(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
This book is devoted to the study of evolution of nonequilibrium systems. Such a system usually consists of regions with different dominant scales, which coexist in the space-time where the system lives. In the case of high nonuniformity in special directions, one can see patterns separated by clearly distinguishable boundaries or interfaces.
The author considers several examples of nonequilibrium systems. One of the examples describes the invasion of the solid phase into the liquid phase during the crystallization process. Another example is the transition from oxidised to reduced states in certain chemical reactions. An easily understandable example of the transition in the temporal direction is a sound beat, and the author describes typical patterns associated with this phenomenon.
The main goal of the book is to present a mathematical approach to the study of highly nonuniform systems and to illustrate it with examples from physics and chemistry. The two main theories discussed are the theory of singular perturbations and the theory of dissipative systems. A set of carefully selected examples of physical and chemical systems nicely illustrates the general methods described in the book.
Translations of Mathematical Monographs (Iwanami Series in Modern Mathematics, Volume 209.
March 2002, approximately 336 pages
Softcover, ISBN 0-8218-2625-5.
Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side, occurring, in particular, in the study of dynamics of economical, social, and biological macrosystems. They are also very useful in proving existence theorems in control theory.
This text provides an introductory treatment to the theory of differential inclusions. The reader is only required to know ordinary differential equations, theory of functions, and functional analysis on the elementary level.
Graduate Studies in Mathematics, Volume 41; 2002; 226 pages
Hardcover ISBN 0-8218-2977-7.
The most prominent example of a complex adaptive system is our brain. It consists of neurons which are connected by synapses to a complex and intricate network which is adaptive, i.e. we can learn with our brain.
In recent years it has become clear that the picture of complex adaptive systems as networks, consisting of many nonlinearly interacting elements which can adapt their dynamical behaviour to external influences applies to many evolutionary processes ranging from the emergence of life our of a network of interacting biopolymers, via Darwinian evolution with its ecological and economical networks, to the emergence of higher brain functions in neural networks and man made, i.e. evolutionary caused, communications networks like the internet.
The investigation of complex adaptive systems has led to a number of exciting results such as the breeding of self-replicating computer programs, the self-organized formation of categories in neural tissue or the emergence of cooperation between egoistic partners in evolutionary games.
This book provides an introduction into this field from a physicist's point of view. New concepts such as robust computation with attractors, measures of complexity and optimal control are introduced on an elementary level. In addition to this solved exercises provide a solid ground for students and researchers who want to enter the field.
Heinz Georg Schuster is Professor of Theoretical Physics at the University of Kiel in Germany. He has been a visiting professor at the Weizmann Institute of Science in Israel and at the California Institute of Technology in Pasadena. his book "Deterministic Chaos" has been translated into five languages.
For further information on this title, please visit:
Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students provides sophisticated numerical methods for the fast and accurate solution of a variety of equations, including ordinary differential equations, delay equations, integral equations, functional equations, and some partial differential equations, as well as boundary value problems. It introduces many modelling techniques and methods for analyzing the resulting equations.
Instructors, students, and researchers will all benefit from this book, which demonstrates how to use software tools to simulate and study sets of equations that arise in a variety of applications. Instructors will learn how to use computer software in their differential equations and modelling classes, while students will learn how to create animations of their equations that can be displayed on the World Wide Web. Researchers will be introduced to useful tricks that will allow them to take full advantage of XPPAUT's capabilities. In addition, readers will learn several concepts from the field of dynamical systems, including chaos theory, how systems depend on parameters, and how simple physical systems can lead to complicated behaviour.
XPPAUT is a tool for simulating, animating, and analyzing
dynamical systems that evolved from tools developed by the
author for studying nonlinear oscillations. XPPAUT offers
several advantages over MATLAB, Maple, and Mathematica,
including the following:
This book will be most useful to researchers and modellers who want to simulate and analyze a system, and to students as an adjunct to a class in modelling or differential equations.
List of Figures; Preface; Chapter 1: Installation; Chapter 2; A Very Brief Tour of XPPAUT; Chapter 3: Writing ODE Files for Differential Equations; Chapter 4: XPPAUT in the Classroom; Chapter 5: More Advanced Differential Equations; Chapter 6: Spatial Problems, PDEs, and BVPs; Chapter 7: Using AUTO: Bifurcation and Continuation; Chapter 8: Animation; Chapter 9; Tricks and Advanced Methods; Appendix A: Colours and Linestyles; Appendix B: The Options; Appendix C: Numerical Methods; Appendix D: Structure of ODE Files; Appendix E: Complete Command List; Appendix F: Error Messages; Appendix G: Cheat Sheet; References; Index
2002 / xiv + 290 pages / Softcover / ISBN 0-89871-506-7
The European Consortium for Mathematics in Industry (ECMI) was founded in 1986 by leading groups of mathematicians in Europe for the following scopes:
ECMI 2000 shows that ECMI has offered a unique example of effective international cooperation thanks to the financial support of the European Framework programmes. In particular they have helped ECMI establishing a set of Special Interest Groups to favour interaction with industry. This volume includes minisymposia about their activities, in particular microelectronics, glass, polymers, finance, traffic, and textiles. Applied mathematicians and other professionals working in academia or industry will find the book to be a useful and stimulating source of mathematical applications related to industrial problems.
Keywords: Mathematics in Industry, Mathematics in Finance, Computational Science and Engineering, Optimization, Mathematics in Medicine.
More information on this title including a detailed Table of Contents can be found at http://www.springer.de/cgi/svcat/search_book.pl?isbn=3-540-42582-9 .
2002. XV, 666 pp. 221 figs., 4 in colour. Hardcover.
Recommended Retail Price: EUR 69,95 *
The first book to bring together, in a consistent statistical framework, the ideas of nonlinear modelling and Bayesian methods.
For further information, visit the Wiley website at:
In this volume, leading experts present current achievements in the forefront of research in the challenging field of chaos in circuits and systems, with emphasis on engineering perspectives, methodologies, circuitry design techniques, and potential applications of chaos and bifurcation. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this field. It is suitable for readers ranging from graduate students, university professors, laboratory researchers and industrial practitioners to applied mathematicians and physicists in electrical, electronic, mechanical, physical, chemical and biomedical engineering and science.
For more details see the web page:
World Scientific Series on Nonlinear Science, Series B - Vol. 11
630 pages (approximately)