Excitable media comprise a class of models for a wide range of physical, chemical, and biological systems that exhibit spontaneous formation of spatial patterns. Patterns in Excitable Media: Genesis, Dynamics, and Control explores several aspects of the dynamics of such patterns-in particular their evolution upon interaction with structural and fun

Pattern formation has traditionally been studied in non-equilibrium physics from the viewpoint of describing the basic structures and their interactions. While this is still an important area of research, the emphasis in the last few years has shifted towards analysis of specific properties of patterns in various complex media. For example, diverse and unexpected phenomena occur in neuro-like media that are characterized by highly non-trivial local dynamics. We carried out an active research program on analysis of spatio-temporal patterns in various physical systems (convection, oscillating fluid layer, soap film), as well as in neuro-like media, with an emphasis on informational aspects of the dynamics. Nonlinear nonequilibrium media and their discrete analogs have a unique ability to represent, memorize, and process the information contained in spatio-temporal patterns. Recent neurophysiological experiments demonstrated a certain universality of spatio-temporal representation of information by neural ensembles. Information processing is also revealed in the spatio-temporal dynamics of cellular patterns in nonequilibrium media. It is extremely important for many applications to study the informational aspects of these dynamics, including the origins and mechanisms of information generation, propagation and storage. Some of our results are: the discovery of self-organization of periodically oscillatory patterns in chaotic heterogeneous media; the analysis of the propagation of the information along a chaotic media as function of the entropy of the signal; the analysis of wave propagation in discrete non-equilibrium media with autocatalytic properties, which simulates the calcium dynamics in cellular membranes. Based on biological experiments we suggest the mechanism by which the spatial sensory information is transferred into the spatio-temporal code in the neural media. We also found a new mechanism of self-pinning in cellular structures and the related phenomenon of stick-slip front motion.

Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of complexity, and in which initial concepts of dissipative structures or synergetics are deeply rooted. In pioneering domains related to hydrodynamics or chemical instabilities, the interactions between experimentalists and theoreticians, sometimes on a daily basis, have been a key to progress. Everyone in the field praises the role played by the interactions and permanent feedbacks between ex perimental, numerical, and analytical studies in the achievements obtained during these years. Many aspects of convective patterns in normal fluids, binary mixtures or liquid crystals are now understood and described in this framework. The generic pres ence of defects in extended systems is now well established and has induced new developments in the physics of laser with large Fresnel numbers. Last but not least, almost 40 years after his celebrated paper, Turing structures have finally been ob tained in real-life chemical reactors, triggering anew intense activity in the field of reaction-diffusion systems.

An integrated approach to the molecular theory of reaction mechanism in heterogeneous catalysis, largely based on the knowledge among the growing theoretical catalysis community over the past half century, and covering all major catalytic systems. The authors develop a general conceptual framework, including in-depth comparisons with enzyme catalysis, biomineralisation, organometallic and coordination chemistry. A chapter dedicated to molecular electrocatalysis addresses the molecular description of reactions at the liquid-solid interphase, while studies range from a quantum-chemical treatment of individual molecular states to dynamic Monte-Carlo simulations, including the full flexibility of the many-particle systems. Complexity in catalysis is explained in chapters on self-organization and self-assembly of catalysts, and other sections are devoted to evolutionary, combinatorial techniques as well as artificial chemistry.

Proceedings of a NATO ARW held in Leeds, UK, September 11-15, 1989

This is the second of two volumes offering the very first comprehensive treatise of self-organization and non-linear dynamics in electrochemical systems. The first volume covers general principles of self-organization as well as temporal instabilities. The content of both volumes is organized so that each description of a particular electrochemical system is preceded by an introduction to basic concepts of nonlinear dynamics, in order to help the reader unfamiliar with this discipline to understand at least fundamental concepts and the methods of stability analysis. The presentation of the systems is not limited to laboratory models but stretches out to real-life objects and processes, including systems of biological importance, such as neurons in living matter. Marek Orlik presents a comprehensive and consistent survey of the field.