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Analysis Of Reaction Diffusion Models With The Taxis Mechanism
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Book Synopsis Analysis of Reaction-Diffusion Models with the Taxis Mechanism by : Yuanyuan Ke
Download or read book Analysis of Reaction-Diffusion Models with the Taxis Mechanism written by Yuanyuan Ke and published by Springer Nature. This book was released on 2022-08-25 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book deals with a rich variety of taxis-type cross-diffusive equations. Particularly, it intends to show the key role played by quasi-energy inequality in the derivation of some necessary a priori estimates. This book addresses applied mathematics and all researchers interested in mathematical development of reaction-diffusion theory and its application and can be a basis for a graduate course in applied mathematics.
Book Synopsis Stability Analysis of Reaction-Diffusion Models with Delayed Reaction Kinetics by : Nancy Khalil
Download or read book Stability Analysis of Reaction-Diffusion Models with Delayed Reaction Kinetics written by Nancy Khalil and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The linear stability of localized spike solutions to the one-dimensional Gierer-Meinhardt activator-inhibitor model with delayed nonlinear reaction kinetics is analyzed both analytically and numerically. In the limit of slow activator diffusivity, we show that delay destabilizes the equilibrium solution, and we find critical values at which a Hopf bifurcation is observed in both the spike position and amplitude. For specific cases of delayed reaction kinetics, we formulate the nonlocal eigenvalue problem and we study the stability of both the small and large eigenvalues. For the small eigenvalues, we show that in some cases the reduced system of ordinary differential equations, for the motion of the slow evolving spikes, undergoes a Hopf bifurcation. Instabilities in the spike profile are also considered, and we show that the equilibrium solution is unstable as delay is increased beyond a critical Hopf bifurcation value. For one-spike solutions, we find that instability in the profile is triggered before the positional instability, except in the case where the degradation of activator is delayed where stable positional oscillations are observed. The analytical results are validated using numerical simulations. In addition, we study an example of quorum sensing behaviour modelled by a two-dimensional cell-bulk model coupled to delayed intracellular dynamics. In this model, the essential process of cell-to-cell communication is achieved by the diffusion of a signalling molecule in a well-mixed bulk medium between spatially segregated active cells. Assuming a very large diffusion limit, we investigate the onset of oscillatory instabilities due to coupling with delayed intracellular dynamics. The cell-bulk model, for the case of a single active cell containing one intracellular species, is reduced to a finite system of nonlinear delay ordinary differential equations and studied both analytically and numerically. Using Hill function-type intracellular kinetics with fixed delay, we show that delayed cell-bulk coupling triggers sustained oscillations as delay increases beyond the critical Hopf bifurcation threshold.
Book Synopsis Progress in Industrial Mathematics at ECMI 2016 by : Peregrina Quintela
Download or read book Progress in Industrial Mathematics at ECMI 2016 written by Peregrina Quintela and published by Springer. This book was released on 2018-03-26 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Using the classification system defined in the EU Framework Programme for Research and Innovation H2020, several of the topics covered belong to the challenge climate action, environment, resource efficiency and raw materials; and some to health, demographic change and wellbeing; while others belong to Europe in a changing world – inclusive, innovative and reflective societies. The 19th European Conference on Mathematics for Industry, ECMI2016, was held in Santiago de Compostela, Spain in June 2016. The proceedings of this conference include the plenary lectures, ECMI awards and special lectures, mini-symposia (including the description of each mini-symposium) and contributed talks. The ECMI conferences are organized by the European Consortium for Mathematics in Industry with the aim of promoting interaction between academy and industry, leading to innovation in both fields and providing unique opportunities to discuss the latest ideas, problems and methodologies, and contributing to the advancement of science and technology. They also encourage industrial sectors to propose challenging problems where mathematicians can provide insights and fresh perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.
Book Synopsis Traveling Front Solutions in Reaction-Diffusion Equations by : Masaharu Taniguchi
Download or read book Traveling Front Solutions in Reaction-Diffusion Equations written by Masaharu Taniguchi and published by . This book was released on 2021-05-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study on traveling fronts in reaction-diffusion equations is the first step to understand various kinds of propagation phenomena in reaction-diffusion models in natural science. One dimensional traveling fronts have been studied from the 1970s, and multidimensional ones have been studied from around 2005. This volume is a text book for graduate students to start their studies on traveling fronts. Using the phase plane analysis, we study the existence of traveling fronts in several kinds of reaction-diffusion equations. For a nonlinear reaction term, a bistable one is a typical one. For a bistable reaction-diffusion equation, we study the existence and stability of two-dimensional V-form fronts, and we also study pyramidal traveling fronts in three or higher space dimensions. The cross section of a pyramidal traveling front forms a convex polygon. It is known that the limit of a pyramidal traveling front gives a new multidimensional traveling front. For the study the multidimensional traveling front, studying properties of pyramidal traveling fronts plays an important role. In this volume, we study the existence, uniqueness and stability of a pyramidal traveling front as clearly as possible for further studies by graduate students. For a help of their studies, we briefly explain and prove the well-posedness of reaction-diffusion equations and the Schauder estimates and the maximum principles of solutions.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
Book Synopsis Analysis of a Reaction Diffusion Model of Gradient Sensing by : J. Krishnan
Download or read book Analysis of a Reaction Diffusion Model of Gradient Sensing written by J. Krishnan and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Reaction Diffusion Systems by : Gabriela Caristi
Download or read book Reaction Diffusion Systems written by Gabriela Caristi and published by CRC Press. This book was released on 2020-10-07 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on the proceedings of the International Conference on Reaction Diffusion Systems held recently at the University of Trieste, Italy. Presents new research papers and state-of-the-art surveys on the theory of elliptic, parabolic, and hyperbolic problems, and their related applications. Furnishes incisive contribution by over 40 mathematicians representing renowned institutions in North and South America, Europe, and the Middle East."
Book Synopsis Advanced Mathematical Methods in Biosciences and Applications by : Faina Berezovskaya
Download or read book Advanced Mathematical Methods in Biosciences and Applications written by Faina Berezovskaya and published by Springer Nature. This book was released on 2019-09-19 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring contributions from experts in mathematical biology and biomedical research, this edited volume covers a diverse set of topics on mathematical methods and applications in the biosciences. Topics focus on advanced mathematical methods, with chapters on the mathematical analysis of the quasispecies model, Arnold’s weak resonance equation, bifurcation analysis, and the Tonnelier-Gerstner model. Special emphasis is placed on applications such as natural selection, population heterogeneity, polyvariant ontogeny in plants, cancer dynamics, and analytical solutions for traveling pulses and wave trains in neural models. A survey on quasiperiodic topology is also presented in this book. Carefully peer-reviewed, this volume is suitable for students interested in interdisciplinary research. Researchers in applied mathematics and the biosciences will find this book an important resource on the latest developments in the field. In keeping with the STEAM-H series, the editors hope to inspire interdisciplinary understanding and collaboration.
Book Synopsis Analysis of Reaction-diffusion Equations on a Time-dependent Domain by : Jane Allwright
Download or read book Analysis of Reaction-diffusion Equations on a Time-dependent Domain written by Jane Allwright and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy by : Manoj Sahni
Download or read book Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy written by Manoj Sahni and published by Springer Nature. This book was released on 2021-02-28 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new knowledge and recent developments in all aspects of computational techniques, mathematical modeling, energy systems, applications of fuzzy sets and intelligent computing. The book is a collection of best selected research papers presented at the International Conference on “Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy,” organized by the Department of Mathematics, Pandit Deendayal Petroleum University, in association with Forum for Interdisciplinary Mathematics, Institution of Engineers (IEI) – Gujarat and Computer Society of India (CSI) – Ahmedabad. The book provides innovative works of researchers, academicians and students in the area of interdisciplinary mathematics, statistics, computational intelligence and renewable energy.
Book Synopsis Hyperbolic Problems: Theory, Numerics and Applications by : Eitan Tadmor
Download or read book Hyperbolic Problems: Theory, Numerics and Applications written by Eitan Tadmor and published by American Mathematical Soc.. This book was released on 2009 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 'HYP2008', was held at the University of Maryland from June 9-13, 2008. This book, the first in a two-part volume, contains nineteen papers based on plenary and invited talks presented at the conference.
Download or read book Applied Analysis written by Takasi Senba and published by World Scientific Publishing Company. This book was released on 2004-04-15 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general introduction to applied analysis; vector analysis with physical motivation, calculus of variation, Fourier analysis, eigenfunction expansion, distribution, and so forth, including a catalogue of mathematical theories, such as basic analysis, topological spaces, complex function theory, real analysis, and abstract analysis. This book also uses fundamental ideas of applied mathematics to discuss recent developments in nonlinear science, such as mathematical modeling of reinforced random motion of particles, semiconductor device equation in applied physics, and chemotaxis in biology. Several tools in linear PDE theory, such as fundamental solutions, Perron's method, layer potentials, and iteration scheme, are described, as well as systematic descriptions on the recent study of the blowup of the solution. Contents: Geometric ObjectsCalculus of VariationInfinite-Dimensional AnalysisRandom Motion of ParticlesLinear PDE TheoryNonlinear PDE TheorySystem of Chemotaxis Readership: Mathematics undergraduates.
Book Synopsis Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by : Bernold Fiedler
Download or read book Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
Book Synopsis Analysis of a Reaction-diffusion System with Local and Nonlocal Diffusion Terms by : Richard D. Tatum
Download or read book Analysis of a Reaction-diffusion System with Local and Nonlocal Diffusion Terms written by Richard D. Tatum and published by . This book was released on 2010 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reaction-diffusion describes the process in which multiple participating chemicals or agents react with each other, while simultaneously diffusing or spreading through a liquid or gaseous medium. Typically, these processes are studied for their ability to produce nontrivial patterns that evolve over time. These patterns, often referred to as Turing structures or Turing patterns, are diffusion driven. In the presence of diffusion, the Turing patterns are observable, but are not present in the absence of diffusion. It is important for reactiondiffusion models to replicate the behavior that is experimentally observed. That is to say that the models must be able to produce solutions with traits, such as pattern type, that are similar to experimentally observed traits. Mathematically, we seek to explain certain aspects of the models such as pattern selection in the hope of broadening our understanding of the underlying process for which the model represents. I analyze a mixed reaction-diffusion system containing an instability that results in nontrivial Turing structures. This system uses a homotopy parameter [beta] to vary the effect of both local ([beta] = 1) and nonlocal ([beta] = 0) diffusion. Furthermore, I consider [element-of symbol]-scaled kernels J such that [th]J is -independent for [th] [element-of symbol] R. For [th]
Book Synopsis Active Particles, Volume 2 by : Nicola Bellomo
Download or read book Active Particles, Volume 2 written by Nicola Bellomo and published by Springer Nature. This book was released on 2019-08-22 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume compiles eight recent surveys that present state-of-the-art results in the field of active matter at different scales, modeled by agent-based, kinetic, and hydrodynamic descriptions. Following the previously published volume, these chapters were written by leading experts in the field and accurately reflect the diversity of subject matter in theory and applications. Several mathematical tools are employed throughout the volume, including analysis of nonlinear PDEs, network theory, mean field approximations, control theory, and flocking analysis. The book also covers a wide range of applications, including: Biological network formation Social systems Control theory of sparse systems Dynamics of swarming and flocking systems Stochastic particles and mean field approximations Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.
Book Synopsis Numerical and Dynamical Studies of Some Reaction-diffusion Models by : Zhen Chen
Download or read book Numerical and Dynamical Studies of Some Reaction-diffusion Models written by Zhen Chen and published by . This book was released on 2002 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Qualitative Analysis of Systems of Reaction-diffusion Equations by : Hiroyasu Takase
Download or read book Qualitative Analysis of Systems of Reaction-diffusion Equations written by Hiroyasu Takase and published by . This book was released on 1999 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Reaction-diffusion Models for Intracellular Communication in Biology by : Austen C. Duffy
Download or read book Numerical Reaction-diffusion Models for Intracellular Communication in Biology written by Austen C. Duffy and published by . This book was released on 2005 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
