. He Also Holds Affiliated Appointments At Princeton University In Applied And Computational Mathematics Program And In Chemical Engineering. Among Other Honors, He Was A John Simon Guggenheim Fellow In 1998. He Has Published Over Two Hundred Journal Articles Across A Variety Of Scientific Disciplines. Part I. Microstructural Characterization: Microstructural Descriptors. Statistical Mechanics Of Particle Systems. Unified Approach. Monodisperse Spheres. Polydisperse Spheres -- Anisotropic Media. Cell And Random-field Models. Percolation And Clustering. Some Continuum Percolation Results. Local Volume Fraction Fluctuation. Computer Simulation And Image Analysis -- Part Ii. Microstructure Property Connections: Local And Homogenized Equations. Variational Principles. Phase-interchange Relations. Exact Results. Single-inclusion Solutions. Effective Medium Approximations. Cluster Expansions. Exact Contrast Expansions. Rigorous Bounds. Evaluation Of Bounds. Cross-property Relations. By Salvatore Torquato.

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by Salvatore Torquato

Torquato, Salvatore

Springer New York : Imprint: Springer

Springer Nature

Springer US

Copernicus

Telos

Interdisciplinary Applied Mathematics -- 16, Interdisciplinary applied mathematics -- 16., New York, NY, United States, 2002

Interdisciplinary applied mathematics, vol. 16, 2nd print, Corr. 2nd printing, New York, 2006

Interdisciplinary applied mathematics -- v. 16., New York, New York State, 2002

Interdisciplinary applied mathematics, vol. 16, New York, cop. 2002

Softcover reprint of the original 1st ed. 2002, New York, NY, 2013

United States, United States of America

Springer Nature, New York, NY, 2013

Corrected, US, 2001

October 25, 2005

4, 20130417

sm23216630

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Includes bibliographical references (p. [663]-692) and index.

Online full text is restricted to subscribers.
Also available in print.
Mode of access: World Wide Web.

<p>The study of random heterogeneous materials is an exciting and rapidly growing multidisciplinary endeavor. This field demands a unified rigorous means of characterizing the microstructures and macroscopic properties of the widely diverse types of heterogeneous materials that abound in nature and synthetic products. This book is the first of its kind to provide such an approach. Emphasis is placed on foundational theoretical methods that can simultaneously yield results of practical utility.</p>
<p>The first part of the book deals with the quantitive characterization of the microstructure of heterogeneous materials. The second part of the book treats a wide variety of macroscopic transport, electromagnetic, mechanical, and chemical properties of heterogeneous materials and describes how they are linked to the microstructure of model and real materials. Contemporary topics covered include the statistical mechanics of many-partical systems, the canonical n-point correlation function, percolation theory, computer-simulation methods, image analyses and reconstructions of real materials, homogenization theory, exact property predictions, variational bounds, expansion techniques, and cross property relations.</p>
<p>This clear and authoritative volume will be of particular interest to graduate students and researchers in applied mathematics, physics, chemistry, material sciences, engineering, geophysics, and biology. Moreover, the book is self-contained and approachable by nonspecialist.</p>
<p>Salvatore Torquato is a professor in the Department of Chemistry and in the Materials Institute at Princeton University. He also holds affiliated appointments at Princeton University in applied and Computational Mathematics Program and in Chemical Engineering. Among other honors, he was a John Simon Guggenheim Fellow in 1998. He has published over two hundred journal articles across a variety of scientific disciplines.</p>

Front Matter....Pages i-xxi
Motivation and Overview....Pages 1-19
Front Matter....Pages 21-21
Microstructural Descriptors....Pages 23-58
Statistical Mechanics of Many-Particle Systems....Pages 59-95
Unified Approach to Characterize Microstructure....Pages 96-118
Monodisperse Spheres....Pages 119-159
Polydisperse Spheres....Pages 160-176
Anisotropic Media....Pages 177-187
Cell and Random-Field Models....Pages 188-209
Percolation and Clustering....Pages 210-233
Some Continuum Percolation Results....Pages 234-256
Local Volume Fraction Fluctuations....Pages 257-268
Computer Simulations, Image Analyses, and Reconstructions....Pages 269-302
Front Matter....Pages 303-303
Local and Homogenized Equations....Pages 305-356
Variational Principles....Pages 357-389
Phase-Interchange Relations....Pages 390-402
Exact Results....Pages 403-436
Single-Inclusion Solutions....Pages 437-458
Effective-Medium Approximations....Pages 459-484
Cluster Expansions....Pages 485-508
Exact Contrast Expansions....Pages 509-551
Front Matter....Pages 303-303
Rigorous Bounds....Pages 552-592
Evaluation of Bounds....Pages 593-631
Cross-Property Relations....Pages 632-655
Equilibrium Hard-Disk Program....Pages 656-660
Interrelations Among Two- and Three-Dimensional Moduli....Pages 661-662
Back Matter....Pages 663-703

The interdisciplinary subject of random heterogeneous materials has experienced remarkable growth since the publication of the well-known monograph Statistical Con tinuum Theories by Beran ( 1968). Many of these advances, especially those concerning the statistical characterization of the microstructure and its effect on the physical prop erties of the material, have not been treated fully in any book. One of the intents of the present book is to fill this gap. This book also distinguishes itself in that it provides a unified rigorous framework to characterize the microstructures and macroscopic properties of the widely diverse types of heterogeneous materials found in nature and synthetic products. Emphasis is placed on providing foundational theoretical methods that can simultaneously yield results of practical utility. This book treats a wide breadth of topics, but the choice of subjects naturally reflects my own interests. The sheer enormity of the field has prevented me from covering many important topics. I apologize to those colleagues, known and unknown, who may not find enough of their own work cited in the ensuing pages.
Erscheinungsdatum: 19.10.2001

The interdisciplinary subject of random heterogeneous materials has experienced remarkable growth since the publication of the well-known monograph Statistical Con tinuum Theories by Beran ( 1968). Many of these advances, especially those concerning the statistical characterization of the microstructure and its effect on the physical prop erties of the material, have not been treated fully in any book. One of the intents of the present book is to fill this gap. This book also distinguishes itself in that it provides a unified rigorous framework to characterize the microstructures and macroscopic properties of the widely diverse types of heterogeneous materials found in nature and synthetic products. Emphasis is placed on providing foundational theoretical methods that can simultaneously yield results of practical utility. This book treats a wide breadth of topics, but the choice of subjects naturally reflects my own interests. The sheer enormity of the field has prevented me from covering many important topics. I apologize to those colleagues, known and unknown, who may not find enough of their own work cited in the ensuing pages.
Erscheinungsdatum: 22.03.2013

This accessible text presents a unified approach of treating the microstructure and effective properties of heterogeneous media. Part I deals with the quantitative characterization of the microstructure of heterogeneous via theoretical methods; Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the microstructure, accomplished by using rigorous methods.

Heterogeneous materials consist of domains of different materials or the same material in different states. This interdisciplinary book on the mathematics of material science concerns the development of macroscopic equations for heterogeneous materials all from a macroscopic view point. Covers the latest advances in the field, written in an easy to comprehend Scientific American style.

"This volume will be of particular interest to graduate students and researchers in applied mathematics, physics, chemistry, materials sciences, engineering, geophysics, and biology. Moreover, the book is self-contained and approachable by the nonspecialist."--BOOK JACKET.

2013-08-01