Spatio-Temporal Pattern Formation

Spatio-Temporal Pattern Formation
Title Spatio-Temporal Pattern Formation PDF eBook
Author Daniel Walgraef
Publisher Springer
Pages 0
Release 1996-12-13
Genre Science
ISBN 9780387948577

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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.

On Growth and Form

On Growth and Form
Title On Growth and Form PDF eBook
Author M. A. J. Chaplain
Publisher John Wiley & Sons
Pages 448
Release 1999
Genre Mathematics
ISBN

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On Growth and Form Spatio-temporal Pattern Formation in Biology M. A. J. Chaplain and G. D. Singh, both of the University of Dundee, UK J. C. McLachlan, St. Andrews University, UK Spatio-temporal pattern formation is a major area of research within the subject of mathematical biology. The topic involves the use of mathematical modelling to analyse how patterns in biology are created and develop. For example, the growth, over time, of the intricate and beautiful patterns on certain sea-shells or the striped markings on a tiger can be modelled and their development predicted in terms of non-linear mathematical processes. The current volume captures the breadth of recent research into various aspects of spatio-temporal pattern and form, such as development biology, reaction-diffusion systems and morphometrics. * Brings the ideas of the classic On Growth and Form by D'Arcy Thompson, the founding classic of mathematical biology, fully up to date and looks to future developments in the subject * Foreword provided by Professor John Tyler Bonner, Princeton University * World class collection of internationally renowned contributors from both experimental and theoretical backgrounds Taking its inspiration from D'Arcy Thompson's classic and still influential volume On Growth and Form, this new volume presents a collection of 21 articles from the Plenary Speakers of the recent D'Arcy Thompson Conference, held at the University of Dundee, 20-24 September 1998. The topics covered include pattern formation in development biology, reaction-diffusion systems, intercellular systems and morphometrics, offering the reader a stimulating blend of theory and experiment. This book will be of particular interest to bio-mathematicians and development biologists. Paediatric clinicians, evolutionary biologists, orthodontists, anatomists, physiologists and many other members of the biology community will also benefit greatly from it.

Spatio-Temporal Pattern Formation

Spatio-Temporal Pattern Formation
Title Spatio-Temporal Pattern Formation PDF eBook
Author Daniel Walgraef
Publisher Springer Science & Business Media
Pages 310
Release 2012-12-06
Genre Science
ISBN 1461218500

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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.

Spatiotemporal Patterns in Ecology and Epidemiology

Spatiotemporal Patterns in Ecology and Epidemiology
Title Spatiotemporal Patterns in Ecology and Epidemiology PDF eBook
Author Horst Malchow
Publisher CRC Press
Pages 464
Release 2007-12-26
Genre Mathematics
ISBN 1482286130

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Although the spatial dimension of ecosystem dynamics is now widely recognized, the specific mechanisms behind species patterning in space are still poorly understood and the corresponding theoretical framework is underdeveloped. Going beyond the classical Turing scenario of pattern formation, Spatiotemporal Patterns in Ecology and Epidemiology:

Nonlinear Dynamics

Nonlinear Dynamics
Title Nonlinear Dynamics PDF eBook
Author Muthusamy Lakshmanan
Publisher Springer Science & Business Media
Pages 628
Release 2012-12-06
Genre Mathematics
ISBN 3642556884

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This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Bifurcation Theory and Spatio-Temporal Pattern Formation

Bifurcation Theory and Spatio-Temporal Pattern Formation
Title Bifurcation Theory and Spatio-Temporal Pattern Formation PDF eBook
Author Wayne Nagata
Publisher American Mathematical Soc.
Pages 186
Release 2006-10-03
Genre Mathematics
ISBN 0821837257

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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).

Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors

Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
Title Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors PDF eBook
Author Eckehard Schöll
Publisher Cambridge University Press
Pages 422
Release 2001-02-22
Genre Mathematics
ISBN 0521451868

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This book brings together concepts from semiconductor physics, nonlinear-dynamics and chaos to examine semiconductor transport phenomena.