The Mathematics Of Diffusion
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The Mathematics Of Diffusion
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Author : John Crank
language : en
Publisher: Oxford University Press
Release Date : 1979
The Mathematics Of Diffusion written by John Crank and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
The Mathematics Of Diffusion
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Author : John Crank
language : en
Publisher:
Release Date : 1956
The Mathematics Of Diffusion written by John Crank and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with Diffusion categories.
The Mathematics Of Diffusion
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Author : Wei-Ming Ni
language : en
Publisher: SIAM
Release Date : 2011-10-13
The Mathematics Of Diffusion written by Wei-Ming Ni and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-13 with Mathematics categories.
Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements and spatial heterogeneity in the classical Lotka–Volterra competition systems. Interspersed throughout the book are many simple, fundamental and important open problems for readers to investigate.
The Mathematics Of Diffusion
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Author : Wei-Ming Ni
language : en
Publisher: SIAM
Release Date : 2011-01-01
The Mathematics Of Diffusion written by Wei-Ming Ni and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements, and spatial heterogeneity in the classical Lotka-Volterra competition systems. Interspersed throughout the book are many simple, fundamental, and important open problems for readers to investigate.
Polymer Permeability
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Author : J. Comyn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Polymer Permeability written by J. Comyn 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 Technology & Engineering categories.
Polymers are permeable, whilst ceramics, glasses and metals are gener ally impermeable. This may seem a disadvantage in that polymeric containers may allow loss or contamination of their contents and aggressive substances such as water will diffuse into polymeric struc tures such as adhesive joints or fibre-reinforced composites and cause weakening. However, in some cases permeability is an advantage, and one particular area where this is so is in the use of polymers in drug delivery systems. Also, without permeable polymers, we would not enjoy the wide range of dyed fabrics used in clothing and furnishing. The fundamental reason for the permeability of polymers is their relatively high level of molecular motion, a factor which also leads to their high levels of creep in comparison with ceramics, glasses and metals. The aim of this volume is to examine some timely applied aspects of polymer permeability. In the first chapter basic issues in the mathema tics of diffusion are introduced, and this is followed by two chapters where the fundamental aspects of diffusion in polymers are presented. The following chapters, then, each examine some area of applied science where permeability is a key issue. Each chapter is reasonably self-contained and intended to be informative without frequent outside reference. This inevitably leads to some repetition, but it is hoped that this is not excessive.
Schr Dinger Equations And Diffusion Theory
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Author : M. Nagasawa
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-07-01
Schr Dinger Equations And Diffusion Theory written by M. Nagasawa 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 1993-07-01 with Mathematics categories.
Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger's conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tell us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level.
Generalized Diffusion Processes
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Author : Nikola_ Ivanovich Portenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1990-12-21
Generalized Diffusion Processes written by Nikola_ Ivanovich Portenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-21 with Mathematics categories.
Diffusion processes serve as a mathematical model for the physical phenomenon of diffusion. One of the most important problems in the theory of diffusion processes is the development of methods for constructing these processes from a given diffusion matrix and a given drift vector. Focusing on the investigation of this problem, this book is intended for specialists in the theory of random processes and its applications. A generalized diffusion process (that is, a continuous Markov process for which the Kolmogorov local characteristics exist in the generalized sense) can serve as a model for diffusion in a medium moving in a nonregular way. The author constructs generalized diffusion processes under two assumptions: first, that the diffusion matrix is sufficiently regular; and second, that the drift vector is a function integrable to some power, or is a generalized function of the type of the derivative of a measure.
Convection Diffusion Problems
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Author : Martin Stynes
language : en
Publisher:
Release Date : 2018
Convection Diffusion Problems written by Martin Stynes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with MATHEMATICS categories.
Many physical problems involve diffusive and convective (transport) processes. When diffusion dominates convection, standard numerical methods work satisfactorily. But when convection dominates diffusion, the standard methods become unstable, and special techniques are needed to compute accurate numerical approximations of the unknown solution. This convection-dominated regime is the focus of the book. After discussing at length the nature of solutions to convection-dominated convection-diffusion problems, the authors motivate and design numerical methods that are particularly suited to this c.
Fractional Diffusion Equations And Anomalous Diffusion
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Author : Luiz Roberto Evangelista
language : en
Publisher: Cambridge University Press
Release Date : 2018-01-25
Fractional Diffusion Equations And Anomalous Diffusion written by Luiz Roberto Evangelista 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 2018-01-25 with Mathematics categories.
Presents a unified treatment of anomalous diffusion problems using fractional calculus in a wide range of applications across scientific and technological disciplines.
A Closer Look Of Nonlinear Reaction Diffusion Equations
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Author : L. Rajendran
language : en
Publisher: Nova Science Publishers
Release Date : 2020-08-26
A Closer Look Of Nonlinear Reaction Diffusion Equations written by L. Rajendran and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-26 with Reaction-diffusion equations categories.
By using mathematical models to describe the physical, biological or chemical phenomena, one of the most common results is either a differential equation or a system of differential equations, together with the correct boundary and initial conditions. The determination and interpretation of their solution are at the base of applied mathematics. Hence the analytical and numerical study of the differential equation is very much essential for all theoretical and experimental researchers, and this book helps to develop skills in this area.Recently non-linear differential equations were widely used to model many of the interesting and relevant phenomena found in many fields of science and technology on a mathematical basis. This problem is to inspire them in various fields such as economics, medical biology, plasma physics, particle physics, differential geometry, engineering, signal processing, electrochemistry and materials science.This book contains seven chapters and practical applications to the problems of the real world. The first chapter is specifically for those with limited mathematical background. Chapter one presents the introduction of non-linear reaction-diffusion systems, various boundary conditions and examples. Real-life application of non-linear reaction-diffusion in different fields with some important non-linear equations is also discussed. In Chapter 2, mathematical preliminaries and various advanced methods of solving non-linear differential equations such as Homotopy perturbation method, variational iteration method, exponential function method etc. are described with examples.Steady and non-steady state reaction-diffusion equations in the plane sheet (chapter 3), cylinder (chapter 4) and spherical (chapter 5) are analyzed. The analytical results published by various researchers in referred journals during 2007-2020 have been addressed in these chapters 4 to 6, and this leads to conclusions and recommendations on what approaches to use on non-linear reaction-diffusion equations.Convection-diffusion problems arise very often in applied sciences and engineering. Non-linear convection-diffusion equations and corresponding analytical solutions in various fields of chemical sciences are discussed in chapter6. Numerical methods are used to provide approximate results for the non-linear problems, and their importance is felt when it is impossible or difficult to solve a given problem analytically. Chapter 7 identifies some of the numerical methods for finding solutions to non-linear differential equations.