Author: Said Slimani
Publisher:
ISBN:
Category :
Languages : en
Pages : 360

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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 36

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Book Description
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.

Author: Daniel Walgraef
Publisher: Springer Science & Business Media
ISBN: 1461218500
Category : Science
Languages : en
Pages : 310

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Book Description
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.

Author: Wayne Nagata
Publisher: American Mathematical Soc.
ISBN: 0821837257
Category : Mathematics
Languages : en
Pages : 186

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Book Description
Nonlinear dynamical systems and the formation of spatio-temporal patterns play an important role in current research on partial differential equations. This book contains articles on topics of current interest in applications of dynamical systems theory to problems of pattern formation in space and time. Topics covered include aspects of lattice dynamical systems, convection in fluid layers with large aspect ratios, mixed mode oscillations and canards, bacterial remediation of waste, gyroscopic systems, data clustering, and the second part of Hilbert's 16th problem. Most of the book consists of expository survey material, and so can serve as a source of convenient entry points to current research topics in nonlinear dynamics and pattern formation. This volume arose from a workshop held at the Fields Institute in December of 2003, honoring Professor William F. Langford's fundamental work on the occasion of his sixtieth birthday. Information for our distributors: Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Author: Innocent Mutabazi
Publisher: Springer
ISBN: 0387251111
Category : Science
Languages : en
Pages : 249

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Book Description
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.

Author: F.H. Busse
Publisher: Springer Science & Business Media
ISBN: 1468457934
Category : Science
Languages : en
Pages : 552

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Book Description
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.

Author: Pierre Coullet
Publisher: Springer Science & Business Media
ISBN: 1468474790
Category : Technology & Engineering
Languages : en
Pages : 341

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Book Description
The basic aim of the NATO Advanced Research Workshop on "New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena: The Geometry of Nonequilibrium" was to bring together researchers from various areas of physics to review and explore new ideas regarding the organisation of systems driven far from equilibrium. Such systems are characterized by a close relationship between broken spatial and tempo ral symmetries. The main topics of interest included pattern formation in chemical systems, materials and convection, traveling waves in binary fluids and liquid crystals, defects and their role in the disorganisa tion of structures, spatio-temporal intermittency, instabilities and large-scale vortices in open flows, the mathematics of non-equilibrium systems, turbulence, and last but not least growth phenomena. Written contributions from participants have been grouped into chapters addressing these different areas. For additional clarity, the first chapter on pattern formation has been subdivided into sections. One of the main concerns was to focus on the unifying features between these diverse topics. The various scientific communities repre sented were encouraged to discuss and compare their approach so as to mutually benefit their respective fields. We hope that, to a large degree, these goals have been met and we thank all the participants for their efforts. The workshop was held in Cargese (Corsica, France) at the Institut d'Etudes Scientifiques from August 2nd to August 12th, 1988. We greatly thank Yves Pomeau and Daniel Walgraef who, as members of the organising committee, gave us valuable advice and encouragements.

Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 764

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Author: G Dangelmayr
Publisher: CRC Press
ISBN: 9780582229297
Category : Mathematics
Languages : en
Pages : 292

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Book Description
The mathematical description of complex spatiotemporal behaviour observed in dissipative continuous systems is a major challenge for modern research in applied mathematics. While the behaviour of low-dimensional systems, governed by the dynamics of a finite number of modes is well understood, systems with large or unbounded spatial domains show intrinsic infinite-dimensional behaviour --not a priori accessible to the methods of finite dimensionaldynamical systems. The purpose of the four contributions in this book is to present some recent and active lines of research in evolution equations posed in large or unbounded domains. One of the most prominent features of these systems is the propagation of various types of patterns in the form of waves, such as travelling and standing waves and pulses and fronts. Different approaches to studying these kinds of phenomena are discussed in the book. A major theme is the reduction of an original evolution equation in the form of a partial differential equation system to a simpler system of equations, either a system of ordinary differential equation or a canonical system of PDEs. The study of the reduced equations provides insight into the bifurcations from simple to more complicated solutions and their stabilities. .

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 89

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Book Description
This document constitutes the final report for the grant. It provides a complete list of publications and presentations that arose from the project as well as a brief description of the highlights of the research results. The research funded by this grant has provided insights into the spontaneous formation of structures of increasing complexity in systems driven far from thermodynamic equilibrium. A classic example of such a system is thermally driven convection in a horizontal fluid layer. Highlights of the research are: (1) explanation of the localized traveling wave pulses observed in binary-mixture convection, (2) explanation of the localized waves in electroconvection, (3) introduction of a new diagnostics for spatially and temporally chaotic states, which is based on the statistics of defect trajectories, (4) prediction of complex states in thermally driven convection in rotating systems. Additional contributions provided insight into the localization mechanism for oscillons, the prediction of a new localization mechanism for traveling waves based on a resonant periodic forcing, and an analysis of the stability of quasi-periodic patterns.