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Amorphous Polymers and Non-Newtonian Fluids (Hardcover, 1987 ed.): Constantine Dafermos, J.L. Ericksen, David Kinderlehrer Amorphous Polymers and Non-Newtonian Fluids (Hardcover, 1987 ed.)
Constantine Dafermos, J.L. Ericksen, David Kinderlehrer
R2,996 Discovery Miles 29 960 Ships in 10 - 15 working days

This IMA Volume in Mathematics and its Applications AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS We are grateful to the Scientific Committee: Haim Brezis Constantine Dafermos Jerry Ericksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface Experiences with amorphous polymers have supplied much of the motivation for developing novel kinds of molecular theory, to try to deal with the more significant features of systems involving very large molecules with many degrees offreedom. Similarly, the observations of many unusual macroscopic phenomena has stimulated efforts to develop linear and nonlinear theories of viscoelasticity to describe them. In either event, we are confronted not with a well-established, specific set of equations, but with a variety of equations, conforming to a loose pattern and suggested by general kinds of reasoning. One challenge is to devise techniques for finding equations capable of delivering definite and reliable predictions. Related to this is the issue of discovering ways to better grasp the nature of solutions ofthose equations showing some promise."

Hans Lewy Selecta - Volume 2 (Hardcover, 2002 ed.): David Kinderlehrer Hans Lewy Selecta - Volume 2 (Hardcover, 2002 ed.)
David Kinderlehrer
R3,262 Discovery Miles 32 620 Ships in 10 - 15 working days

The work of Hans Lewy (1904--1988) has had a profound influence in the direction of applied mathematics and partial differential equations, in particular, from the late 1920s. Two of the particulars are well known. The Courant--Friedrichs--Lewy condition (1928), or CFL condition, was devised to obtain existence and approximation results. This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. Lewy's example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regularity theory of elliptic equations and systems, the Monge-- AmpSre Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and several complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help one understand the essential concepts embedded in an issue, although at a cost in generality. This approach was extremely successful. In this two-volume work, most all of Lewy's papers are presented, in chronological order. They are preceded by several short essays about Lewy himself, prepared by Helen Lewy, Constance Reid, and David Kinderlehrer, and commentaries on his work by Erhard Heinz, Peter Lax, Jean Leray, Richard MacCamy, Fran?ois Treves, and Louis Nirenberg. Additionally, there are Lewy's own remarks on the occasion of his honorary degree from the University of Bonn.

Hans Lewy Selecta - Volume 1 (Hardcover, 2002 ed.): David Kinderlehrer Hans Lewy Selecta - Volume 1 (Hardcover, 2002 ed.)
David Kinderlehrer
R3,236 Discovery Miles 32 360 Ships in 10 - 15 working days

The work of Hans Lewy (1904--1988) has had a profound influence in the direction of applied mathematics and partial differential equations, in particular, from the late 1920s. Two of the particulars are well known. The Courant--Friedrichs--Lewy condition (1928), or CFL condition, was devised to obtain existence and approximation results. This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. Lewy's example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regularity theory of elliptic equations and systems, the Monge--AmpA]re Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and several complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help one understand the essential concepts embedded in an issue, although at a cost in generality. This approach was extremely successful. In this two-volume work, most all of Lewy's papers are presented, in chronological order. They are preceded by several short essays about Lewy himself, prepared by Helen Lewy, Constance Reid, and David Kinderlehrer, and commentaries on his work by Erhard Heinz, Peter Lax, Jean Leray, Richard MacCamy, FranAois Treves, and Louis Nirenberg. Additionally, there are Lewy's own remarks on the occasion of his honorarydegree from the University of Bonn.

Theory and Applications of Liquid Crystals (Paperback, Softcover reprint of the original 1st ed. 1987): Jerald L. Ericksen,... Theory and Applications of Liquid Crystals (Paperback, Softcover reprint of the original 1st ed. 1987)
Jerald L. Ericksen, David Kinderlehrer
R1,545 Discovery Miles 15 450 Ships in 10 - 15 working days

This IMA Volume in Mathematics and its Applications AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS We are grateful to the Scientific Committee: Haim Brezis Constantine Dafermos Jerry Eri cksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface The diversity of experimental phenomena and the range of applications of liquid crystals present timely and challenging questions for experimentalists, mechanists, and mathematicians. The scope of this workshop was to bring together research workers and practitioners in these areas from laboratories, industry, and universities to explore common issues. The contents of this volume vary from descriptions of experimental phenomena, of which our understanding is insufficient, to questions of a mathematical nature and of efficient computation."

Amorphous Polymers and Non-Newtonian Fluids (Paperback, Softcover reprint of the original 1st ed. 1987): Constantine Dafermos,... Amorphous Polymers and Non-Newtonian Fluids (Paperback, Softcover reprint of the original 1st ed. 1987)
Constantine Dafermos, J.L. Ericksen, David Kinderlehrer
R2,851 Discovery Miles 28 510 Ships in 10 - 15 working days

This IMA Volume in Mathematics and its Applications AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS We are grateful to the Scientific Committee: Haim Brezis Constantine Dafermos Jerry Ericksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface Experiences with amorphous polymers have supplied much of the motivation for developing novel kinds of molecular theory, to try to deal with the more significant features of systems involving very large molecules with many degrees offreedom. Similarly, the observations of many unusual macroscopic phenomena has stimulated efforts to develop linear and nonlinear theories of viscoelasticity to describe them. In either event, we are confronted not with a well-established, specific set of equations, but with a variety of equations, conforming to a loose pattern and suggested by general kinds of reasoning. One challenge is to devise techniques for finding equations capable of delivering definite and reliable predictions. Related to this is the issue of discovering ways to better grasp the nature of solutions ofthose equations showing some promise.

Homogenization and Effective Moduli of Materials and Media (Paperback, Softcover reprint of the original 1st ed. 1986): Jerry... Homogenization and Effective Moduli of Materials and Media (Paperback, Softcover reprint of the original 1st ed. 1986)
Jerry L. Ericksen, David Kinderlehrer, Robert Kohn, J.L. Lions
R2,870 Discovery Miles 28 700 Ships in 10 - 15 working days

This IMA Volume in Mathematics and its Applications Homogenization and Effective Moduli of Materials and Media represents the proceedings of a workshop which was an integral part of the 19R4-R5 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS. We are grateful to the Scientific Committee: J . L. Ericksen D. Kinderlehrer H. Brezis C. Dafermos for their dedication and hard work in rleveloping an imaginative, stimulating, and productive year-long program. George R. Sell Hans Weinherger PREFACE The papers in this volume were presented at a workshop on homogenization of differential equations and the determination of effective moduli of materials and media, primarily in the context of continuum theory. These areas are closely linked to a variety of phenomena, such as the elastic and dielectric responses of composites, and the effective properties of shales and soils. For instance, the ability to predict the effective stiffness response of a composite across a broad range of frequencies allows its performance under given circumstances to be assessed by means of nondestructive testing. A fundamental mathematical tool is homogenization, the study of partial differential equations with rapidly varying coefficients or boundary conditions. The recent alliance of homogenization with optimal design has stimulated the development of both fields. The presentations at the workshop emphasized recent advances and open questions.

Metastability and Incompletely Posed Problems (Paperback, Softcover reprint of the original 1st ed. 1987): Stuart S. Antman,... Metastability and Incompletely Posed Problems (Paperback, Softcover reprint of the original 1st ed. 1987)
Stuart S. Antman, J.L. Ericksen, David Kinderlehrer, Ingo Muller
R1,550 Discovery Miles 15 500 Ships in 10 - 15 working days

This IMA Volume in Mathematics and its Applications Metastability and Incompletely Posed Problems represents the proceedings of a workshop which was an integral part of the 19R4-R5 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EOIIATIONS. We are grateful to the Scientific Committee:, I.L. Eri cksen D. Kinderlehrer H. Rrezis C. Dafermos for their dedication and hard work in developing an imaginative, stimulating, and productive year-long program. George R. Sell Hans Weinberger Preface Most equilibrium events in nature do not realize configurations of minimum energy. They are only metastable. Available knowledge of constitutive relations and environmental interactions may be limiterl. As a result, many configurations may he compatible with the rlata. Such questions are incompletely poserl. The papers in this volume address a wide variety of these issues as they are perceived by the material scientist and the mathematician. They represent a portion of the significant activity which has been underway in recent years, from the experimental arena and physical theory to the analysis of differential equations and computation.

Hans Lewy Selecta - Volume 2 (Paperback, Softcover reprint of the original 1st ed. 2002): David Kinderlehrer Hans Lewy Selecta - Volume 2 (Paperback, Softcover reprint of the original 1st ed. 2002)
David Kinderlehrer
R2,956 Discovery Miles 29 560 Ships in 10 - 15 working days

The work of Hans Lewy (1904--1988) has had a profound influence in the direction of applied mathematics and partial differential equations, in particular, from the late 1920s. Two of the particulars are well known. The Courant--Friedrichs--Lewy condition (1928), or CFL condition, was devised to obtain existence and approximation results. This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. Lewy's example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regularity theory of elliptic equations and systems, the Monge-- AmpSre Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and several complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help one understand the essential concepts embedded in an issue, although at a cost in generality. This approach was extremely successful. In this two-volume work, most all of Lewy's papers are presented, in chronological order. They are preceded by several short essays about Lewy himself, prepared by Helen Lewy, Constance Reid, and David Kinderlehrer, and commentaries on his work by Erhard Heinz, Peter Lax, Jean Leray, Richard MacCamy, Fran?ois Treves, and Louis Nirenberg. Additionally, there are Lewy's own remarks on the occasion of his honorary degree from the University of Bonn.

Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids - A Collection of Reprints of 14... Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids - A Collection of Reprints of 14 Seminal Papers (Paperback, Softcover reprint of the original 1st ed. 1999)
John M Ball; Introduction by E. Fried; Edited by David Kinderlehrer, Paulo Podio-Guidugli, Marshall Slemrod
R3,174 Discovery Miles 31 740 Ships in 10 - 15 working days

A traditional way to honor distinguished scientists is to combine collections of papers solicited from friendly colleagues into dedicatory volumes. To honor our friend and colleague Mort Gurtin on the occasion of his sixty-fifth birthday, we followed a surer path to produce a work of intrinsic and lasting scientific value: We collected pa pers that we deemed seminal in the field of evolving phase interfaces in solids, a field to which Mort Gurtin himself has made fundamental contributions. Our failure for lack of space to include in this volume every paper of major significance is mitigated by the ma gisterial introduction prepared by Eliot Fried, which assesses the contributions of nu merous works. We hope that this collection will prove useful and stimulating to both researchers and students in this exciting field. August 1998 JohnM. Ball David Kinderlehrer Paulo Podio-Guidugli Marshall Slemrod Contents Introduction: Fifty Years of Research on Evolving Phase Interfaces By Eliot Fried. 0 ************************************************ 0 ***** 1 I. Papers on Materials Science Surface Tension as a Motivation for Sintering By C. Herring 33 Two-Dimensional Motion of Idealized Grain Boundaries By W. W. Mullins 0 *********** 0 ******************* 70 Morphological. Stability of a Particle Growing by Diffusion or Heat Flow By w. w. Mullins and R. F. Sekerka 75 Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics By J. D. Eshelby 82 The Interactions of Composition and Stress in Crystalline Solids By F. e. Larche and 1. W. Cahn 120 II.

Hans Lewy Selecta - Volume 1 (Paperback, Softcover reprint of the original 1st ed. 2002): David Kinderlehrer Hans Lewy Selecta - Volume 1 (Paperback, Softcover reprint of the original 1st ed. 2002)
David Kinderlehrer
R2,941 Discovery Miles 29 410 Ships in 10 - 15 working days

The work of Hans Lewy (1904-1988) has had a profound influence in the direc tion of applied mathematics and partial differential equations, in particular, from the late 1920s. We are all familiar with two of the particulars. The Courant-Friedrichs Lewy condition (1928), or CFL condition, was devised to obtain existence and ap proximation results. This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. His example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regu larity theory of elliptic equations and systems, the Monge-Ampere Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and sev eral complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help us understand the essential concepts embedded in an issue, although at a cost in generality. This was extremely successful."

Microstructure and Phase Transition (Paperback, Softcover reprint of the original 1st ed. 1993): David Kinderlehrer, Richard... Microstructure and Phase Transition (Paperback, Softcover reprint of the original 1st ed. 1993)
David Kinderlehrer, Richard James, Mitchell Luskin, Jerry L. Ericksen
R2,856 Discovery Miles 28 560 Ships in 10 - 15 working days

This IMA Volume in Mathematics and its Applications MICROSTRUCTURE AND PHASE TRANSITION is based on the proceedings of a workshop which was an integral part of the 1990-91 IMA program on "Phase Transitions and Free Boundaries." We thank R. Fosdick, M.E. Gurtin, W.-M. Ni and L.A. Peletier for organizing the year-long program and, especially, D. Kinderlehrer, R. James, M. Luskin and J. Ericksen for organizing the meeting and editing these proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, and the National Science Foun dation. A vner Friedman Willard Miller. Jr. PREFACE Much of our traditional knowledge of materials and processes is achievf'd by observa tion and analysis of small departures from equilibrium. Many materials, especially modern alloys, ceramics, and their composites, experience not only larger but more dramatic changes, such as the occurrence of phase transitions and t.he creation of defect structures, when viewed at the microscopic scale. How is this observed, how can it be interpreted, and how does it influence macroscopic behavior? These are the principle concerns of this volume, which constitutes the proceedings of an IMA workshop dedicated to these issues.

Calculus of Variations and Partial Differential Equations - Proceedings of a Conference, held in Trento, Italy, June 16-21,... Calculus of Variations and Partial Differential Equations - Proceedings of a Conference, held in Trento, Italy, June 16-21, 1986 (Paperback, 1988 ed.)
Stefan Hildebrandt, David Kinderlehrer, Mario Miranda
R1,410 Discovery Miles 14 100 Ships in 10 - 15 working days
Mathematics and Materials (Hardcover): Mark J. Bowick, David Kinderlehrer, Govind Menon, Charles Radin Mathematics and Materials (Hardcover)
Mark J. Bowick, David Kinderlehrer, Govind Menon, Charles Radin
R3,228 Discovery Miles 32 280 Ships in 12 - 19 working days

Articles in this volume are based on lectures presented at the Park City summer school on ``Mathematics and Materials'' in July 2014. The central theme is a description of material behavior that is rooted in statistical mechanics. While many presentations of mathematical problems in materials science begin with continuum mechanics, this volume takes an alternate approach. All the lectures present unique pedagogical introductions to the rich variety of material behavior that emerges from the interplay of geometry and statistical mechanics. The topics include the order-disorder transition in many geometric models of materials including nonlinear elasticity, sphere packings, granular materials, liquid crystals, and the emerging field of synthetic self-assembly. Several lectures touch on discrete geometry (especially packing) and statistical mechanics. The problems discussed in this book have an immediate mathematical appeal and are of increasing importance in applications, but are not as widely known as they should be to mathematicians interested in materials science. The volume will be of interest to graduate students and researchers in analysis and partial differential equations, continuum mechanics, condensed matter physics, discrete geometry, and mathematical physics.

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