Numerical Bifurcation Analysis For Reaction Diffusion Equations

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Numerical Bifurcation Analysis For Reaction Diffusion Equations

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Author : Zhen Mei
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-06-21

Numerical Bifurcation Analysis For Reaction Diffusion Equations written by Zhen Mei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-21 with Mathematics categories.

This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Many examples and figures illustrate analysis of bifurcation scenario and implementation of numerical schemes. Readers will gain a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations.

Numerical Bifurcation Analysis For Reaction Diffusion Equations

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Author : Zhen Mei
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Numerical Bifurcation Analysis For Reaction Diffusion Equations written by Zhen Mei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Reaction-diffusion equations are typical mathematical models in biology, chemistry and physics. These equations often depend on various parame ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ ent substances. The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters. Cor respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions. This kind of phe nomena is called bifurcation. Nonlinearity in the system makes bifurcation take place constantly in reaction-diffusion processes. Bifurcation in turn in duces uncertainty in outcome of reactions. Thus analyzing bifurcations is essential for understanding mechanism of pattern formation and nonlinear dynamics of a reaction-diffusion process. However, an analytical bifurcation analysis is possible only for exceptional cases. This book is devoted to nu merical analysis of bifurcation problems in reaction-diffusion equations. The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of a dass of reaction-diffusion equations. This is realized with a combination of three mathematical approaches: numerical methods for con tinuation of solution curves and for detection and computation of bifurcation points; effective low dimensional modeling of bifurcation scenario and long time dynamics of reaction-diffusion equations; analysis of bifurcation sce nario, mode-interactions and impact of boundary conditions.

Computational Science Iccs 2004

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Author : Marian Bubak
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-05-25

Computational Science Iccs 2004 written by Marian Bubak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-25 with Computers categories.

The International Conference on Computational Science (ICCS 2004) held in Krak ́ ow, Poland, June 6–9, 2004, was a follow-up to the highly successful ICCS 2003 held at two locations, in Melbourne, Australia and St. Petersburg, Russia; ICCS 2002 in Amsterdam, The Netherlands; and ICCS 2001 in San Francisco, USA. As computational science is still evolving in its quest for subjects of inves- gation and e?cient methods, ICCS 2004 was devised as a forum for scientists from mathematics and computer science, as the basic computing disciplines and application areas, interested in advanced computational methods for physics, chemistry, life sciences, engineering, arts and humanities, as well as computer system vendors and software developers. The main objective of this conference was to discuss problems and solutions in all areas, to identify new issues, to shape future directions of research, and to help users apply various advanced computational techniques. The event harvested recent developments in com- tationalgridsandnextgenerationcomputingsystems,tools,advancednumerical methods, data-driven systems, and novel application ?elds, such as complex - stems, ?nance, econo-physics and population evolution.

Bifurcation Analysis Of Fluid Flows

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Author : Henk A. Dijkstra
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-24

Bifurcation Analysis Of Fluid Flows written by Henk A. Dijkstra and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-24 with Science categories.

A better understanding of the mechanisms leading a fluid system to exhibit turbulent behavior is one of the grand challenges of the physical and mathematical sciences. Over the last few decades, numerical bifurcation methods have been extended and applied to a number of flow problems to identify critical conditions for fluid instabilities to occur. This book provides a state-of-the-art account of these numerical methods, with much attention to modern linear systems solvers and generalized eigenvalue solvers. These methods also have a broad applicability in industrial, environmental and astrophysical flows. The book is a must-have reference for anyone working in scientific fields where fluid flow instabilities play a role. Exercises at the end of each chapter and Python code for the bifurcation analysis of canonical fluid flow problems provide practice material to get to grips with the methods and concepts presented in the book.

Numerical Methods For Bifurcation Problems And Large Scale Dynamical Systems

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Author : Eusebius Doedel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Numerical Methods For Bifurcation Problems And Large Scale Dynamical Systems written by Eusebius Doedel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. In the past 25 years computational methods have been developed for calculating fixed points, limit cycles, and bifurcation points. A remaining challenge is to develop robust methods for calculating more complicated objects, such as higher- codimension bifurcations of fixed points, periodic orbits, and connecting orbits, as well as the calcuation of invariant manifolds. Another challenge is to extend the applicability of algorithms to the very large systems that result from discretizing partial differential equations. Even the calculation of steady states and their linear stability can be prohibitively expensive for large systems (e.g. 10_3- -10_6 equations) if attempted by simple direct methods. Several of the papers in this volume treat computational methods for low and high dimensional systems and, in some cases, their incorporation into software packages. A few papers treat fundamental theoretical problems, including smooth factorization of matrices, self -organized criticality, and unfolding of singular heteroclinic cycles. Other papers treat applications of dynamical systems computations in various scientific fields, such as biology, chemical engineering, fluid mechanics, and mechanical engineering.

Practical Bifurcation And Stability Analysis

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Author : Rüdiger Seydel
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-14

Practical Bifurcation And Stability Analysis written by Rüdiger Seydel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-14 with Mathematics categories.

Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.

Computational Modelling Of Bifurcations And Instabilities In Fluid Dynamics

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Author : Alexander Gelfgat
language : en
Publisher: Springer
Release Date : 2018-07-06

Computational Modelling Of Bifurcations And Instabilities In Fluid Dynamics written by Alexander Gelfgat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-06 with Technology & Engineering categories.

Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.

Patterns Of Dynamics

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Author : Pavel Gurevich
language : en
Publisher: Springer
Release Date : 2018-02-07

Patterns Of Dynamics written by Pavel Gurevich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-07 with Mathematics categories.

Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.The contributions build and develop mathematical techniques, and use mathematical approaches for prediction and control of complex systems. The underlying mathematical theories help extract structures from experimental observations and, conversely, shed light on the formation, dynamics, and control of spatio-temporal patterns in applications. Theoretical areas covered include geometric analysis, spatial dynamics, spectral theory, traveling-wave theory, and topological data analysis; also discussed are their applications to chemotaxis, self-organization at interfaces, neuroscience, and transport processes.

Combustion Thermodynamics And Dynamics

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Author : Joseph Powers
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-18

Combustion Thermodynamics And Dynamics written by Joseph Powers and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-18 with Science categories.

This textbook combines rigorous mathematical analysis with combustion science to address standard problems in reactive fluid mechanics.

Algorithms In Algebraic Geometry

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Author : Alicia Dickenstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-10

Algorithms In Algebraic Geometry written by Alicia Dickenstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-10 with Mathematics categories.

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its Applications on September 2006 is one tangible indication of the interest. This volume of articles captures some of the spirit of the IMA workshop.