Download or read book Spatio Temporal Pattern Formation written by Daniel Walgraef and published by Springer. This book was released on 1996-12-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On Growth and Form written by M. A. J. Chaplain and published by John Wiley & Sons. This book was released on 1999 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spatio Temporal Pattern Formation written by Daniel Walgraef and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spatiotemporal Patterns in Ecology and Epidemiology written by Horst Malchow and published by CRC Press. This book was released on 2007-12-26 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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:
Download or read book Nonlinear Dynamics written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spatio temporal Patterns in Nonequilibrium Complex Systems written by P. E. Cladis and published by . This book was released on 1995 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Spatio Temporal Dynamics and Chaos in Semiconductors written by Eckehard Schöll and published by Cambridge University Press. This book was released on 2001-02-22 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together concepts from semiconductor physics, nonlinear-dynamics and chaos to examine semiconductor transport phenomena.
Download or read book Pattern Formation and Dynamics in Nonequilibrium Systems written by Michael Cross and published by Cambridge University Press. This book was released on 2009-07-16 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account of how complex patterns form in sustained nonequilibrium systems; for graduate students in biology, chemistry, engineering, mathematics, and physics.
Download or read book Cellular Automaton Modeling of Biological Pattern Formation written by Andreas Deutsch and published by Birkhäuser. This book was released on 2018-03-09 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the use of cellular automata in modeling pattern formation in biological systems. It describes several mathematical modeling approaches utilizing cellular automata that can be used to study the dynamics of interacting cell systems both in simulation and in practice. New in this edition are chapters covering cell migration, tissue development, and cancer dynamics, as well as updated references and new research topic suggestions that reflect the rapid development of the field. The book begins with an introduction to pattern-forming principles in biology and the various mathematical modeling techniques that can be used to analyze them. Cellular automaton models are then discussed in detail for different types of cellular processes and interactions, including random movement, cell migration, adhesive cell interaction, alignment and cellular swarming, growth processes, pigment cell pattern formation, tissue development, tumor growth and invasion, and Turing-type patterns and excitable media. In the final chapter, the authors critically discuss possibilities and limitations of the cellular automaton approach in modeling various biological applications, along with future research directions. Suggestions for research projects are provided throughout the book to encourage additional engagement with the material, and an accompanying simulator is available for readers to perform their own simulations on several of the models covered in the text. QR codes are included within the text for easy access to the simulator. With its accessible presentation and interdisciplinary approach, Cellular Automaton Modeling of Biological Pattern Formation is suitable for graduate and advanced undergraduate students in mathematical biology, biological modeling, and biological computing. It will also be a valuable resource for researchers and practitioners in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science. PRAISE FOR THE FIRST EDITION “An ideal guide for someone with a mathematical or physical background to start exploring biological modelling. Importantly, it will also serve as an excellent guide for experienced modellers to innovate and improve their methodologies for analysing simulation results.” —Mathematical Reviews
Download or read book Bifurcation Theory and Spatio Temporal Pattern Formation written by Wayne Nagata and published by American Mathematical Soc.. This book was released on 2006-10-03 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book From Pattern Formation to Material Computation written by Jeff Jones and published by Springer. This book was released on 2015-05-15 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses topics of mobile multi-agent systems, pattern formation, biological modelling, artificial life, unconventional computation, and robotics. The behaviour of a simple organism which is capable of remarkable biological and computational feats that seem to transcend its simple component parts is examined and modelled. In this book the following question is asked: How can something as simple as Physarum polycephalum - a giant amoeboid single-celled organism which does not possess any neural tissue, fixed skeleton or organised musculature - can approximate complex computational behaviour during its foraging, growth and adaptation of its amorphous body plan, and with such limited resources? To answer this question the same apparent limitations as faced by the organism are applied: using only simple components with local interactions. A synthesis approach is adopted and a mobile multi-agent system with very simple individual behaviours is employed. It is shown their interactions yield emergent behaviour showing complex self-organised pattern formation with material-like evolution. The presented model reproduces the biological behaviour of Physarum; the formation, growth and minimisation of transport networks. In its conclusion the book moves beyond Physarum and provides results of scoping experiments approximating other complex systems using the multi-agent approach. The results of this book demonstrate the power and range of harnessing emergent phenomena arising in simple multi-agent systems for biological modelling, computation and soft-robotics applications. It methodically describes the necessary components and their interactions, showing how deceptively simple components can create powerful mechanisms, aided by abundant illustrations, supplementary recordings and interactive models. It will be of interest to those in biological sciences, physics, computer science and robotics who wish to understand how simple components can result in complex and useful behaviours and who wish explore the potential of guided pattern formation themselves.
Download or read book Mathematical Models for Biological Pattern Formation written by Philip K. Maini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 121st IMA volume, entitled MATHEMATICAL MODELS FOR BIOLOGICAL PATTERN FORMATION is the first of a new series called FRONTIERS IN APPLICATION OF MATHEMATICS. The FRONTIERS volumes are motivated by IMA pro grams and workshops, but are specially planned and written to provide an entree to and assessment of exciting new areas for the application of mathematical tools and analysis. The emphasis in FRONTIERS volumes is on surveys, exposition and outlook, to attract more mathematicians and other scientists to the study of these areas and to focus efforts on the most important issues, rather than papers on the most recent research results aimed at an audience of specialists. The present volume of peer-reviewed papers grew out of the 1998-99 IMA program on "Mathematics in Biology," in particular the Fall 1998 em phasis on "Theoretical Problems in Developmental Biology and Immunol ogy." During that period there were two workshops on Pattern Formation and Morphogenesis, organized by Professors Murray, Maini and Othmer. James Murray was one of the principal organizers for the entire year pro gram. I am very grateful to James Murray for providing an introduction, and to Philip Maini and Hans Othmer for their excellent work in planning and preparing this first FRONTIERS volume. I also take this opportunity to thank the National Science Foundation, whose financial support of the IMA made the Mathematics in Biology pro gram possible.
Download or read book Handbook of Spatial Point Pattern Analysis in Ecology written by Thorsten Wiegand and published by CRC Press. This book was released on 2013-12-20 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understand How to Analyze and Interpret Information in Ecological Point PatternsAlthough numerous statistical methods for analyzing spatial point patterns have been available for several decades, they haven't been extensively applied in an ecological context. Addressing this gap, Handbook of Spatial Point-Pattern Analysis in Ecology shows how the t
Download or read book Complex Population Dynamics written by Bernd Blasius and published by World Scientific. This book was released on 2007 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of review articles is devoted to the modeling of ecological, epidemiological and evolutionary systems. Theoretical mathematical models are perhaps one of the most powerful approaches available for increasing our understanding of the complex population dynamics in these natural systems. Exciting new techniques are currently being developed to meet this challenge, such as generalized or structural modeling, adaptive dynamics or multiplicative processes. Many of these new techniques stem from the field of nonlinear dynamics and chaos theory, where even the simplest mathematical rule can generate a rich variety of dynamical behaviors that bear a strong analogy to biological populations.
Download or read book Nonlinear Dynamics and Pattern Formation in the Natural Environment written by A. Van Harten and published by Taylor & Francis. This book was released on 2022-09-16 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note aims to provide an insight into recent developments in the theory of pattern formation. In the last decade there has been considerable progress in this field, both from a theoretical and a practical point of view. Recent mathematical developments concern the study of the nonlinear stability of systems at near-critical conditions by an appropriate system of modulation equations. The complexity of the original problem can be reduced drastically by this approximation. Moreover, it provides unifying point of view for a wide range of problems. New applications of the theory arise in a multitude of scientific areas such as hydrodynamics, reaction-diffusion problems, oceanography, meteorology, combustion, geophysical and biological morphodynamics and semi-conductors.This book is intended to show the interactions between the mathematical theory of nonlinear dynamics and the study of pattern generating phenomena in the natural environment. There is an intimate relationship between new insights in the mathematical aspects of nonlinear pattern formation and the comprehension of such phenomena. Therefore there are two partly overlapping main themes: one in which the emphasis is on generally applicable mathematical theories and techniques and one in which the phenomenology of pattern evolution in various areas is discussed.The book comprises 19 contributions by experts in the field. Although the emphasis changes considerably from paper to paper, in each contribution the same two themes are present; all the authors have aimed to achieve a suitable balance between the mathematical theory and the physical phenomena.
Download or read book Spatial Simulation written by David O'Sullivan and published by John Wiley & Sons. This book was released on 2013-08-05 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ground-up approach to explaining dynamic spatial modelling for an interdisciplinary audience. Across broad areas of the environmental and social sciences, simulation models are an important way to study systems inaccessible to scientific experimental and observational methods, and also an essential complement to those more conventional approaches. The contemporary research literature is teeming with abstract simulation models whose presentation is mathematically demanding and requires a high level of knowledge of quantitative and computational methods and approaches. Furthermore, simulation models designed to represent specific systems and phenomena are often complicated, and, as a result, difficult to reconstruct from their descriptions in the literature. This book aims to provide a practical and accessible account of dynamic spatial modelling, while also equipping readers with a sound conceptual foundation in the subject, and a useful introduction to the wide-ranging literature. Spatial Simulation: Exploring Pattern and Process is organised around the idea that a small number of spatial processes underlie the wide variety of dynamic spatial models. Its central focus on three ‘building-blocks’ of dynamic spatial models – forces of attraction and segregation, individual mobile entities, and processes of spread – guides the reader to an understanding of the basis of many of the complicated models found in the research literature. The three building block models are presented in their simplest form and are progressively elaborated and related to real world process that can be represented using them. Introductory chapters cover essential background topics, particularly the relationships between pattern, process and spatiotemporal scale. Additional chapters consider how time and space can be represented in more complicated models, and methods for the analysis and evaluation of models. Finally, the three building block models are woven together in a more elaborate example to show how a complicated model can be assembled from relatively simple components. To aid understanding, more than 50 specific models described in the book are available online at patternandprocess.org for exploration in the freely available Netlogo platform. This book encourages readers to develop intuition for the abstract types of model that are likely to be appropriate for application in any specific context. Spatial Simulation: Exploring Pattern and Process will be of interest to undergraduate and graduate students taking courses in environmental, social, ecological and geographical disciplines. Researchers and professionals who require a non-specialist introduction will also find this book an invaluable guide to dynamic spatial simulation.
Download or read book Patterns and Interfaces in Dissipative Dynamics written by L.M. Pismen and published by Springer Science & Business Media. This book was released on 2006-07-07 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.
