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Author:   Salvatore Torquato
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1st ed. 2001. Corr. 2nd printing 2001
Volume:   16
Dimensions:   Width: 17.80cm , Height: 3.90cm , Length: 23.50cm
Weight:   1.428kg
ISBN:  

9780387951676

ISBN 10:   0387951679
Pages:   703
Publication Date:   19 October 2001
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Replaced By:   9780387740324
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

1 Motivation and Overview.- 2 Microstructural Descriptors.- 3 Statistical Mechanics of Many-Particle Systems.- 4 Unified Approach to Characterize Microstructure.- 5 Monodisperse Spheres.- 6 Polydisperse Spheres.- 7 Anisotropic Media.- 8 Cell and Random-Field Models.- 9 Percolation and Clustering.- 10 Some Continuum Percolation Results.- 11 Local Volume Fraction Fluctuations.- 12 Computer Simulations, Image Analyses, and Reconstructions.- 13 Local and Homogenized Equations.- 14 Variational Principles.- 15 Phase-Interchange Relations.- 16 Exact Results.- 17 Single-Inclusion Solutions.- 18 Effective-Medium Approximations.- 19 Cluster Expansions.- 20 Exact Contrast Expansions.- 21 Rigorous Bounds.- 22 Evaluation of Bounds.- 23 Cross-Property Relations.- A Equilibrium Hard-Disk Program.- B Interrelations Among Two- and Three-Dimensional Moduli.- References.

Reviews

From the reviews: This interdisciplinary book is an excellent example of the modern scope of issues of interest to many sciences, namely applied mathematics, physics, chemistry, material science, engineering, geology and biology!This book is to a high degree self-contained!It is the first of its kind to provide a unified rigorous means of characterizing the microstructure and macroscopic properties of the wide class of heterogeneous materials which are distinct in nature. All these circumstances will mean great use of this volume by researchers in different scientific fields, interested in the study of heterogeneous materials, as well as in the preparation of courses for graduate students of corresponding specialties. (Mathematical Reviews) Since the author has been at the forefront of this research field, he has deep insight into many of the theoretical developments of the past two decades, and as a result has produced an outstanding book with many insightful comments. In my opinion, every serious researcher and advanced graduate student who is interested in heterogeneous materials should have a copy of this book. (Journal of Statistical Physics) This is an important book, which is recommended to all stochastic geometers as well as spatial statisticians, at least to learn what a leading physicist has to say about stochastic geometry ... [Many] of the formulas in Part II are perfectly general and make no assumption about the type of microstructure, i.e., they are valid for foams, heterogeneous polymer phases, granular media, colloids, composites, etc... [This] is a book which is very important and which merits great attention in the mathematical-statistical community. (D. Stoyan, Metrika, December 2003) Random Hetergeneous Materials should become a standard reference for those beginning a study of random hetergeneous media. (Applied Mechanics Reviews) The book at hand has at least two aims: to bring to the literature the current state of the analytic theory of random heterogeneous structures and to expose the tools that have led to a resurgence of interest in these and related materials. The author is in a very good position to achieve these goals, since he is responsible for much of the recent progress in this subject area, and because of his interest in the study of complex systems. Furthermore, much of the material has not appeared in any previous book on the subject ... This is a well-written monograph with a high degree of originality. The pedagogy is strong, with most of the mathematical derivations elaborated in detail and without excessive verbiage. Much of the book is written so as to be accessible to specialists and advanced students. The mathematical background required of the reader is not extensive. In fact, a number of open research questions are outlined in the course of presentation. Torquato's book does not contain any exercises, but on the other hand there are many carefully worked out examples and meticulous notes about the history and literature in the field ... [This book] answers a demand for a long awaited textbook for those who wish to learn about this fascinating and still poorly understood area of condensed matter physics which is sure to remain a focus of intense research activity in the years to come. Torquato's monograph should make an excellent text for self-study or for a graduate course in disordered materials. It will be welcomed by the physical and materials science communities. (Christian Brosseau, Optics & Photonics News, February 2003) This book ... primarily concerns the mathematical analysis of random structures. This work can serve as a foundation for those who wish to design random heterogeneous structures with specified bulk properties. A major contribution of the book is to clearly and rigorously explain the statistical characterization of the microstructure of these materials ... . An extensive reference list is provided. Random Heterogeneous Materials ... should become a standard reference for those beginning a study of random heterogeneous media. (H.W. Haslach Jr., Applied Mechanics Reviews, 55:4, 2002) The aim of the book is to give broad information about random heterogeneous materials, particularly based on microstructural and macrostructural properties of the constituent materials. ... The book is well written and might be very useful to researchers working in the area of composite materials and porous media. I, therefore, strongly recommend to personal users and to the institute libraries to keep the book on their shelves. (Hilmi Demiray, Zentralblatt MATH, 988:13, 2002) This book contains an incredible amount of (nontrivial) results, many of which were first obtained by the author himself (in collaboration with his Princeton group). ... A large number of exact results, too many to summarize here, as well as upper and lower bounds for the effective properties are provided together with an extensive list of references (30 pages). This book should be useful to anybody interested in the quantitative study of complex materials, whatever their origin. (M. Baus, Physicalia, 38:4, 2002)

"From the reviews: ""This interdisciplinary book is an excellent example of the modern scope of issues of interest to many sciences, namely applied mathematics, physics, chemistry, material science, engineering, geology and biology…This book is to a high degree self-contained…It is the first of its kind to provide a unified rigorous means of characterizing the microstructure and macroscopic properties of the wide class of heterogeneous materials which are distinct in nature. All these circumstances will mean great use of this volume by researchers in different scientific fields, interested in the study of heterogeneous materials, as well as in the preparation of courses for graduate students of corresponding specialties."" (Mathematical Reviews) ""Since the author has been at the forefront of this research field, he has deep insight into many of the theoretical developments of the past two decades, and as a result has produced an outstanding book with many insightful comments. In my opinion, every serious researcher and advanced graduate student who is interested in heterogeneous materials should have a copy of this book.” (Journal of Statistical Physics) ""This is an important book, which is recommended to all stochastic geometers as well as spatial statisticians, at least to learn what a leading physicist has to say about stochastic geometry . . . [Many] of the formulas in Part II are perfectly general and make no assumption about the type of microstructure, i.e., they are valid for foams, heterogeneous polymer phases, granular media, colloids, composites, etc. . . . [This] is a book which is very important and which merits great attention in the mathematical-statistical community.” (D. Stoyan, Metrika, December 2003) ""Random Hetergeneous Materials should become a standard reference for those beginning a study of random hetergeneous media."" (Applied Mechanics Reviews) ""Thebook at hand has at least two aims: to bring to the literature the current state of the analytic theory of random heterogeneous structures and to expose the tools that have led to a resurgence of interest in these and related materials. The author is in a very good position to achieve these goals, since he is responsible for much of the recent progress in this subject area, and because of his interest in the study of complex systems.  Furthermore, much of the material has not appeared in any previous book on the subject . . . This is a well-written monograph with a high degree of originality. The pedagogy is strong, with most of the mathematical derivations elaborated in detail and without excessive verbiage. Much of the book is written so as to be accessible to specialists and advanced students. The mathematical background required of the reader is not extensive. In fact, a number of open research questions are outlined in the course of presentation. Torquato’s book does not contain any exercises, but on the other hand there are many carefully worked out examples and meticulous notes about the history and literature in the field . . . [This book] answers a demand for a long awaited textbook for those who wish to learn about this fascinating and still poorly understood area of condensed matter physics which is sure to remain a focus of intense research activity in the years to come. Torquato’s monograph should make an excellent text for self-study or for a graduate course in disordered materials. It will be welcomed by the physical and materials science communities.” (Christian Brosseau, Optics & Photonics News, February 2003) ""This book ... primarily concerns the mathematical analysis of random structures. This work can serve as a foundation for those who wish to design random heterogeneous structures with specified bulk properties. A major contribution of the book is to clearly and rigorously explain the statisticalcharacterization of the microstructure of these materials ... . An extensive reference list is provided. Random Heterogeneous Materials ... should become a standard reference for those beginning a study of random heterogeneous media."" (H.W. Haslach Jr., Applied Mechanics Reviews, 55:4, 2002) ""The aim of the book is to give broad information about random heterogeneous materials, particularly based on microstructural and macrostructural properties of the constituent materials. ... The book is well written and might be very useful to researchers working in the area of composite materials and porous media. I, therefore, strongly recommend to personal users and to the institute libraries to keep the book on their shelves."" (Hilmi Demiray, Zentralblatt MATH, 988:13, 2002) ""This book contains an incredible amount of (nontrivial) results, many of which were first obtained by the author himself (in collaboration with his Princeton group). ... A large number of exact results, too many to summarize here, as well as upper and lower bounds for the effective properties are provided together with an extensive list of references (30 pages). This book should be useful to anybody interested in the quantitative study of complex materials, whatever their origin."" (M. Baus, Physicalia, 38:4, 2002)"

From the reviews: This interdisciplinary book is an excellent example of the modern scope of issues of interest to many sciences, namely applied mathematics, physics, chemistry, material science, engineering, geology and biology!This book is to a high degree self-contained!It is the first of its kind to provide a unified rigorous means of characterizing the microstructure and macroscopic properties of the wide class of heterogeneous materials which are distinct in nature. All these circumstances will mean great use of this volume by researchers in different scientific fields, interested in the study of heterogeneous materials, as well as in the preparation of courses for graduate students of corresponding specialties. (Mathematical Reviews) Since the author has been at the forefront of this research field, he has deep insight into many of the theoretical developments of the past two decades, and as a result has produced an outstanding book with many insightful comments. In my opinion, every serious researcher and advanced graduate student who is interested in heterogeneous materials should have a copy of this book. (Journal of Statistical Physics) This is an important book, which is recommended to all stochastic geometers as well as spatial statisticians, at least to learn what a leading physicist has to say about stochastic geometry ... [Many] of the formulas in Part II are perfectly general and make no assumption about the type of microstructure, i.e., they are valid for foams, heterogeneous polymer phases, granular media, colloids, composites, etc... [This] is a book which is very important and which merits great attention in the mathematical-statistical community. (D. Stoyan, Metrika, December 2003) Random Hetergeneous Materials should become a standard reference for those beginning a study of random hetergeneous media. (Applied Mechanics Reviews) The book at hand has at least two aims: to bring to the literature the current state of the analytic theory of random heterogeneous structures and to expose the tools that have led to a resurgence of interest in these and related materials. The author is in a very good position to achieve these goals, since he is responsible for much of the recent progress in this subject area, and because of his interest in the study of complex systems. Furthermore, much of the material has not appeared in any previous book on the subject ... This is a well-written monograph with a high degree of originality. The pedagogy is strong, with most of the mathematical derivations elaborated in detail and without excessive verbiage. Much of the book is written so as to be accessible to specialists and advanced students. The mathematical background required of the reader is not extensive. In fact, a number of open research questions are outlined in the course of presentation. Torquato's book does not contain any exercises, but on the other hand there are many carefully worked out examples and meticulous notes about the history and literature in the field ... [This book] answers a demand for a long awaited textbook for those who wish to learn about this fascinating and still poorly understood area of condensed matter physics which is sure to remain a focus of intense research activity in the years to come. Torquato's monograph should make an excellent text for self-study or for a graduate course in disordered materials. It will be welcomed by the physical and materials science communities. (Christian Brosseau, Optics & Photonics News, February 2003) This book ... primarily concerns the mathematical analysis of random structures. This work can serve as a foundation for those who wish to design random heterogeneous structures with specified bulk properties. A major contribution of the book is to clearly and rigorously explain the statistical characterization of the microstructure of these materials ... . An extensive reference list is provided. Random Heterogeneous Materials ... should become a standard reference for those beginning a study of random heterogeneous media. (H.W. Haslach Jr., Applied Mechanics Reviews, 55:4, 2002) The aim of the book is to give broad information about random heterogeneous materials, particularly based on microstructural and macrostructural properties of the constituent materials. ... The book is well written and might be very useful to researchers working in the area of composite materials and porous media. I, therefore, strongly recommend to personal users and to the institute libraries to keep the book on their shelves. (Hilmi Demiray, Zentralblatt MATH, 988:13, 2002) This book contains an incredible amount of (nontrivial) results, many of which were first obtained by the author himself (in collaboration with his Princeton group). ... A large number of exact results, too many to summarize here, as well as upper and lower bounds for the effective properties are provided together with an extensive list of references (30 pages). This book should be useful to anybody interested in the quantitative study of complex materials, whatever their origin. (M. Baus, Physicalia, 38:4, 2002)

From the reviews: <p> This interdisciplinary book is an excellent example of the modern scope of issues of interest to many sciences, namely applied mathematics, physics, chemistry, material science, engineering, geology and biologya ]This book is to a high degree self-containeda ]It is the first of its kind to provide a unified rigorous means of characterizing the microstructure and macroscopic properties of the wide class of heterogeneous materials which are distinct in nature. All these circumstances will mean great use of this volume by researchers in different scientific fields, interested in the study of heterogeneous materials, as well as in the preparation of courses for graduate students of corresponding specialties. (Mathematical Reviews) <p> Since the author has been at the forefront of this research field, he has deep insight into many of the theoretical developments of the past two decades, and as a result has produced an outstanding book with many insightful comments. In my opinion, every serious researcher and advanced graduate student who is interested in heterogeneous materials should have a copy of this book.a (Journal of Statistical Physics) <p> This is an important book, which is recommended to all stochastic geometers as well as spatial statisticians, at least to learn what a leading physicist has to say about stochastic geometry . . . [Many] of the formulas in Part II are perfectly general and make no assumption about the type of microstructure, i.e., they are valid for foams, heterogeneous polymer phases, granular media, colloids, composites, etc. . . . [This] is a book which is very important and which merits great attention in the mathematical-statisticalcommunity.a (D. Stoyan, Metrika, December 2003) <p> Random Hetergeneous Materials should become a standard reference for those beginning a study of random hetergeneous media. (Applied Mechanics Reviews) <p> The book at hand has at least two aims: to bring to the literature the current state of the analytic theory of random heterogeneous structures and to expose the tools that have led to a resurgence of interest in these and related materials. The author is in a very good position to achieve these goals, since he is responsible for much of the recent progress in this subject area, and because of his interest in the study of complex systems. Furthermore, much of the material has not appeared in any previous book on the subject . . . This is a well-written monograph with a high degree of originality. The pedagogy is strong, with most of the mathematical derivations elaborated in detail and without excessive verbiage. Much of the book is written so as to be accessible to specialists and advanced students. The mathematical background required of the reader is not extensive. In fact, a number of open research questions are outlined in the course of presentation. Torquatoa (TM)s book does not contain any exercises, but on the other hand there are many carefully worked out examples and meticulous notes about the history and literature in the field . . . [This book] answers a demand for a long awaited textbook for those who wish to learn about this fascinating and still poorly understood area of condensed matter physics which is sure to remain a focus of intense research activity in the years to come. Torquatoa (TM)s monograph should make an excellent text for self-study or for a graduatecourse in disordered materials. It will be welcomed by the physical and materials science communities.a (Christian Brosseau, Optics & Photonics News, February 2003) <p> This book ... primarily concerns the mathematical analysis of random structures. This work can serve as a foundation for those who wish to design random heterogeneous structures with specified bulk properties. A major contribution of the book is to clearly and rigorously explain the statistical characterization of the microstructure of these materials ... . An extensive reference list is provided. Random Heterogeneous Materials ... should become a standard reference for those beginning a study of random heterogeneous media. (H.W. Haslach Jr., Applied Mechanics Reviews, 55: 4, 2002) <p> The aim of the book is to give broad information about random heterogeneous materials, particularly based on microstructural and macrostructural properties of the constituent materials. ... The book is well written and might be very useful to researchers working in the area of composite materials and porous media. I, therefore, strongly recommend to personal users and to the institute libraries to keep the book on their shelves. (Hilmi Demiray, Zentralblatt MATH, 988: 13, 2002) <p> This book contains an incredible amount of (nontrivial) results, many of which were first obtained by the author himself (in collaboration with his Princeton group). ... A large number of exact results, too many to summarize here, as well as upper and lower bounds for the effective properties are provided together with an extensive list of references (30 pages). This book should be useful to anybody interested in the quantitative study of complex materials, whatever their origin. (M. Baus, Physicalia, 38: 4, 2002)

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