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Statistical Thermodynamics and Differential Geometry of Microstructured Materials
Substances possessing heterogeneous microstructure on the nanometer and micron scales are scientifically fascinating and technologically useful. Examples of such substances include liquid crystals, microemulsions, biological matter, polymer mixtures and composites, vycor glasses, and zeolites. In this volume, an interdisciplinary group of researchers report their developments in this field. Topics include statistical mechanical free energy theories which predict the appearance of various microstructures, the topological and geometrical methods needed for a mathematical description of the subparts and dividing surfaces of heterogeneous materials, and modern computer-aided mathematical models and graphics for effective exposition of the salient features of microstructured materials.
Systems and Control Theory for Power Systems
The articles in this volume cover power system model reduction, transient and voltage stability, nonlinear control, robust stability, computation and optimization and have been written by some of the leading researchers in these areas. This book should be of interest to power and control engineers, and applied mathematicians.
Adaptive Control, Filtering, and Signal Processing
The area of adaptive systems, which encompasses recursive identification, adaptive control, filtering, and signal processing, has been one of the most active areas of the past decade. Since adaptive controllers are fundamentally nonlinear controllers which are applied to nominally linear, possibly stochastic and time-varying systems, their theoretical analysis is usually very difficult. Nevertheless, over the past decade much fundamental progress has been made on some key questions concerning their stability, convergence, performance, and robustness. Moreover, adaptive controllers have been successfully employed in numerous practical applications, and have even entered the marketplace.
Linear Algebra for Signal Processing
Signal processing applications have burgeoned in the past decade. During the same time, signal processing techniques have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This trend will continue as many new signal processing applications are opening up in consumer products and communications systems. In particular, signal processing has been making increasingly sophisticated use of linear algebra on both theoretical and algorithmic fronts. This volume gives particular emphasis to exposing broader contexts of the signal processing problems so that the impact of algorithms and hardware can be better understood; it brings together the writings of signal processing engineers, computer engineers, and applied linear algebraists in an exchange of problems, theories, and techniques. This volume will be of interest to both applied mathematicians and engineers.
Microlocal Analysis and Nonlinear Waves
This IMA Volume in Mathematics and its Applications MICROLOCAL ANALYSIS AND NONLINEAR WAVES is based on the proceedings of a workshop which was an integral part of the 1988- 1989 IMA program on "Nonlinear Waves". We thank Michael Beals, Richard Melrose and Jeffrey Rauch for organizing the meeting and editing this proceedings volume. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE Microlocal analysis is natural and very successful in the study of the propagation of linear hyperbolic waves. For example consider the initial value problem Pu = f E e'(RHd), supp f C {t ;::: O} u = 0 for t
Turbulence in Fluid Flows
The articles in this volume are based on recent research on the phenomenon of turbulence in fluid flows collected by the Institute for Mathematics and its Applications. This volume looks into the dynamical properties of the solutions of the Navier-Stokes equations, the equations of motion of incompressible, viscous fluid flows, in order to better understand this phenomenon. Although it is a basic issue of science, it has implications over a wide spectrum of modern technological applications. The articles offer a variety of approaches to the Navier-Stokes problems and related issues. This book should be of interest to both applied mathematicians and engineers.
Discrete Event Systems, Manufacturing Systems, and Communication Networks
This IMA Volume in Mathematics and its Applications DISCRETE EVENT SYSTEMS, MANUFACTURING SYSTEMS AND COMMUNICATION NETWORKS is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory. " The study of discrete event dynamical systems (DEDS) has become rapidly popular among researchers in systems and control, in communication networks, in manufacturing, and in distributed computing. This development has created problems for re searchers and potential "consumers" of the research. The first problem is the veritable Babel of languages, formalisms, and approaches, which makes it very difficult to determine the commonalities and distinctions am...
Nonlinear Conservation Laws and Applications
This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of vis...
Nonlinear Stochastic PDEs
This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is based on the proceedings of the period of concentration on Stochas tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "Emerging Applications of Probability." We thank Tadahisa Funaki and Wojbor A. Woyczynski for organizing this meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE A workshop on Nonlinear Stochastic Partial Differential Equations...
Microstructure and Phase Transition
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 knowledg...
