K.-H. Hoffmann - Böcker

Interest in the area of control of systems defined by partial differential Equations has increased strongly in recent years. A major reason has been the requirement of these systems for sensible continuum mechanical modelling and optimization or control techniques which account for typical physical phenomena. Particular examples of problems on which substantial progress has been made are the control and stabilization of mechatronic structures, the control of growth of thin films and crystals, the control of Laser and semi-conductor devices, and shape optimization problems for turbomachine blades, shells, smart materials and microdiffractive optics. This volume contains original articles by world reknowned experts in the fields of optimal control of partial differential equations, shape optimization, numerical methods for partial differential equations and fluid dynamics, all of whom have contributed to the analysis and solution of many of the problems discussed. The collection provides a state-of-the-art overview of the most challenging and exciting recent developments in the field. It is geared towards postgraduate students and researchers dealing with the theoretical and practical aspects of a wide variety of high technology problems in applied mathematics, fluid control, optimal design, and computer modelling.

The theory of complex Ginzburg-Landau type phase transition and its applica­ tions to superconductivity and superfluidity has been a topic of great interest to theoretical physicists and has been continuously and persistently studied since the 1950s. Today, there is an abundance of mathematical results spread over numer­ ous scientific journals. However, before 1992, most of the studies concentrated on formal asymptotics or linear analysis. Only isolated results by Berger, Jaffe and Taubes and some of their colleagues touched the nonlinear aspects in great detail. In 1991, a physics seminar given by Ed Copeland at Sussex University inspired Q. Tang, the co-author of this monograph, to study the subject. Independently in Munich, K.-H. Hoffmann and his collaborators Z. Chen and J. Liang started to work on the topic at the same time. Soon it became clear that at that time, groups of mathematicians at Oxford and Virginia Tech had already studied the subject for a couple of years. They inspired experts in interface phase transition problems and their combined effort established a rigorous mathematical framework for the Ginzburg-Landau system. At the beginning Q. Tang collaborated with C.M. Elliott and H. Matano.

In recent years statistical physics has made significant progress as a result of advances in numerical techniques. While good textbooks exist on the general aspects of statistical physics, the numerical methods and the new developments based on large-scale computing are not usually adequately presented. In this book 16 experts describe the application of methods of statistical physics to various areas in physics such as disordered materials, quasicrystals, semiconductors, and also to other areas beyond physics, such as financial markets, game theory, evolution, and traffic planning, in which statistical physics has recently become significant. In this way the universality of the underlying concepts and methods such as fractals, random matrix theory, time series, neural networks, evolutionary algorithms, becomes clear. The topics are covered by introductory, tutorial presentations.

The book contains lectures presented during the meeting "1st caesarium" held on the topic "Smart Materials" 1999 in Bonn. Recent results in theory and engineering of smart materials were discussed. Special emphasis was put on thin film technology and its role in sensor and actuator applications.This book will be of particular interest to physicists, engineers and mathematicians working in academia as well as in industry on the field of new materials with special interest in finding intelligent solutions of complex technological problems.

In recent years statistical physics has made significant progress as a result of advances in numerical techniques. While good textbooks exist on the general aspects of statistical physics, the numerical methods and the new developments based on large-scale computing are not usually adequately presented. In this book 16 experts describe the application of methods of statistical physics to various areas in physics such as disordered materials, quasicrystals, semiconductors, and also to other areas beyond physics, such as financial markets, game theory, evolution, and traffic planning, in which statistical physics has recently become significant. In this way the universality of the underlying concepts and methods such as fractals, random matrix theory, time series, neural networks, evolutionary algorithms, becomes clear. The topics are covered by introductory, tutorial presentations.

Der vorliegende Band vermittelt einen aktuellen Einblick in fünfzig Verbundprojekte zwischen Hochschulinstituten und Industrieunternehmen, die gefördert werden durch das Bundesministrium für Bildung, Wissenschaft, Forschung und Technologie. Die vorliegenden Artikel entstanden auf der Grundlage von Vorträgen, die anläßlich des BMBF-Statusseminars im Oktober 1995 in München gehalten wurden. Sie beschreiben sowohl die grundlegenden mathematischen Fortschritte, als auch die Ansätze zur Lösung konkreter Anwenderprobleme. Deren Spektrum reicht von der Bildverarbeitung über chemische Reaktionen, Computertomographie, Fahrzeugdynamik, Muster- und Strukturerkennung, Prozeßsteuerung und Roboter in der industriellen Praxis bis hin zu Strömungsvorgängen und Verkehrsführungssystemen.

Of all the zoological classes the insects are the most numerous in species and the most varied in structure. Estimates of the number 18 of species vary from 1 to 10 million, and 10 individuals are es­ timated to be alive at any given moment. In their evolution, in­ sects are relatively ancient and, therefore, they have proved to be a phenomenally successful biological design which has survived unchanged in its basic winged form during the last 300 m. y. In­ sects were the first small animals to colonize the land with full suc­ cess. Their small size opened many more ecological niches to them and permitted a greater diversification than the vertebrates. What is it about this design that has made insects so successful in habitats stretching from arid deserts to the Arctic and Antarctic and from freshwater brooks to hot springs and salines? Is it due to the adapta­ bility of their behavior, physiology, and biochemistry to changing environmental conditions? Three features of insects are of particular importance in determin­ ing their physiological relationship with the environment: their small size, as mentioned above, the impermeability and rigidity of their exoskeleton, and their poikilothermy. Of course, as with any other animals, the insects' success in its environment depends on its ability to maintain its internal state within certain tolerable limits of temperature, osmotic pressure, pH or oxygen concentra­ tion (homoeostasis).

This volume contains the contributions of participants of the conference "Optimal Control of Partial Differential Equations" which, under the chairmanship of the editors, took place at the Mathematisches Forschungsinstitut Oberwolfach from May 18 to May 24, 1986. The great variety of topics covered by the contributions strongly indicates that also in the future it will be impossible to develop a unifying control theory of partial differential equations. On the other hand, there is a strong tendency to treat prob­ lems which are directly connected to practical applications. So this volume contains real-world applications like optimal cooling laws for the production of rolled steel or concrete solutions for the problem of optimal shape design in mechanics and hydrody­ namics. Another main topic is the construction of numerical methods. This includes applications of the finite element method as well as of Quasi-Newton-methods to con­ strained and unconstrained control problems. Also, very complex problems arising in the theory of free boundary value problems are treated. ]~inally, some contribu­ tions show how practical problems stimulate the further development of the theory; in particular, this is the case for fields like suboptimal control, necessary optimality conditions and sensitivity analysis. As usual, the lectures and stimulating discussions took place in the pleasant at­ mosphere of the Mathematisches Forschungsinstitut Oberwolfach. Special thanks of the participants are returned to the Director as well as to the staff of the institute.

The theory of complex Ginzburg-Landau type phase transition and its applica­ tions to superconductivity and superfluidity has been a topic of great interest to theoretical physicists and has been continuously and persistently studied since the 1950s. Today, there is an abundance of mathematical results spread over numer­ ous scientific journals. However, before 1992, most of the studies concentrated on formal asymptotics or linear analysis. Only isolated results by Berger, Jaffe and Taubes and some of their colleagues touched the nonlinear aspects in great detail. In 1991, a physics seminar given by Ed Copeland at Sussex University inspired Q. Tang, the co-author of this monograph, to study the subject. Independently in Munich, K.-H. Hoffmann and his collaborators Z. Chen and J. Liang started to work on the topic at the same time. Soon it became clear that at that time, groups of mathematicians at Oxford and Virginia Tech had already studied the subject for a couple of years. They inspired experts in interface phase transition problems and their combined effort established a rigorous mathematical framework for the Ginzburg-Landau system. At the beginning Q. Tang collaborated with C.M. Elliott and H. Matano.