Analysis of a Reaction Diffusion Model of Gradient Sensing
Author: J. Krishnan
Publisher:
Published: 2002
Total Pages:
ISBN-13:
DOWNLOAD EBOOKPosts
Gradient Sensing in Chemotaxis
Author: K. K. Subramanian
Publisher:
Published: 2002
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAnalysis of Reaction-Diffusion Models with the Taxis Mechanism
Author: Yuanyuan Ke
Publisher: Springer Nature
Published: 2022-08-25
Total Pages: 418
ISBN-13: 981193763X
DOWNLOAD EBOOKThis 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.
Stochastic Processes in Cell Biology
Author: Paul C. Bressloff
Publisher: Springer Nature
Published: 2022-01-10
Total Pages: 724
ISBN-13: 3030725197
DOWNLOAD EBOOKThis book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes. A wide range of biological topics are covered in the new edition, including stochastic ion channels and excitable systems, molecular motors, stochastic gene networks, genetic switches and oscillators, epigenetics, normal and anomalous diffusion in complex cellular environments, stochastically-gated diffusion, active intracellular transport, signal transduction, cell sensing, bacterial chemotaxis, intracellular pattern formation, cell polarization, cell mechanics, biological polymers and membranes, nuclear structure and dynamics, biological condensates, molecular aggregation and nucleation, cellular length control, cell mitosis, cell motility, cell adhesion, cytoneme-based morphogenesis, bacterial growth, and quorum sensing. The book also provides a pedagogical introduction to the theory of stochastic and nonequilibrium processes – Fokker Planck equations, stochastic differential equations, stochastic calculus, master equations and jump Markov processes, birth-death processes, Poisson processes, first passage time problems, stochastic hybrid systems, queuing and renewal theory, narrow capture and escape, extreme statistics, search processes and stochastic resetting, exclusion processes, WKB methods, large deviation theory, path integrals, martingales and branching processes, numerical methods, linear response theory, phase separation, fluctuation-dissipation theorems, age-structured models, and statistical field theory. This text is primarily aimed at graduate students and researchers working in mathematical biology, statistical and biological physicists, and applied mathematicians interested in stochastic modeling. Applied probabilists should also find it of interest. It provides significant background material in applied mathematics and statistical physics, and introduces concepts in stochastic and nonequilibrium processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.
Handbook of Differential Equations: Evolutionary Equations
Author: C.M. Dafermos
Publisher: Elsevier
Published: 2011-09-22
Total Pages: 653
ISBN-13: 008046565X
DOWNLOAD EBOOKThe material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's. Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savaré discusses the most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionary partial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell's capability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other. The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function. The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class of non-linear equations is investigated, with applications to stochastic control and differential games. The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations,parabolic equations with coefficients of low regularity, and some fluid-structure interaction models. - Volume 1 focuses on the abstract theory of evolution - Volume 2 considers more concrete probelms relating to specific applications - Volume 3 reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear PDEs
Stability Analysis of Reaction-Diffusion Models with Delayed Reaction Kinetics
Author: Nancy Khalil
Publisher:
Published: 2019
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKThe 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.
Reaction Diffusion Systems
Author: Gabriela Caristi
Publisher: CRC Press
Published: 2020-10-07
Total Pages: 428
ISBN-13: 1000117197
DOWNLOAD EBOOK"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."
Analysis of a Reaction-diffusion System with Local and Nonlocal Diffusion Terms
Author: Richard D. Tatum
Publisher:
Published: 2010
Total Pages: 434
ISBN-13:
DOWNLOAD EBOOKReaction-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]
Scientific and Technical Aerospace Reports
Author:
Publisher:
Published: 1995
Total Pages: 702
ISBN-13:
DOWNLOAD EBOOKCytoplasmic Structures—Advances in Research and Application: 2012 Edition
Author:
Publisher: ScholarlyEditions
Published: 2012-12-26
Total Pages: 388
ISBN-13: 1464994137
DOWNLOAD EBOOKCytoplasmic Structures—Advances in Research and Application: 2012 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Cytoplasmic Structures. The editors have built Cytoplasmic Structures—Advances in Research and Application: 2012 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Cytoplasmic Structures in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Cytoplasmic Structures—Advances in Research and Application: 2012 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
