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 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 Pattern Formation in Continuous and Coupled Systems written by Martin Golubitsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications PATTERN FORMATION IN CONTINUOUS AND COUPLED SYSTEMS is based on the proceedings of a workshop with the same title, but goes be yond the proceedings by presenting a series of mini-review articles that sur vey, and provide an introduction to, interesting problems in the field. The workshop was an integral part of the 1997-98 IMA program on "EMERG ING APPLICATIONS OF DYNAMICAL SYSTEMS." I would like to thank Martin Golubitsky, University of Houston (Math ematics) Dan Luss, University of Houston (Chemical Engineering), and Steven H. Strogatz, Cornell University (Theoretical and Applied Mechan ics) for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Foundation (NSF), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE Pattern formation has been studied intensively for most of this cen tury by both experimentalists and theoreticians, and there have been many workshops and conferences devoted to the subject. In the IMA workshop on Pattern Formation in Continuous and Coupled Systems held May 11-15, 1998 we attempted to focus on new directions in the patterns literature.
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 Dynamics and Bifurcation in Networks written by Martin Golubitsky and published by SIAM. This book was released on 2023-04-24 with total page 867 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, there has been an explosion of interest in network-based modeling in many branches of science. This book synthesizes some of the common features of many such models, providing a general framework analogous to the modern theory of nonlinear dynamical systems. How networks lead to behavior not typical in a general dynamical system and how the architecture and symmetry of the network influence this behavior are the book’s main themes. Dynamics and Bifurcation in Networks: Theory and Applications of Coupled Differential Equations is the first book to describe the formalism for network dynamics developed over the past 20 years. In it, the authors introduce a definition of a network and the associated class of “admissible” ordinary differential equations, in terms of a directed graph whose nodes represent component dynamical systems and whose arrows represent couplings between these systems. They also develop connections between network architecture and the typical dynamics and bifurcations of these equations and discuss applications of this formalism to various areas of science, including gene regulatory networks, animal locomotion, decision-making, homeostasis, binocular rivalry, and visual illusions. This book will be of interest to scientific researchers in any area that uses network models, which includes many parts of biology, physics, chemistry, computer science, electrical and electronic engineering, psychology, and sociology.
Download or read book Nonlinear Dynamics and Spatial Complexity in Optical Systems written by R. G. Harrison and published by CRC Press. This book was released on 2018-05-04 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of prestigious postgraduate lectures, Nonlinear Dynamics and Spatial Complexity in Optical Systems reviews developments in the theory and practice of nonlinear dynamics and structural complexity, and explores modern-day applications in nonlinear optics. The book addresses systems including both singlemode and multimode lasers, bistable and multistable devices, optical fibers, counter-propagating beam interactions, nonlinear mixing, and related optical phenomena.
Download or read book Lectures on Global Optimization written by Thomas Frederick Coleman and published by American Mathematical Soc.. This book was released on 2009 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large number of mathematical models in many diverse areas of science and engineering have lead to the formulation of optimization problems where the best solution (globally optimal) is needed. This book covers a small subset of important topics in global optimization with emphasis on theoretical developments and scientific applications.
Download or read book Universality and Renormalization written by Ilia Binder and published by American Mathematical Soc.. This book was released on 2007 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a wide range of phenomena in the natural sciences dominated by notions of universality and renormalization. The contributions in this volume are equally broad in their approach to these phenomena, offering the mathematical as well as the perspective of the applied sciences. They explore renormalization theory in quantum field theory and statistical physics, and its connections to modern mathematics as well as physics on scales from the microscopic to the macroscopic. Information for our distributors: Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Download or read book New Perspectives in Mathematical Biology written by Society for Mathematical Biology. Conference and published by American Mathematical Soc.. This book was released on 2010 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an overview of the distinct variety and diversity of current research in this field. In every chapter of this book, which covers themes ranging from cancer modelling to infectious diseases to orthopaedics and musculoskeletal tissue mechanics, there is clear evidence of the strong connections and interactions of mathematics with the biological and biomedical sciences that have spawned new models and novel insights.
Download or read book Localized States in Physics Solitons and Patterns written by Orazio Descalzi and published by Springer Science & Business Media. This book was released on 2011-01-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems driven far from thermodynamic equilibrium can create dissipative structures through the spontaneous breaking of symmetries. A particularly fascinating feature of these pattern-forming systems is their tendency to produce spatially confined states. These localized wave packets can exist as propagating entities through space and/or time. Various examples of such systems will be dealt with in this book, including localized states in fluids, chemical reactions on surfaces, neural networks, optical systems, granular systems, population models, and Bose-Einstein condensates. This book should appeal to all physicists, mathematicians and electrical engineers interested in localization in far-from-equilibrium systems. The authors - all recognized experts in their fields - strive to achieve a balance between theoretical and experimental considerations thereby giving an overview of fascinating physical principles, their manifestations in diverse systems, and the novel technical applications on the horizon.
Download or read book Numerical Continuation and Bifurcation in Nonlinear PDEs written by Hannes Uecker and published by SIAM. This book was released on 2021-08-19 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D, and 3D. Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. After a concise review of some analytical background and numerical methods, the author explains the free MATLAB package pde2path by using a large variety of examples with demo codes that can be easily adapted to the reader's given problem. Numerical Continuation and Bifurcation in Nonlinear PDEs will appeal to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It can be used as a supplemental text in courses on nonlinear PDEs and modeling and bifurcation.
Download or read book Bifurcation and Chaos in Complex Systems written by and published by Elsevier. This book was released on 2006-06-30 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems.· New Views for Difficult Problems· Novel Ideas and Concepts · Hilbert's 16th Problem· Normal Forms in Polynomial Hamiltonian Systems · Grazing Flow in Non-smooth Dynamical Systems· Stochastic and Fuzzy Nonlinear Dynamical Systems· Fuzzy Bifurcation· Parametrical, Nonlinear Systems· Mode Interactions in nonlinear dynamical systems
Download or read book The Symmetry Perspective written by Martin Golubitsky and published by Birkhäuser. This book was released on 2012-12-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS
Download or read book Mathematics in Engineering Sciences written by Mangey Ram and published by CRC Press. This book was released on 2019-09-09 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes research studies, novel theory, as well as new methodology and applications in mathematics and management sciences. The book will provide a comprehensive range of mathematics applied to engineering areas for different tasks. It will offer an international perspective and a bridge between classical theory and new methodology in many areas, along with real-life applications. Features Offers solutions to multi-objective transportation problem under cost reliability using utility function Presents optimization techniques to support eco-efficiency assessment in manufacturing processes Covers distance-based function approach for optimal design of engineering processes with multiple quality characteristics Provides discrete time sliding mode control for non-linear networked control systems Discusses second law of thermodynamics as instruments for optimizing fluid dynamic systems and aerodynamic systems
Download or read book Algebraic Curves and Cryptography written by Vijaya Kumar Murty and published by American Mathematical Soc.. This book was released on 2010 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields the topics covered in this volume include Schoof's $\ell$-adic point counting algorithm, the $p$-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on the Jacobians of $C_{ab}$ curves and zeta functions.
Download or read book Perspectives on Noncommutative Geometry written by Masoud Khalkhali and published by American Mathematical Soc.. This book was released on 2011 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008. Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture. Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples. Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume. This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.
Download or read book International Conference on Differential Equations Berlin Germany 1 7 August 1999 written by Bernold Fiedler and published by World Scientific. This book was released on 2000 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences
