Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Polymer Permeability written by J. Comyn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Mathematics of Diffusion written by Wei-Ming Ni and published by SIAM. This book was released on 2011-01-01 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Growth and Diffusion Phenomena written by Robert B. Banks and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion and growth phenomena abound in the real world surrounding us. Someexamples: growth of the world's population, growth rates of humans, public interest in news events, growth and decline of central city populations, pollution of rivers, adoption of agricultural innovations, and spreading of epidemics and migration of insects. These and numerous other phenomena are illustrations of typical growth and diffusion problems confronted in many branches of the physical, biological and social sciences as well as in various areas of agriculture, business, education, engineering medicine and public health. The book presents a large number of mathematical models to provide frameworks forthe analysis and display of many of these. The models developed and utilizedcommence with relatively simple exponential, logistic and normal distribution functions. Considerable attention is given to time dependent growth coefficients and carrying capacities. The topics of discrete and distributed time delays, spatial-temporal diffusion and diffusion with reaction are examined. Throughout the book there are a great many numerical examples. In addition and most importantly, there are more than 50 in-depth "illustrations" of the application of a particular framework ormodel based on real world problems. These examples provide the reader with an appreciation of the intrinsic nature of the phenomena involved. They address mainly readers from the physical, biological, and social sciences, as the only mathematical background assumed is elementary calculus. Methods are developed as required, and the reader can thus acquire useful tools for planning, analyzing, designing,and evaluating studies of growth transfer and diffusion phenomena. The book draws on the author's own hands-on experience in problems of environmental diffusion and dispersion, as well as in technology transfer and innovation diffusion.
Download or read book Fractional Diffusion Equations and Anomalous Diffusion written by Luiz Roberto Evangelista and published by Cambridge University Press. This book was released on 2018-01-25 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary treatment of this process, this book examines the recent literature on anomalous diffusion and covers a rich class of problems in which surface effects are important, offering detailed mathematical tools of usual and fractional calculus for a wide audience of scientists and graduate students in physics, mathematics, chemistry and engineering. Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of fundamental and practical problems in a fast-growing field of research.
Download or read book Numerical Bifurcation Analysis for Reaction Diffusion Equations written by Zhen Mei and published by Springer Science & Business Media. This book was released on 2000-06-21 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Convection diffusion Problems written by Martin Stynes and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Aspects of Reacting and Diffusing Systems written by P. C. Fife and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and of course can interact with real chemical species (ions) which are transported through the membrane. These facts gave rise to Hodgkin's and Huxley's celebrated model for the propagation of nerve signals. On the level of populations, individuals interact and move about, and so it is not surprising that here, again, the simplest continuous space-time interaction-migration models have the same g- eral appearance as those for diffusing and reacting chemical systems.
Download or read book Revival Numerical Solution Of Convection Diffusion Problems 1996 written by K.W. Morton and published by CRC Press. This book was released on 2019-02-25 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurate modeling of the interaction between convective and diffusive processes is one of the most common challenges in the numerical approximation of partial differential equations. This is partly due to the fact that numerical algorithms, and the techniques used for their analysis, tend to be very different in the two limiting cases of elliptic and hyperbolic equations. Many different ideas and approaches have been proposed in widely differing contexts to resolve the difficulties of exponential fitting, compact differencing, number upwinding, artificial viscosity, streamline diffusion, Petrov-Galerkin and evolution Galerkin being some examples from the main fields of finite difference and finite element methods. The main aim of this volume is to draw together all these ideas and see how they overlap and differ. The reader is provided with a useful and wide ranging source of algorithmic concepts and techniques of analysis. The material presented has been drawn both from theoretically oriented literature on finite differences, finite volume and finite element methods and also from accounts of practical, large-scale computing, particularly in the field of computational fluid dynamics.
Download or read book Transient Techniques in Electrochemistry written by Digby Macdonald and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of electrochemical reactions by relaxation or transient techniques has expanded rapidly over the last two decades. The impetus for the develop ment of these techniques has been the desire to obtain quantitative data on the rates of "fast" electrochemical processes, including those coupled to homogeneous chemical reactions in solution. This has necessarily meant the development of techniques that are capable of delineating the effects of mass transport and charge transfer at very short times. The purpose of this book is to describe how the various transient techniques may be used to obtain the desired information. Emphasis is placed upon the detailed mathematical development of the subject, since this aspect is the most frequently ignored in other texts in this field. In any relaxation or transient technique for the study of rate processes, it is necessary to disturb the reaction from equilibrium or the steady state by applying a perturbing impulse to the system. The system is then allowed to relax to a new equilibrium or steady-state position, and. the transient (i. e. , the response as a function of time) is analyzed to extract the desired kinetic information. In electrochemical studies the heterogeneous rate constants are, in general, dependent upon the potential difference across the interface, so that the perturbing impulse frequently takes the form of a known variation in potential as a function of time.
Download or read book The Mathematics of Diffusion written by J. Crank and published by . This book was released on 1975 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Differential Equations and Diffusion Processes written by N. Ikeda and published by Elsevier. This book was released on 2014-06-28 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.
Download or read book Industrial Mathematics written by Glenn Fulford and published by Cambridge University Press. This book was released on 2002 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: An undergraduate text focussing on mathematical modelling stimulated by contemporary industrial problems.
Download or read book Smoothing and Decay Estimates for Nonlinear Diffusion Equations written by Juan Luis Vázquez and published by Oxford University Press. This book was released on 2006-08-03 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is concerned with quantitative aspects of the theory of nonlinear diffusion equations, whichappear as mathematical models in different branches of Physics, Chemistry, Biology and Engineering.
Download or read book Introduction to Diffusion Tensor Imaging written by Susumu Mori and published by Academic Press. This book was released on 2013-08-02 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concepts behind diffusion tensor imaging (DTI) are commonly difficult to grasp, even for magnetic resonance physicists. To make matters worse, a many more complex higher-order methods have been proposed over the last few years to overcome the now well-known deficiencies of DTI. In Introduction to Diffusion Tensor Imaging: And Higher Order Models, these concepts are explained through extensive use of illustrations rather than equations to help readers gain a more intuitive understanding of the inner workings of these techniques. Emphasis is placed on the interpretation of DTI images and tractography results, the design of experiments, and the types of application studies that can be undertaken. Diffusion MRI is a very active field of research, and theories and techniques are constantly evolving. To make sense of this constantly shifting landscape, there is a need for a textbook that explains the concepts behind how these techniques work in a way that is easy and intuitive to understand—Introduction to Diffusion Tensor Imaging fills this gap. Extensive use of illustrations to explain the concepts of diffusion tensor imaging and related methods Easy to understand, even without a background in physics Includes sections on image interpretation, experimental design, and applications Up-to-date information on more recent higher-order models, which are increasingly being used for clinical applications
Download or read book The Mathematics of Diffusion written by J. Crank and published by . This book was released on 1964 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Degenerate Nonlinear Diffusion Equations written by Angelo Favini and published by Springer. This book was released on 2012-05-08 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce relevant solving methods for each of them.
