The impact of Benard's discovery on 20th century physics is crucial to any modern research area such as fluid dynamics, nonlinear dynamics, and non-equilibrium thermodynamics, just to name a few. This centenary review shows the broad scope and development including modern applications, edited and written by experts in the field.

This volume contains papers contributed to the NATO Advanced Research Workshop "Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems" held in Streitberg, Fed. Rep. Germany, Sept. 24 through 30, 1989. The purpose of the rather long title has been to focus attention on a particularly fruitful direction of research within the broad field covered by terms like Nonlinear Dynamics or Non-Equilibrium Systems. After physicists have been occupied for several decades mainly with the microscopic structure of matter, recent years have witnessed a resurgence of interest in macroscopic patterns and dynamics. Research on these latter phenomena has not been dormant, of course, since fluid dynamicists interested in the origin of turbulence, meteorologists studying weather patterns and numerous other scientists have continued to advance the understanding of the structures relevant to their disciplines. The recent progress in the dynamics of nonl inear systems wi th few degrees of freedom and the discovery of universal laws such as the Feigenbaum scaling of period-doubling cascades has given rise to new hopes for the understanding of common principles underlying the spontaneous formation of structures in extended continuous systems.

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.

Goal is to contribute to understanding of localized spatial and spatio-temporal structures far from thermodynamic equilibrium. Here we report on our progress in the study of three classes of systems. (1) We have studied cellular flame structures arising in a circular burner. Using numerical computations we have found a number of traveling-wave structures in which different cells undergo different motion. Most strikingly, we have found a localized wave traveling through the array of steady cells. Results are interpreted using various asymptotic approaches. They are in qualitative agreement with recent experiments. (2) We have continued our investigation of localized waves in binary-mixture convection. Starting from the extended Ginzburg-Landau equations introduced earlier, we have derived equations of motion for interacting fronts connecting the conductive and the convective state. These equations reveal a repulsive interaction between the fronts which implies a new localization mechanism for waves. It is solely due to the long-wavelength mode specific to the extended Ginzburg-Landau equations. The stability properties of the resulting localized waves are in qualitative agreement with very recent experiments. (3) We have extended our investigation of domain structures to include their temporal evolution.

From artificial surfaces to living cells, Molecular Nano Dynamics, Vol. I and Vol. II explores more than 40 important methods for dynamic observation of the nanoscale. Edited by absolute science greats from Japan, this two-volume set covers all important aspects of this topic: nanoscale spectroscopy and characterization tools, nanostructure dynamics, single living cell dynamics, active surfaces, and single crystals. Destined to be the definitive reference work on nanoscale molecular dynamics and their observation for years to come, this is a must-have reference for chemists, physicists, physical chemists, theoretical chemists, and materials scientists.

Dynamic Biological Organization is a fascinating account of the living organisms as dynamic systems, based on the concept that the spatio-temporal coherence of events within a living system result from the intrinsic dynamics of the processes taking place within that sysem. The authors of this important work, Miguel Aon and Sonia Cortassa have travelled widely to work in some of the leading research laboratories to accumulate a large information base on which to assemble this book. Taking a transdisciplinary approach, the authors draw on work at the interface of biochemistry, genetics, physiology, thermodynamics, kinetics and biomathematics, using mathematical models throughout to corroborate and analyze the biological complexity presented. Emphasizing biological processes occuring at the cellular level. Dynamic Biological Organization gives exciting insights into the experimental and theoretical applications of modern scientific paradigms to fundamental biological processes.

This textbook on rotating fluid dynamics combines a pedagogical development of theoretical ideas with a description and analysis of many of the fascinating examples of rotating flows found in nature. The book is self-contained, starting in Part I with introductory chapters on fluid dynamics and waves. The largest section of the book is Part II, where a broad theoretical framework is developed for rotating flows, including Ekman layers, inertial waves, Taylor columns, Rossby waves, precession, instabilities, rotating convection, vortex breakdown, and rotating turbulence. The book ends, in Part III, with an analysis of some naturally occurring rotating flows, including tornadoes and dust devils, tidal vortices, tropical cyclones, convection in planetary cores, zonal winds in planetary atmospheres, and astrophysical accretion discs. Davidson presents a unique combination of a deep but broad theoretical framework with a detailed discussion of many naturally occurring flows. Moreover, the book places great emphasis on the pedagogical development of theoretical ideas and the physical insight that brings.