Descriptions of the IMA Volumes in Mathematics and its Applications

Published by Springer Science + Business Media, LLC

Current Volumes

Volume 1: Homogenization and Effective Moduli of Materials and Media
Editors: Jerry Ericksen, David Kinderlehrer, Robert Kohn, and J.-L. Lions
Contents: pdf postscript

The first in a series of volumes dedicated to the study of continuum physics and partial differential equations. "This volume is a collection of papers by world experts in both homogenization and optimal structural design. The emphasis of all the papers is on applications and examples. The papers are of high quality, well written, and happily one need not be a specialist to gain insight from reading them. I recommend the collection to anyone interested in seeing what is happening on the applied side of homogenization and optimal structural design.
Volume 2: Oscillation Theory, Computation, and Methods of Compensated Compactness
Editors: Constantine Dafermos, Jerry Ericksen, David Kinderlehrer, and Marshall Slemrod
Contents: pdf postscript
Brings together both the analytical and numerical sides of conservation law research. The objective is to examine recent trends in the investigation of systems of conservation laws and in particular to focus on the roles of dispersive and diffusion limits for singularly perturbed conservation laws. Special attention is devoted to the new ideas of compensated compactness and oscillation theory in the hope that these new methods may lead to new existence theorems for systems of conservation laws and perhaps provide a greater understanding of convergence of finite difference schemes.
Volume 3: Metastability and Incompletely Posed Problems
Editors: S. Antman, J.L. Ericksen, K. Kinderlehrer, and I. Müller
Contents: pdf postscript
Available knowledge of constitutive relations and environmental interactions may be limited; thus, many configurations may be compatible with the data. This volume addresses such incompletely posed questions and addresses a variety of issues as they are perceived by the material scientist and 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 computations. While there is speculative character to much of this work, by grappling with specific problems, the authors provide experience from which one may aspire to abstract viable methods for the analysis and production of metastable behavior.
Volume 4: Dynamical Problems in Continuum Physics
Editors: Jerry Bona, Constantine Dafermos, Jerry Ericksen, and David Kinderlehrer
Contents: pdf postscript
The behavior of matter and waves in a dynamical setting offers many challenging problems to the mathematician and the materials scientist alike. Under review in this volume are a variety of nonlinear phenomena whose consideration entails new perspectives, not commonly found in the literature. Attention has been given to the interaction of electromagnetic and mechanical properties of materials. Attempts are made to describe and to understand phenomena which are far from equilibrium or which suffer abrupt changes in behavior through tentative physical or analytical assumptions.
Volume 5: Theory and Applications of Liquid Crystals
Editors: Jerry Ericksen and David Kinderlehrer
Contents: pdf postscript
The diversity of experimental phenomena and the range of applications of liquid crystals present timely and challenging questions for experimentalists , mechanists, and mathematicians. The contents of this volume vary from descriptions of experimental phenomena to questions of a mathematical nature of efficient computation. Interest in this area is stimulated by problems relating to the many familiar devices as well as by questions which arise in the processing of high strength polymer fibers such as Kevlar. The objective of this volume is to foster improved theory and more effective computational methods through better mathematical understanding.
Volume 6: Amorphous Polymers and Non-Newtonian Fluids
Editors: Constantine Dafermos, Jerry Ericksen, and David Kinderlehrer
Contents: pdf postscript
Experiences with amorphous polymers have supplied much of the motivation for developing novel kinds of molecular theory to deal with the more significant featuares of systems involving very large molecules with many degrees of freedom. Similarly, the observations of many unusual macroscopic phenomena has stimulated efforts to develop linear and nonlinear theories of viscoelasticity to describe them. This volume brings together research workers in chemistry, engineering, mathematics and physics from laboratory, industrial and academic environments. The objective is to devise techniques for finding equations capable of delivering definite and reliable predictions.
Volume 7: Random Media
Editor: George Papanicolaou
Contents: pdf postscript
This volume brings together researchers who work in a broad area of applications and mathematical methodology related to random media. Papers represent a cross section of problems and methods that are currently of interest: Brownian motion, random PDE's, random Schrödinger operators, wave propagation, amorphous semiconductors, lattice models, diffusion processes, etc. One dimensional problems, such as Lyapunov indices, density of states, and localization, receive considerable attention. There is considerable progress in several dimensional problems as well, in particular on localization of cases in multidimensional random media. The volume should be of interest to chemists, physicists and mathematicians.
Volume 8: Percolation Theory and Ergodic Theory of Infinite Particle Systems
Editor: Harry Kesten
Contents: pdf postscript
Percolation theory and infinite particle systems both deal with probability mode ls with great appeal to pure probabilists and to statistical physicists. The percolatio n model was invented about 30 years ago. One of its attractions is that it is extremely simple to state. It exhibits a phase transition, which turns out to be quite difficult to analyze. It is precisely this phase transition which makes the mod el interesting to physicists, because they have studied such phenomena for a much longer time in statistical mechanics (e.g. in models for magnetism). Infinite particle systems deal with the evolution of collections of interacting particles . The interaction is of course required if one wants to mimic any physical phenomenon, but it makes the mathematical problems challenging and difficult. Percolation theory and the study of infinite particle systems have many tools in common and there is a similarity of flavor between the two fields.
This volume contains the Proceedings of a workshop held at the Institute for Mathematics and its Applications, Minneapolis, in Feb. 1986. It reports recent results in the above fields (and some related ones) and gives an impression of the state of the art at the time of the workshop. There is a survey on fractal structures in percolation. Several papers prove new results completely; others merely state results, with proofs to appear in technical journals.
Volume 9: Hydrodynamic Behavior and Interacting Particle Systems
Editor: George Papanicolaou
Contents: pdf postscript
Fifteen papers are presented containing research in various directions currently being pursued on the hydrodynamic behavior of interacting particle systems. Papers are concerned with
- experimental and theoretical results on suspensions
- time dependent effects in sedimentation
- continuum limit of boundary problems in regions with many small inclusions
- the vortex method
  - propagation of chaos for Burgers equation
  - probabilistic aspects of particle systems
- continuum mechanics model for flow of a slurry. The volume should be of interest to chemists, physicists and mathematicians.
Volume 10: Stochastic Differential Systems, Stochastic Control Theory, and Applications
Editors: Wendell Fleming and Pierre-Louis Lions
Contents: pdf postscript
This volume is the Proceedings of a Workshop on stochastic control and related topics in applied probability, held at the Institute for Mathematics and its Applications in June 1986. The choice of topics was deliberately made to obtain a mix of traditional areas of stochastic control theory and topics arising in newer areas of application. The papers included in this volume represent a diversity of approaches and viewpoints. They emphasize variously underlying mathematical theory, modelling issues and questions of computational implementation.
The volume will interest several audiences in mathematics, electrical/computer engineering, and management science. Mathematicians working in probability theory and related areas of partial differential equations would find of interest the papers on stochastic differential systems theory as well as those dealing with its application to stochastic control and nonlinear filtering. Among the newer areas emphasized are stochastic scheduling and queueing networks. These topics arise in analyses of computer networks and scheduling of complex manufacturing operations. Another newer area included is simulated annealing, which provides a stochastic algorithm for many kinds of large-scale optimization problems.
Volume 11: Numerical Simulation in Oil Recovery
Editor: Mary Fanett Wheeler
Contents: pdf postscript
This volume is the Proceedings of a workshop on the numerical simulation of oil recovery held at the Institute for Mathematics and its Applications in December 1986. This volume contains a collection of articles by well known mathematicians, engineers, and scientists. The major research focus is the modeling of geologically realistic media. Several important topics discussed include heterogeneities, diffusion-dispersion, viscous fingering, three phase flow and fractures.
The audience for this volume would include researchers in production research in the petroleum industry (major oil companies), academia (applied mathematics, civil, petroleum, and chemical engineering departments), and government laboratories (DOE, EPA). In addition many of the articles are of interest to hydrologists and engineers modelling containment transport in ground water (U.S. Geological Survey).
Volume 12: Computational Fluid Dynamics and Reacting Gas Flows
Editors: Bjorn Engquist, M. Luskin, and Andrew Majda
Contents: pdf postscript
This volume contains papers presented at the workshop on Computational Fluid Dynamics and Reacting Gas Flows held at the Institute for Mathematics and Its Applications during September, 1986. Computational fluid dynamics has become a research area of central importance to mathematics, science, and technology. It is a subject which brings together applied mathematics and numerical analysis to solve problems in fluid dynamics. Included in this volume is the description of new algorithms which can make possible the discovery of important new scientific phenomena and the development of new technological processes. This volume will be of interest to mathematicians, scientists, and engineers who are interested in the current research of international leaders in numerical analysis and scientific computing.
Volume 13: Numerical Algorithms for Modern Parallel Computer Architectures
Editor: Martin H. Schultz
Contents: pdf postscript
Parallel computers have the potential of providing additional memory and cpu cycles at low cost. They may completely revolutionize the outer limits of scientific computation. The papers in this volume represent simultaneous consideration of applied mathematical, computer science, and application aspects of parallel scientific computing. Such an interdisciplinary approach is likely to lead to the most rapid possible advances in multiprocessor architectures, parallel algorithm development and analysis, and parallel systems and programming languages.
Volume 14: Mathematical Aspects of Scientific Software
Editor: J.R. Rice
Contents: pdf postscript
This volume is the Proceedings of a Workshop on mathematical problems that arise from creating large scientific software systems. The topics lie at the interface between mathematics and computer science, yet some fundamental mathematical questions arise from efforts to understand scientific software. Papers in the volume include a lengthy overview of the area plus treatments of computational geometry, symbolic computation, performance evaluation issues and mathematical systems.
The volume will interest several audiences in mathematics plus the computationally oriented people in a variety of science and engineering disciplines. Of course, those computer scientists working on scientific software will also find the volume of interest.
Volume 15: Mathematical Frontiers in Computational Chemical Physics
Editor: D. Truhlar
Contents: pdf postscript
This volume consists of the lectures at an IMA Workshop on Atomic and Molecular Structure and Dynamics. It focuses on areas where new mathematical developments are currently allowing for advances in computations and where further mathematical developements are required for important progress.
The volume begins with two introductory lectures; the following nine lecturers develope individual strains of research. The book should be of interest to students in mathematics, chemistry, and physics, as well as to senior researchers interested in new research topics. All chapters were specially prepared with this kind of audience in mind and with special emphasis on pedagogy. Emphasis is placed on frontier aspects of mathematical chemistry and physics where unsolved problems provide fertile ground for future research. The areas discussed include the theory of partial differential equations, integral equations, analytic continuation, quantum mechanics, molecular dynamics, and statistical mechanics.
Volume 16: Mathematics in Industrial Problems
by Avner Friedman
The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1987-88. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The consists of twenty-two chapters, each one being independent of the others. Each chapter is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The topics of the book include scattering, control and coding, conservation laws, inverse problems, network optimization, fluid problems, and a variety of free boundary problems in fluid mechanics. The book will be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It will also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their own work.
Volume 17: Applications of Combinatorics and Graph Theory to the Biological and Social Sciences
Editor: Fred Roberts
Contents: pdf postscript
This volume is the Proceedings of a Workshop on the applications of combinatorics and graph theory in the biological and social sciences, held at the Institute for Mathematics and its Applications in January 1988. Combinatorial and graph-theoretical methods are increasingly important in the biological and social sciences. The Workshop emphasized mathematical techniques and open problems arising in such fields as ecology, genetics, enzyme kinetics, economics, political science, sociology, and psychology.
Two illustrations will indicate the type of material in the volume. In biology, the Workshop paid considerable attention to the analysis of protein, DNA, and RNA sequences. This is an area where combinatorial analysis has historically played a very critical role, and where in the future it can be expected to be important as the United States undertakes the massive scientific project of mapping the human genome. In the social sciences, the Workshop paid considerable attention to the theory of measurement. Using both combinatorial and graph-theoretical methods, the Workshop explored the question: What kinds of statements using scales and index numbers can be meaningfully made? The answer to this question has applications to group decisionmaking, performance analysis of new technologies, the analysis of price indices, and so on.
Other areas of special emphasis in the biological sciences were the use of signed graphs in the analysis of stability in ecosystems if only patterns of interaction are known; analysis of competition in ecosystems in general through the use of competition graphs and niche overlap graphs; the use of tree structures in immunology; and combinatorial aspects of enzyme kinetics.
Other areas of special emphasis in the social sciences were the use of median rankings and spatial metrics in group choice and voting; the use of partially ordered sets to analyze knowledge spaces which describe how a person learns and the use of lattice structures to analyze concepts; the use of graphs and signed graphs to study small group behavior and social networks; and the use of signed graphs to study stability in economic models when only sign patterns are known.
The biological and social scientific applications described in the volume are closely related. Some of the uses of graph theory in the study of food webs in ecology are also used to model preference and indifference in psychology and economics. Some of the models used to describe how groups should make choices also have application to finding consensus structures in numerical taxonomy. The problems of measurement and classification discussed are common to the biological and social sciences, as are the methods for analyzing stability when only sign patterns are known.
The volume will interest audiences in mathematics, statistics, operations research, ecology genetics, kinetics, economics, psychology, sociology, and political science. Mathematicians working in graph theory, combinatorics, random discrete structures, lattice theory, partially ordered sets, and finite stochastic processes, should find this volume particularly interesting.
Volume 18: q-series and Partitions
Editor: Dennis Stanton
Contents: pdf postscript
This volume is the proceedings of a workshop held for the Applied Combinatorics program in March, 1988. The central idea of the workshop is the recent interplay of the classical analysis of q-series, and the combinatorial analysis of partitions of integers. Many related topics are discussed, including orthogonal polynomials, the Macdonald conjectures for root systems, and related integrals. Those people interested in combinatorial enumeration and special functions will find this volume of interest. Recent applications of q-series (and related functions) to exactly solvable statistical mechanics models and to statistics makes this volume of interest to non-specialists. Included are several expository papers, and a series of papers on new work on the unimodality of the q-binomial coefficient.
Volume 19: Invariant Theory and Tableaux
Editor: Dennis Stanton
Contents: pdf postscript
This volume is the proceedings of a workshop held for the Applied Combinatorics program in March, 1988. The principal speaker was Gian-Carlo Rota, whose introductory lectures on invariant theory are included here. Several related topics are discussed in other papers: from recent applications of invariant theory to differential equations, to combinatorial questions on Coxeter groups and tableaux. Particularly noteworthy for non-specialists is a self-contained, elementary introduction to Young tableaux and the representations of the symmetric group.
Volume 20: Coding Theory and Design Theory Part I: Coding Theory
Editor: Dijen Ray-Chaudhuri
Contents: pdf postscript
Coding Theory and Design Theory are areas of Combinatorics which found rich applications of algebraic structures. Combinatorial designs are generalizations of finite geometries. Probably, the history of Design Theory begins with the 1847 paper of Reverand T.P. Kirkman "On a problem of Combinatorics," Cambridge and Dublin Math. Journal. The great Statistician R.A. Fisher reinvented the concept of combinatorial 2-design in the twentieth century. Extensive application of algebraic structures for construction of 2-designs (balanced incomplete block designs) can be found in R.C. Bose's 1939 Annals of Eugenics paper, "On the construction of balanced incomplete block designs." Coding Theory and Design Theory are closely interconnected. Hamming codes can be found (in disguise) in R.C. Bose's 1947 Sankhyä paper "Mathematical theory of the symmetrical factorial designs." The same paper also introduced the packing problem in projective spaces - the central problem in the construction of optimum linear codes. Coding theory has developed into a rich and beautiful example of abstract sophisticated mathematics being applied successfully to solve real-life problems of communication. Applications of deep theorems of Algebraic Geometry for construction of linear codes by V.D. Goppa and others created much excitement. Much work remains to be done to make the algebraic geometric codes practical and implementable. Theory of $t$-designs for $t>2$ is in a state of rapid development. The 1987-88 Applied Combinatorics Program of IMA decided to devote the period from May 1, 1988 to June 25, 1988 to concentration on Design Theory and Coding Theory. It was particularly appropriate as many of the specialists that were invited worked in both of these areas.
The purpose of this section of the Applied Combinatorics Year was to bring together Coding Theorists, Design Theorists and Statisticians in the area of experimental designs, to exchange informations and ideas on the latest developments, to encourage interactions and to create an inspiring and stimulating research environment. This purpose was well served. Before the beginning of the workshops from May 1 to June 10, 1988 the pace was relaxed with plenty of time for research exchanges. During this period lectures of J.H. van Lint on Algebraic Geometric Codes was a particularly popular event. In this period there were also lectures by E. Assmus, R.A. Bailey, C-S. Cheng, M. Deza, A.S. Hedayat, S.L. Ma, V. Pless, D.K. Ray-Chaudhuri, N. Singhi, R.M. Wilson and L. Teirlinck. The periods of workshops, Coding Theory, June 13-17, 1988 and Design Theory, June 20-25, 1988 were much more intense with forty (40) lectures altogether. Symposium on Statistical theory of Experimental Designs attracted many statisticians with lively lectures by eight prominent statisticians. Most of the participants submitted their papers for publication in this volume on Coding Theory and Design Theory. Unfortunately a few fine lectures are not submitted for inclusion in these Proceedings.
Volume 21: Coding Theory and Design Theory Part II: Coding Theory
Editor: Dijen Ray-Chaudhuri
See Volume 20 for description.
Contents: pdf postscript
Volume 22: Signal Processing: Part I Signal Processing Theory
Editors: L. Auslander, F. A. Grünbaum, W. Helton, T. Kailath, P. Khargonekar and S. Mitter
Contents: pdf postscript
The two volumes of Signal Processing are based on lectures delivered during a six week program held at the IMA during the summer of 1988. The first two weeks of the program dealt with general areas and methods of Signal Processing. The problem areas included imaging and analysis of recognition, x-ray crystallography, radar and sonar, signal analysis and 1-D signal processing, speech, vision, and VLSI implementation. The methods discussed included harmonic analysis and wavelets, operator theory, algorithm complexity, filtering and estimation, and inverse scattering. The topics of weeks three and four were digital filter, VLSI implementation, and integrable circuit modelling. In week five the concentration was on robust and nonlinear control with aerospace applications, and in week six the emphasis was on problems in radar, sonar and medical imaging.
Because of the large overlap between the various one-week and two-week segments of the program, we found it more convenient to divide the material somewhat differently. Part I deals with general signal process theory and Part II deals with (i) application of signal processing, (ii) control theory related themes.
Signal Processing is undergoing tremendous developments; it is our hope that these two volumes will serve as a source of information and stimulation to mathematical scientists who wish to get acquainted with this field.
Volume 23: Signal Processing: Part II Control Theory and Applications of Control Processing
Editors: L. Auslander, F. A. Grünbaum, W. Helton, T. Kailath, P. Khargonekar and S. Mitter
See Volume 22 for description.
Contents: pdf postscript
Volume 24: Mathematics in Industrial Problems, Part 2
by Avner Friedman
The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1988-89. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of nineteen chapters, each one being independent of the others. Each of the first eighteen chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The last chapter of the book contains references to solutions of problems presented in the previous volume of "Mathematics in Industrial Problems" published in the IMA series, as volume 16. The topics of the book include electro-chemical processes, magneto-optics, aerosol modeling, nonlinear optics, semiconductors and communication. The book will be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It will also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their own work.
Volume 25: Solitons in Physics, Mathematics, and Nonlinear Optics
Editors: Peter J. Olver and David H. Sattinger
Contents: pdf postscript
This volume includes some of the lectures given at two workshops, Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 I.M.A. year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry. The present contributions represent only a fraction of these areas, but give the reader a good overview of several current research directions, including optics, fluid dynamics, inverse scattering, cellular automata, Backlund transformations, monodromy, Painlevé equations, symmetries and Hamiltonian systems.
Volume 26: Two Phase Flows and Waves
Editors: Daniel D. Joseph and David G. Schaeffer
Contents: pdf postscript
This Workshop, held from January 3-10, 1989 at IMA, focused on the properties of materials which consist of many small particles or grains. These include granular materials, in which the particles interact through direct contact, and suspensions or two phase materials, in which particles interact through the influence of the surrounding viscous fluid. Such materials are important in many industrial and geological applications, especially fluidized beds.
This volume contains advanced scientific papers in this rapidly developing subject by authors from several different disciplines (e.g., engineering, physics, mathematics). Some papers attempt to derive continuum constitutive behavior from micromechanics. Others analyze theoretically or solve numerically the partial differential equations which result when an ad hoc constitutive law is assumed. Experimental phenomena exhibited by such materials are reported in other papers. Still others consider the application to fluidized beds.
Volume 27: Nonlinear Evolution Equations that Change Type
Editors: Barbara Lee Keyfitz and Michael Shearer
Contents: pdf postscript
This volume will be of interest to applied mathematicians, to researchers in Partial Differential Equations, and to Fluid Dynamicists and Numerical Analysts examining models for viscoelastic flows, porous medium and granular flows, and flows exhibiting phase transitions. As papers in this volume indicate, physical processes whose simplest models may involve change of type occur also in other dynamic contexts, such as in the simulation of oil reservoirs, involving multiphase flow in a porous medium, and in granular flow.
Volume 28: Computer Aided Proofs in Analysis
Editors: Kenneth Meyer and Dieter Schmidt
Contents: pdf postscript
Since the dawn of the computer revolution the vast majority of scientific computation has dealt with a small cadre seeking precise solutions of equations and rigorous proofs of mathematical results. For example, the number theory and combinatorics have a long history of computer-assisted proofs; such methods are now well established in these fields. In analysis the use of computers to obtain exact results has been fragmented into several schools. This volume is the proceedings of a conference which brought together people in symbolic algebra and in interval arithmetic with some independent entrepreneurs who where interested in obtaining precise answers to questions in analysis by computer methods. There were mathematical physicists interested in the stability of matter, functional analyst computing norms in strange function spaces, celestial mechanists analyzing bifurcations, symbolic algebraists interested in exact integration, numerical analysts who had developed interval arithmetic, plus much more. The mix included developers and end users. The papers within reflect the heterogeneous background of the participants.
Volume 29: Multidimensional Hyperbolic Problems and Computations
Editors: Andrew Majda and Jim Glimm
Contents: pdf postscript
This volume is the proceedings of a two week workshop on multi-dimensional hyperbolic problems held during April 1989. The twenty-six papers in this volume emphasize the interdisciplinary nature of contemporary research in this field involving combinations of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation and experiments. This volume incoudes several expository papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves. In addition, there are two papers in the book devoted to open problems with this interdisciplinary emphasis. This book should be very interesting for any researcher pursuing modern developments in the theory and applications of hyperbolic conservation laws.
Volume 30: Microlocal Analysis and Nonlinear Waves
Editors: Michael Beals, R. Melrose, and J. Rauch
Contents: pdf postscript
The behavior of linear hyperbolic waves has long been analyzed by decomposing the waves into pieces in space-time and into different frequencies. The linear nature of the equations involved allows the reassembling of the pieces in a simple fashion; the individual pieces do not interact. For nonlinear waves the interaction of the pieces seemed to preclude such an analysis, but in the late 1970s it was shown that a similar procedure could be undertaken in this case and would yield important information. The analysis of the decomposed waves, and of waves with special smoothness or size in certain directions, has been fruitful in describing a variety of the properties of nonlinear waves.
This volume presents a number of articles on topics of current interest which involve the use of the techniques described above. The results established include descriptions of the smoothness of such waves as determined by their geometry, the properties of solutions with high frequency oscillations, and the long-time smoothness and size estimates satisfied by nonlinear waves.
Volume 31: Mathematics in Industrial Problems, Part 3
by Avner Friedman
The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1989-90. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of eighteen chapters each one being independent of the others. Each of the first seventeen chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The last chapter of the book contains references to solutions of problems presented in the previous volume of "Mathematics in Industrial Problems, Part 2" published in the IMA series, as volume 24. The topics of the book include electro-chemical processes, polymers, waveguides, diffractive optics, semiconductors and optimization. The book will be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It will also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their own work.
Volume 32: Radar and Sonar, Part I
by Richard Blahut, Willard Miller, Jr., and Calvin Wilcox
Contents: pdf postscript
This volume contains the lecture notes from the three sets of tutorial lectures which were given during the first week of the IMA summer program RADAR AND SONAR, June 18-June 29, 1990. (The second week was devoted to research problems and the proceedings of that part of the program will appear in a second IMA volume.) The first week was run as a summer school with an audience consisting mainly of mathematicians and engineers. The tutorial topics were on mathematics (Topics in Harmonic Analysis with Applications to Radar and Sonar, by Willard Miller, Jr.), on the physical aspects of scattering (Sonar and Radar Echo Structure, by Calvin H. Wilcox), and on the engineering modelling and processing of the phenomena under consideration (Theory of Remote Surveillance Algorithms, by Richard E. Blahut), the famous 1960 technical report by Wilcox (The Synthesis Problem for Radar Ambiguity Functions) was featured prominently in the program and is also published here for the first time. A great effort was made by the lecturers to insure that the participants covered two or all three short courses in detail: mathematicians needed to spend more time and effort in the engineering and physical components and a corresponding distribution of effort was encouraged for engineers and physicists. One of the main goals of this effort was to ensure that people with different backgrounds would help each other, and learn in the process a bit about each others language and approach to problems in Radar and Sonar. We believe that the effort was a great success and offer these notes for the benefit of the wider mathematical sciences community.
Volume 33: Directions in Robust Statistics and Diagnostics: Part I
Editors: Werner A. Stahel and Sanford Weisberg
Contents: pdf postscript
Robust statistical procedures and diagnostics are complementary methodologies to deal with models which may be incomplete or incorrectly specified. These volumes contain the proceedings of a month long workshop on the two fields, held at the Institute for Mathematics and its Applications in Minneapolis in the Summer of 1989. They provide an overview of current directions in research in these two important areas of statistical theory and practice. Care has been taken to provide overview papers as well as easily accessible introductions to the more technical contributions.
These volumes are a point of reference for those researchers with a special interest in robust statistics and diagnostics as well as for other statisticians who have a general interest in these fields.
Volume 34: Directions in Robust Statistics and Diagnostics: Part II
Editors: Werner A. Stahel and Sanford Weisberg
Contents: pdf postscript
See Volume 33 for description.
Volume 35: Dynamical Issues in Combustion Theory
Editors: P. Fife, A. Liñán, and F.A. Williams
Contents: pdf postscript
This volume is the Proceedings of the Workshop of Dynamical Issues in Combustion, held at the Institute of Mathematics and its Applications in November, 1989. The world of combustion phenomena is rich in problems intriguing to the mathematical scientists, offering challenges on several fronts: mathematical modeling, devising appropriate asymptotic and computational methods, and developing sound mathematical theories.
Papers in the present volume describe how all these challenges have been met for particular examples within a number of common combustion scenarios: reactive shocks, low Mach number premised reactive flow, nonpremixed phenomena, and solid propellants.
The types of phenomena they examine are also diverse: properties of interfaces and shocks including curvature effects, the stability and other properties of steady structures, the long time dynamics of evolving solutions, and spatio-temporal patterns. These issues are foremost in combustion research; the papers collected here provide a good representative sampling of contemporary activity in this field.
Volume 36: Computing and Graphics in Statistics
Editors: Andreas Buja and Paul Tukey
Contents: pdf postscript
This volume covers the computational part of IMA activities in statistics during the summer of 1989. The areas of statistical computing and graphics encompass a broad range of research, much of it representated here. The vigor of this research is probably best demonstrated by the fact that as of this writing two new journals are being launched, both entirely dedication to these areas.
The major topics of statistical computing can be traced largely to problems in data analysis and to a lesser extent, in statistical theory. They involve integrated software systems, visualization of high-dimensional data and mathematical functions, numerical and combinatorial algorithms, tools for data handling, and simulation.
Problems arising in the development of integrated statistical software systems have lead to the adaptation of ideas from computer science, particularly programming environments, programming paradigms, and artificial intelligence. In this general area fall the papers by Dumouchel-O'Brien, Hurley-Oldford, McDonald-Pedersen, Nelder, Pedersen, and Young-Smith. Object-oriented programming has left a special mark in some of this research. Of growing importance for the future will be symbolic computing, especially if integrated eith data analyisis and simulation software (Cabrera).
Visualization has been an integral part of statistical methodology long before it became a major scientific initiative in recent years. What distinguishes the problems of statistics from many physical sciences is that they mostly concern genuine high-dimensional objects, such as multivariate data or functions of many variables. Along these lines is the work by Miller-Wegman, Scott, Stuetzle, and Young-Rheingans. A problem which fascinates with its simplicity and seeming intractability, is attacked in Wilkinson's paper on automatic methods for finding reasonable domains and ranges for plotting univariate functions.
Finally, we should point out the importance of numerical methods and Monte Carlo methods in statistics. Statistical problems are often messy and do require care (Grier). Computer intensive methodology has been at the forefront of statistics research in the last decade. Besides the bootstrap method, Bayesian inference and its associated integration problems have attracted much attention (Hesterberg).
Volume 37: Patterns and Dynamics in Reactive Media
Editors: Harry Swinney, Gus Aris, and Don Aronson
Contents: pdf postscript
This volume contains some of the lectures given at the workshop "Patterns and Dynamics in Reactive Media" held from October 16-20, 1989 as part of the year on Dynamical systems and their Applications at the Institute for Mathematics and its Applications, Minneapolis, Minnesota.
Ever since the seminal works on traveling waves and on morphogenesis by Fisher, by Kolmogorov, Petrovski & Piscunov, and by Turing, scientists from many disciplines have been fascinated by questions concerning the formation of steady or dynamic patterns in reactive media. The contributors to this volume include chemists, chemical engineers, mathematicians (both pure and applied), and physicists. Their contributions range from reports of experimental studies, through descriptions of numerical experiments, to rather abstract theoretical investigations, each exhibiting different aspects of a very diverse field. Although this small volume can hardly claim to cover the whole range of current research in patterns in reactive media, it nevertheless presents a representative sample.
Volume 38: Mathematics in Industrial Problems, Part 4
by Avner Friedman
The book is based on a seminar conducted by the author at the Institute for Mathematics and its applications during 1990-91. In this seminar, scientists from industry presented industrail problems to mathematicians, including the mathematical formulation of the problems. The book consists of twenty-one chapters, each one being independent of the others. Each of the first twenty chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and in some cases, reference to a solution or a partial solution of the problem. Most of the problems however, are still open and they are addressed to mathematicians. The last chapter of the book contains references to solutions of problems presented in the previous volume of "Mathematics in Industrial Problems, Part 3" published in the IMA series, as volume 31. The topics of the book include semiconductor devices ahd processing; particles dynamics; polymer chains and electrophoresis; catalytic converte, robotics and CFD in the automobile industry, superconductivity, magnetic storage devices, signal processing, and experimental design.
The book will be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It willl also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their worn work.
Volume 39: Radar and Sonar, Part II
Editors: F. Alberto Grünbaum, Marvin Bernfeld, and Richard E. Blahut
Contents: pdf postscript
This volume contains a representative discussion of mathematical problems that arise in radar and sonar and is based on the lectures that were given during the second week of the IMA summer program RADAR AND SONAR, June 18-June 29, 1990. (The first week was devoted to three sets of tutorial lectures and the lecture notes from that part of the program appear in an earlier IMA volume.) The second week was run as a workshop of contributed papers without formal review. The speakers were selected to cover a broad range of problems in this area.
The summer program was organized to stimulate a dialogue between engineers and applied mathematicians. The design of waveforms for radar and sonar and the development of algorithms for the processing of these waveforms lead to many interesting and difficult problems of applied mathematics. It is timely to separate these problems from the engineering tasks of radar and sonar so as to form a minitopic of applied mathematics. The range of such problems contained herein probably cannot be found in any other volume. There are applications of group theory, modern topics of signal processing, inverse problems, array processing and beamforming, estimation-theoretic imaging, and phase tracking. We believe the program was a great success. As these and related topics develop further a future sequel to this program will be a success as well.
Volume 40: Nonlinear Phenomena in Atmospheric and Oceanic Sciences
Editors: George F. Carnevale and Raymond T. Pierrehumbert
Contents: pdf postscript
"Nonlinear Phenomena in Athmospheric and Oceanic Sciences" is a collection of treatises contributed by distinguished physicists, mathematicians and geophysicists, concerning the fluid mechanical behavior of atmospheres, oceans and related systems. The primary emphasis is on a large scale dynamics, and accordingly, most of the chapters deal with the flow of two-dimensional or quasi-two-dimensional fluids. Topics covered include two-dimensional turbulence, fractal geometry and spectra, chaotic mixing, nonlinear stability theory, and coherent vortices. There are also contributions on convection, nonlinear stratified flow over obstacles, and chaotic eigenvalue problems appearing in dynamo theory. The geometric structures appearing in these flows are liberally illustrated through the use of color graphics.
This book will be of interest to mathematicians seeking to understand the range of problems of interest in geophysical fluid dynamics, and to geophysicists seeking to understand the range of modern mathematical techniques that can be brought to bear on geophysical fluid dynamics problems. It would be ideal as a text for graduate seminars intended to quickly bring students up to speed on this fascinating.
Volume 41: Chaotic Processes in the Geological Sciences
Editor: David A. Yuen
Contents: pdf postscript
The subject matter of chaos and nonlinear dynamics has begun to spread to the geological sciences in the last several years. The articles from this book come from a workshop held at the University of Minnesota in June 1990 in which well-renowned geophysicists, geologists and applied mathematicians were in attendance. There were three areas of focus in the workshop: thermal convection as applied to the earth's mantle, magmatic dynamics and processes in geodynamo. The nonlinear nature of convection ws discussed especially in light of recent advances made in the physics community of the phenomenon of hard-turbulent convection. This book can be useful for graduate students and researchers in geophysics, applied mechanics, and applied mathematics. It should also of interest to workers in other areas of thermal convection.
Volume 42: Partial Differential Equations with Minimal Smoothness and Applications
Editors: B. Dahlberg, E. Fabes, R. Fefferman, D. Jerison, C. Kenig, and J. Pipher
Contents: pdf postscript
In this volume we have collected articles presented at a workshop held at the University of Chicago, March 21-25, 1990. The articles address issues in the theoretical and applied aspects of partial differential equations with an emphasis on minimal smoothness.
Volume 43: On the Evolution of Phase Boundaries
Editors: Morton E. Gurtin and Geoffrey B. McFadden
Contents: pdf postscript
This volume is the proceedings of a one week workshop on phase transitions held during September 1990. A primary goal of this workshop was to emphasize the interdisciplinary nature of contempomporary research in this field, research which involves ideas from nonlinear partial differential equations, asymptotic analysis, numerical computation and experiment. The ten papers in this volume span a wide cross-section of this research. Topics covered include the treatment of scaling laws that describe the coarsening or ripening behavior observed during the later stages of phase transitions; novel numerical methods for treating interface dynamics; the mathematical description of geometric models of interface dynamics; determination of the governing equations and interfacial boundary conditions in the context of fluid flow and elasticity. This book should be interesting for any researcher pursuing modern developments in the theory and applications of phase transitions and interface dynamics.
Volume 44: Twist Mappings and Their Applications
Editors: Richard McGehee and Kenneth R. Meyer
Contents: pdf postscript
This is a collection of papers contributed by distinguished mathematicians and mathematical physicists on the dynamics of twist maps. Twist maps arise naturally in the study of stability questions in mechanical systems and applications in many areas of physical and mechanics.
This book contains many of the most recent developments by some of the leading figures in the field. It will be of interest to mathematicians, physicists, and engineers wishing to keep abreast of this fundamental and evolving area of classical mechanics.
Volume 45: New Directions in Time Series Analysis, Part I
Editors: David Brillinger, Peter Caines, John Geweke, Emanuel Parzen, Murray Rosenblatt, and Murad S. Taqqu
Contents: pdf postscript
Time Series Analysis is truly an interdisciplinary field, because development of its theory and methods requires interaction between the diverse disciplines in which it is applied. The goal of the IMA 1990 summer program from which these proceedings are drawn was to promote strong interaction among the diverse community of statisticians and other scientists whose research involves the analysis of time series data. The themes of the program were:
1. Non-linear and non-Gaussian models and processes (higher order moments and spectra, nonlinear systems, applilcations in astronomy, geophysics, enginering simulation);
2. Self-similar processes and long-range dependence (time series with long memory, fractals, 1/f noise, stable noise);
3. Interactions of Time Series Analysis and Statistics (topics include information, model identification, categorical valued time series, nonparametric and semiparametric methods);
4. Time Series research common to engineers and economists (topics include modeling of multivariate (possibly non-stationary) time series, especially by state space and adaptive methods).
The time series volumes should be of interest to researchers in all of these fields.
Volume 46: New Directions in Time Series Analysis, Part II
Editors: David Brillinger, Peter Caines, John Geweke, Emanuel Parzen, Murray Rosenblatt, and Murad S. Taqqu
See IMA Volume 45 for description.
Contents: pdf postscript
Volume 47: Degenerate Diffusions
Editors: Wei-Ming Ni, L.A. Peletier, and J.-L. Vazquez
Contents: pdf postscript
This volume is the proceedings of the IMA workshop "Degenerate Diffusion" held at the University of Minnesota from May 13 to May 18, 1991.
The workshop consisted of two parts. The emphasis of the first four days was on current progress or new problems in nonlinear diffusions involving free boundaries or sharp interfaces. The analysts and geometers will find some of the mathematical models described in this volume interesting and the papers of more pure mathematical nature included here should provide applied mathematicians with powerful methods and useful techniques in handling singular perturbation problems as well as free boundary problems.
Volume 48: Linear Algebra, Markov Chains, and Queueing Models
Editors: Carl D. Meyer and Robert J. Plemmons
This volume contains some of the lectures given at the workshop Linear Algebra, Markov Chains, and Queueing Models held January 13-17, 1992, as part of the year of Applied Linear Algebra at the Institute for Mathematics and its applications.
Markov chains and queueing models play an increasingly important role in the understanding of complex systems such as computer, communication, and transportation systems. Linear algebra is an indispensable tool in such research, and this volume collects a selection of important papers in this area. The articles contained herein are representative of the underlying purpose of the workshop which was to bring together practitioners and researchers from the areas of linear algebra, numerical analysis, and queueing theory who share a common interest of analyzing and solving finite state Markov chains. The papers in this volume are grouped into three mejor categories-perturbation theory and error analysis, iterative methods, and applications regarding queueing models.
It is hoped that these contributions can provide the reader with an enlarged perspective of some of the major issues which are of current concern to both the pure and applied communities.
Volume 49: Mathematics in Industrial Problems, Part 5
by Avner Friedman
The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1991-92. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of twenty chapters, each one being independent of the others. Each of the first nineteen chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or a partial solution of the problem. Most of the problems, however, are stilll open and they are addressed to mathematicians. The last chapter of the book contains references to solutions of problems presented in the previous volumes of "Mathematics in Industrial Problems, Parts 2, 3, and 4" published in the IMA series, as volume 24, volume 31, and volume 38. The topics included in Part 5 are imaging and visualization, diffusion in glassy and swelling polymers, composite materials, plastic flows, coating of fiber optics, communication, colloidal dispersion, stress in semiconductor, micromagnetics, photobleaching, and machine vision.
The book will be of interest to mathematicians seeking to work on mathematical roblems which arise in industry. It will also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their own work.
Volume 50: Combinatorial and Graph-Theoretic Problems in Linear
Editors: Richard A. Brualdi, Shmuel Friedland, and Victor Klee
Contents: pdf postscript
This volume is the proceeding of a workshop on combinatorial and graphp-theoretical problems in linear algebra held during the week of November 11-15, 1991. A primary goal of the workshop was to foster interaction among the people who work on linear algebra problems in which combinatorial or graph-theoretical analysis is a major component and those that work on combinatorial or graph- theoretical problems for which linear algebra is a major tool. The fifteen papers in this volume span a wide cross-section of past and current research in the topic of the workshop. Specific topics covered in the papers include matrix problems and results in symbolic dynamics, block-triangular decompositions of mixed matrices, algebraic and geometric properties of Laplacian matrices of graphs, the use of eigenvalues in combinatorial optimization, eigenvalues and associated eigenspaces of graphs and tournaments, qualitative and combinatorial aspects of matrices, perturbation effects on rank and eigenvalues, and polynomial spaces. This book should be of interest to researchers in linear algebra, combinatorics and graph theory, and to anyone who wishes to get a glimpse of this fascinating area.
Volume 51: Statistical Thermodynamics and Differential Geometry of Microstructured Materials
Editors: H. Ted Davis and Johannes C.C. Nitsche
Contents: pdf postscript
Dynamic phase transitions and the consequent issues of rapid solidification, liquification, and vaporization, gives rise to difficult experimental, physical and mathematical questions. The articles herein collected are from a workshop held at the University of Minnesota in October, 1990 and include presentations by some of the principal workkers in their respective fields on molecular dynamics, shear induced dynamic phase transitions, the Riemann problem for systems that allow change of type, adiabatic shear band formation, shock stability, and the implications of higher spatial gradients of deformation entering into the constitutive structure. The book should be of interest to physicists, mechanicians, and applied mathematicians.
Volume 52: Shock Induced Transitions and Phase Structures in General Media
Editors: R. Fosdick, E. Dunn and M. Slemrod
Contents: pdf postscript
Dynamic phase transitions and the consequent issues of rapid solidification, liquification, and vaporization, gives rise to difficult experimental, physical and mathematical questions. The articles herein collected are from a workshop held at the University of Minnesota in October, 1990 and include presentations by some of the principal workers in their respective fields on molecular dynamics, shear induced dynamic phase transitions, the Riemann problem for systems that allow change of type, adiabatic shear band formation, shock stability, and the implications of higher spatial gradients of deformation entering into the constitutive structure. The book should be of interest to physicists, mechanicians, and applied mathematicians.
Volume 53: Variational Problems
Editors: A. Friedman and J. Spruck
Contents: pdf postscript
This volume contains articles based on lectures given at the workshop "Variational and Free Boundary Problems'' held April 1990 as a part of the year of Phase Transitions and Free Boundaries at the Institute for Mathematics and its Applications. The book provides a wide cross section of current research in far growing area. The articles are based on models which arise in phase transitions, in elastic/plastic contact problems, Hele-Shaw cells, crystal growth, variational formulation of computer vision models, magneto-hydrodynamics, bubble growth, hydrodynamics (jets and cavities), and in stochastic control and economics. They present mathematical methods which hopefully can be further extended and developed for other models. The book should be of interest both to mathematicians and to engineers who are working with mathematical models.
Volume 54: Microstructure and Phase Transition
Editors: D. Kinderlehrer, R. James, J.L. Ericksen and M. Luskin
Contents: pdf postscript
Much of our traditional knowledge of materials and processes is achieved by observation 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 the 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 constitute the proceedings of an IMA workshop dedicated to these issues.
Volume 55: Turbulence in Fluid Flows: A Dynamical Systems Approach
Editors: George R. Sell, Ciprian Foias, and Roger Temam
Contents: pdf postscript
The Institute of Mathematical Applications workshop on a Dynamical System Approach to Turbulence in Fluid Flows was one of a trio of workshops which closed the year-long program on Dynamical Systems and their Applications. The papers contained in this volume represent various approaches for studying the interrelated concepts of turbulence and long-time dynamics of the Navier-Stokes equations and related problems.
Volume 56: Graph Theory and Sparse Matrix Computation
Editors: Alan George, John Gilbert and Joseph W.H. Liu
Contents: pdf postscript
When reality is modeled by computation, matrices are often the connection between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer. Efficiency demands that every possible advantage be exploited: sparse structure, advanced computer architectures, efficient algorithms. Therefore sparse matrix computation knits together threads from linear algebra, parallel computing, data structures, geometry, and both numerical and discrete algorithms. One of the strongest threads is graph theory, which has been ubiquitous in sparse matrix computation ever since Seymour Parter used undirected graphs to model symmetric Gaussian elimination more than 30 years ago.
The Institute for Mathematics and Its Applications held a workshop on "Sparse Matrix Computations: Graph Theory Issues and Algorithms," organized by the editors of this volume, from October 14 to 18, 1991. The workshop included fourteen invited and several contributed talks, software demonstrations, an open problem session, and a great deal of stimulating discussion between mathematicians, numerical analysts, and theoretical computer scientists. After the workshop we invited some of the participants to submit papers for this collection. We intend the result to be a resource for the researcher or advanced student of either graphs or sparse matrices who wants to explore their connections. Therefore we asked the authors to undertake the challenging task of making current research accessible to both communities.
Volume 57: Mathematics in Industrial Problems, Part 6
by Avner Friedman
This is the sixth volume in Avner Friedman's collection of Mathematics in Industrial Problems. These books aim to foster interaction between industry and mathematics at the "grass root" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The author's sources are affiliated with a variety of industrial enterprises including Eastman Kodak Company, Ford Motor Company, 3M, General Motors, Paramax, IBM/T.J. Watson Research Center, Xerox Corporation/Webster Research Center, Cray Research Inc., and Motorola.
The topics explored in this volume include magnetization in recording media; effective medium theory for color, particle simulation in xerography; amorphous semiconductors, small device semiconductor, and smart power device; dopant diffusion in network; reaction-diffusion and dissolution of crystals in solution; permeation through flawed surfaces; statistical quality control; glassy polymers; wettability for heterogeneous surfaces; electrorheological fluids; remote sensing and data fusion; micromechanical structures, and sensors. Open problems and references to mathematical literature are incorporated into many chapters. The final chapter contains solutions to problems raised in parts of the preceding volumes of Mathematics in Industrial Problems, published in the IMA Volumes in Mathematics and its Applications.
Volume 58: Semiconductors, Part I
Editors: W.M. Coughran, Jr., Julian Cole, Peter Lloyd and Jacob White
Contents: pdf postscript
Semiconductor and integrated-circuit modeling are an important part of the high-technology "chip" industry, whose high-performance, low-cost microprocessors and high-density memory designs form the basis for supercomputers, engineering workstations, laptop computers, and other modern information appliances. There are a variety of differential equation problems that must be solved to facilitate such modeling.
During July 15-August 9, 1991, the Institute for Mathematics and its Applications at the University of Minnesota ran a special program on "Semiconductors." The four weeks were broken into three major topic areas:
- Semiconductor technology computer-aided design and process modeling during the first week (July 15-19, 1991).
- Semiconductor device modeling during the second and third weeks (July 22-August 2, 1991).
- Circuit analysis during the fourth week (August 5-9, 1991).
This organization was natural since process modeling provides the geometry and impurity doping characteristics that are prerequisites for device modeling; device modeling, in turn, provides static current and transient charge characteristics needed to specify the so-called compact models employed by circuit simulators. The goal of this program was to bring together scientists and mathematicians to discuss open problems, algorithms to solve such, and to form bridges between the diverse disciplines involved.
The program was championed by Farouk Odeh of the IBM T.J. Watson Research Center. Sadly, Dr. Odeh met an untimely death. We have dedicated the proceedings volumes to him.
In this volume, we have combined the papers from the process modeling (week 1) and circuit simulation (week 4) portions of the program.
Volume 59: Semiconductors, Part II
Editors: W.M. Coughran, Jr., Julian Cole, Peter Lloyd and Jacob White
Contents: pdf postscript
In 1991, semiconductor device modeling for practical engineering problems was largely based on the so-called drift-diffusion equations, a Poisson equation for the electrostatic potential coupled with advection-diffusion transport equations for the electrons and holes (in silicon, for example). Another popular model equation is the Boltzmann transport equation ( bte) of which the drift-diffusion equations are an approximation. For sufficiently small structures or iii-v (like GaAs) devices, some of the assumptions of the drift-diffusion model are incorrect. Alternate derivatives of the bte, such as energy-balance (or energy-transport) and hydrodynamic models, are of considerable interest. In fact, Dr. Odeh made a number of influential contributions to the hydrodynamic model and algorithms for it. The papers in this volume describe a variety of models and effectual techniques for dealing with them.
Volume 60: Recent Advances in Iterative Methods
Editors: Gene Golub, Anne Greenbaum and Mitchell Luskin
Contents: pdf postscript
The solution of very large sparse or structured linear algebra problems is an integral part of many scientific computations. Direct methods for solving such problems are often infeasible because of computation time and memory requirements, and so iterative techniques are used instead. In recent years much research has focussed on the efficient solution of large systems of linear equations, least squares problems, and eigenvalue problems using iterative methods. The IMA Workshop on Iterative Methods for Sparse and Structured Problems brought together researchers from all over the world to discuss topics of current research. Areas addressed included the development of efficient iterative techniques for solving nonsymmetric linear systems and eigenvalue problems, estimating the convergence rate of such algorithms, and constructing efficient preconditioners for special classes of matrices such as Toeplitz and Hankel matrices. Iteration strategies and preconditioners that could exploit parallelism were of special interest. The papers in this volume represent the latest results of mathematical and computational research into the development and analysis of robust iterative methods for numerical linear algebra problems.
Volume 61: Free Boundaries in Viscous Flows
Editors: Robert A. Brown and Stephen H. Davis
Contents: pdf postscript
It is increasingly the case that models of natural phenomena and materials processing systems involve viscous flows with free surfaces. These free boundaries are interfaces of the fluid with either second immiscible fluids or else deformable solid boundaries. The deformation can be due to mechanical displacement or as is the case here, due to phase transformation; the solid can melt or freeze. This volume of the IMA Proceedings highlights a broad range of subjects on interfacial phenomena. There is an overview of the mathematical description of viscous free-surface flows, a description of the current understanding of mathematical issues that arise in these models and a discussion of high-order-accuracy boundary-integral methods for the solution of viscous free surface flows. There is the mathematical analysis of particular flows: long-wave instabilities in viscous-film flows, analysis of long-wave instabilities leading to Marangoni convection, and descriptions of the interaction of convection with morphological stability during directional solidification.
Volume 62: Linear Algebra for Control Theory
Editors: Paul Van Dooren and Bostwick Wyman
Contents: pdf postscript
During the past decade the interaction between control theory and linear algebra has been ever increasing, giving rise to new results in both areas. As a consequence it was quite natural to include in the Applied Linear Algebra Year held at the IMA, a workshop dedicated to this interdisciplinary area.
This volume contains invited papers presented at this Workshop on Linear Algebra for Control Theory. The cross-fertilization between control and linear algebra can be found in subfields as Numerical Linear Algebra, Canonical Forms, Ring-theoretic Methods, Matrix Theory, and Robust Control.
The challenge of the workshop was to present the latest results in these areas and to find points of common interest. The present volume reflects very nicely this interaction: the range of topics seems very wide indeed but the basic problems and techniques are always closely connected. And the common denominator in all this is of course linear algebra.
Volume 63: Hamiltonian Dynamical Systems: History, Theory, and Applications
Editors: H.S. Dumas, K.R. Meyer, and D.S. Schmidt
Contents: pdf postscript
From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems held at the University of Cincinnati in March of 1992. Its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, these proceedings are a slice not only of state-of-the-art methodology in Hamiltonian dynamics, but also of the bigger picture in which that methodology is embedded.
Volume 64: Systems and Control Theory for Power Systems
Editors: Joe H. Chow, Petar V. Kokotovic, and Robert J. Thomas
Contents: pdf postscript
The articles in this book are from a workshop on power systems held at the Institute of Mathematics and its Applications at the University of Minnesota. Their topics include power system model reduction, transient and voltage stability, nonlinear control, robust stability, computation and optimization. The articles are authored by some of the leading researchers in these areas. The book should be of interest to power and control engineers, and applied mathematicians.
Volume 65: Mathematical Finance
Editors: Mark H.A. Davis, Darrell Duffie, Wendell H. Fleming, and Steven E. Shreve
Contents: pdf postscript
This volume is the Proceedings of the Workshop on Mathematical Finance held at the Institute for Mathematics and its Applications, June 14-18, 1993. A workshop on mathematical finance can be held only because of two revolutions that have taken place on Wall Street in the latter half of the twentieth century. The first revolution, which was the introduction of quantitative methods to the black art of equity fund management, began with the 1952 publication of his PhD dissertation "Portfolio Selection" by Harry Markowitz. The second revolution in finance began with the 1973 publication of the solution by Fischer Black and Myron Scholes (in consultation with Robert Merton) to the option pricing problem. The Black-Scholes formula brought to the finance industry the modern methodology of martingales and stochastic calculus, methodology which enables investment banks to produce, price and hedge an endless variety of "derivative securities." These two revolutions in finance have created a stream of practical problems whose solutions require the expertise of research mathematicians. This workshop addressed a number of these problems.
Volume 66: Robust Control Theory
Editors: Bruce A. Francis and Pramod P. Khargonekar
Contents: pdf postscript
Robust control is motivated by the need to cope with systems with modeling uncertainty. Uncertainty is always present, fundamentally because no mathematical system can exactly model a physical system. For example, there are always uncertain parameters and unmodeled dynamics; simplifying assumptions are often made; only incomplete or inexact data from identification experiments is available. Robust control theory is a central subfield of control theory and deals with the analysis and synthesis of control systems in the face of plant uncertainty.
The 1992 IMA Workshop on Robust Control Theory brought together leading experts and covered most major research directions in the field of robust control This volume contains papers based on some of the talks that were presented.
Volume 67: Mathematics in Industrial Problems, Part 7
by Avner Friedman
This is the seventh volume in Avner Friedman's collection of Mathematics in Industrial Problems. These books aim to foster interaction between industry and mathematics at the "grass root" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The author's sources are affiliated with a variety of industrial enterprises including General Motors, Eastman Kodak, Ford Motor Company, Oak Ridge National Laboratory, Bellcore, 3M, IBM, Siemens, Honeywell, UNISYS and Motorola.
The topics explored in this volume include heat sensors for automobiles, battery cells, colloidal dispersions, polymers, crack propagation, coating by electrostatic sprayers, neural networks, head-tape interaction in magnetic tapes, layered manufacturing, image analysis, landmarks identification by robots, communication for multi-users, data fusion, doping profile in semiconductors, effective medium estimates, and scattering by electromagnetic waves.
Open problems and references to mathematical literature are incorporated into most of the chapters. The final chapter contains solutions to problems raised in parts of the preceding volumes of Mathematics in Industrial Problems, published in the IMA Volumes in Mathematics and its Applications.