Contents:Experimental Studies of Chaotic Mixing (J M Ottino et al)Using Random Maps in the Analysis of Experimental Fluid Flows (J C Sommerer)Chaos, Patterns and Defects in Stimulated Scattering Phenomena (R G Harrison)Test of the Normal Form for a Subcritical Bifurcation (K Wiesenfeld et al)Controlling Symbolic Dynamics for Communication (S Hayes et al)Control of Chaos in a CO2 Laser (J M Perez et al)Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure (M A Davies & F C Moon)Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source (R G Holt et al)Quantum Chaos Experiments Using Microwave Cavities (A Kudrolli & S Sridhar)When Small Noise Imposed on Deterministic Dynamics Becomes Important (M Franaszek & L Fronzoni)Chaos Control for Cardiac Arrhythmias (J N Weiss et al)Broad-Band Synchronization in Monkey Neocortex (S L Bressler et al)Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats (Y Almog et al)Tests for Deterministic Chaos in Noisy Time Series (T Chang et al)The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance (E Pantazelou et al)Chaos During Heterogeneous Chemical Reactions (J L Hudson)Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems (V Petrov et al)Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System (P Parmananda et al)Temperature Patterns on Catalytic Surfaces (D Luss)and other papers
Readership: Physicists, mathematicians, engineers, biologists and chemists.keywords:
Readership: Graduate students of mathematical physics and nonlinear science.
Keywords:Quasicrystals;Disordered Patterns;Defects;Spirals;Turbulence;Synchronization;Convection;Capillary Waves;Chaotic Dynamics;Biological PatternsReviews:
“This beautifully illustrated book brings together a remarkable array of pattern-forming phenomena … The authors have assembled an impressive collection of striking photographs and computer-generated images, and the book would be worth buying for this alone … the Appendix describing key experiments is a highlight. Here the authors outline the historical development of experiments in parametrically-excited patterns, thermal convection and diffusive chemical reactions.”UK Nonlinear News
“This book contains a very impressive account of key ideas and results in nonlinear dynamics and an equally excellent description of important experiments in pattern formation … readers can gain quite comprehensive knowledge about all possible patterns and their mathematical theories by reading a single chapter, coupled with Appendix I.”Mathematical Reviews
The fascinating part is that field equations can have localized solutions exhibiting the typical characteristics of particles. Regarding the field equations this book focuses on, the field phenomenon of localized solutions can be described in the context of a particle formalism, which leads to a set of ordinary differential equations covering the time evolution of the position and the velocity of each particle. Moreover, starting from these particle dynamics and making the transition to many body systems, one considers typical phenomena of many body systems as shock waves and phase transitions, which themselves can be described as field phenomena. Such transitions between different level of modelling are well known from conservative systems, where localized solutions of quantum field theory lead to the mechanisms of elementary particle interaction and from this to field equations describing the properties of matter. However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. This model allows to understand the existence of localized structures, their mechanisms of movement, and their interaction, at least, on a qualitative level. But this model is also the starting point for developing a data analysis method that enables the detection of movement and interaction mechanisms of the investigated localized solutions. The topic is rounded of by applying the data analysis to real experimental data and comparing the experimental observations to the predictions of the model.
A comprehensive publication covering the interesting topic of localized solutions in reaction diffusion systems in its width and its relation to the well known phenomena of spirals and patterns does not yet exist, and this is the third reason for writing this book. Although the book focuses on a specific experimental system the model equations are as simple as possible so that the discussed methods should be adaptable to a large class of systems showing particle-like structures.
Therefore, this book should attract not only the experienced scientist, who is interested in self-organization phenomena, but also the student, who would like to understand the investigation of a complex system on the basis of a continuous description.