Just a few decades ago, chemical oscillations were thought to be exotic reactions of only theoretical interest. Now known to govern an array of physical and biological processes, including the regulation of the heart, these oscillations are being studied by a diverse group across the sciences. This book is the first introduction to nonlinear chemical dynamics written specifically for chemists. It covers oscillating reactions, chaos, and chemical pattern formation, and includes numerous practical suggestions on reactor design, data analysis, and computer simulations. Assuming only an undergraduate knowledge of chemistry, the book is an ideal starting point for research in the field. The book begins with a brief history of nonlinear chemical dynamics and a review of the basic mathematics and chemistry. The authors then provide an extensive overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Throughout the authors emphasize the chemical mechanistic basis for self-organization. The overview is followed by a series of chapters on more advanced topics, including complex oscillations, biological systems, polymers, interactions between fields and waves, and Turing patterns. Underscoring the hands-on nature of the material, the book concludes with a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory.

Tbis book is intended to provide a few asymptotic methods which can be applied to the dynamics of self-oscillating fields of the reaction-diffusion type and of some related systems. Such systems, forming cooperative fields of a large num of interacting similar subunits, are considered as typical synergetic systems. ber Because each local subunit itself represents an active dynamical system function ing only in far-from-equilibrium situations, the entire system is capable of showing a variety of curious pattern formations and turbulencelike behaviors quite unfamiliar in thermodynamic cooperative fields. I personally believe that the nonlinear dynamics, deterministic or statistical, of fields composed of similar active (Le., non-equilibrium) elements will form an extremely attractive branch of physics in the near future. For the study of non-equilibrium cooperative systems, some theoretical guid ing principle would be highly desirable. In this connection, this book pushes for ward a particular physical viewpoint based on the slaving principle. The dis covery of tbis principle in non-equilibrium phase transitions, especially in lasers, was due to Hermann Haken. The great utility of this concept will again be dem onstrated in tbis book for the fields of coupled nonlinear oscillators.

Concerned with chemical wave mechanics arising from reaction in transport systems. Demonstrates that, as with free particles in quantum mechanics, certain simple elements can serve as organizing tools for understanding the complex phenomena treated. The rich diversity of waves and patterns, running the gamut from standing, oscillating, flames and nerve impulses to reactive geological media, are derived from the analysis of their underlying mathematical structures.

Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart; traffic jams move in waves down lanes crowded with vehicles. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, thus making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as an acquaintance with fluid mechanics, elasticity and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers.

Assuming no more than an undergraduate knowledge of chemistry, the authors take the reader through the necessary mathematical and theoretical background of oscillating reactions, chaos and chemical waves to advanced topics of current research interest in chemical systems.

In the past few years, there has been a rapidly growing interest in the properties of spin waves (or magnons) in ordered magnetic materials. These are the low-lying excitations that characterize the dynamical behavior of the magnetization variables in ferromagnets, ferrimagnets and antiferromagnets, particularly at low temperatures. Many of the recent developments concerning spin waves have been directed towards understanding their behavior in limited magnetic samples. At the same time, there have been dramatic advances in the experimental techniques, both for preparing high-quality magnetic samples in the form of thin films and superlattices and for the study of the spin-wave excitations themselves. Magnetic thin films have long been of technological as well as scientific interest and an understanding of both the linear and nonlinear aspects of their magnetic behavior is important.

Presents a clear systematic molecular-based description of nonlinear optical polarization analysis of chemical and biological assemblies.