Download Full eBooks in PDF
The Mathematics Of Diffusion Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of The Mathematics Of Diffusion book. This book definitely worth reading, it is an incredibly well-written.
Author : John Crank
Publisher : Oxford University Press
Page : 428 pages
File Size : 55,8 Mb
Release : 1979
Category : Mathematics
ISBN : 0198534116
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.
Author : John Crank
Publisher : Unknown
Page : 364 pages
File Size : 43,8 Mb
Release : 1956
Category : Diffusion
ISBN : STANFORD:36105010847064
Author : Wei-Ming Ni
Publisher : SIAM
Page : 122 pages
File Size : 47,9 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 1611971977
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.
Author : Rutherford Aris
Publisher : Oxford University Press, USA
Page : 470 pages
File Size : 51,8 Mb
Release : 1975
Category : Science
ISBN : UOM:39015002091992
Author : J. Comyn
Publisher : Springer Science & Business Media
Page : 387 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9789400948587
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.
Author : Nikola_ Ivanovich Portenko
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 42,6 Mb
Release : 1990-12-21
Category : Mathematics
ISBN : 0821898264
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.
Author : Robert B. Banks
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 48,6 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662030523
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.
Author : J. Crank
Publisher : Unknown
Page : 128 pages
File Size : 51,7 Mb
Release : 1964
Category : Electronic
ISBN : OCLC:258070191
Author : Haiyan Wang,Feng Wang,Kuai Xu
Publisher : Springer Nature
Page : 153 pages
File Size : 43,5 Mb
Release : 2020-03-16
Category : Mathematics
ISBN : 9783030388522
The book lies at the interface of mathematics, social media analysis, and data science. Its authors aim to introduce a new dynamic modeling approach to the use of partial differential equations for describing information diffusion over online social networks. The eigenvalues and eigenvectors of the Laplacian matrix for the underlying social network are used to find communities (clusters) of online users. Once these clusters are embedded in a Euclidean space, the mathematical models, which are reaction-diffusion equations, are developed based on intuitive social distances between clusters within the Euclidean space. The models are validated with data from major social media such as Twitter. In addition, mathematical analysis of these models is applied, revealing insights into information flow on social media. Two applications with geocoded Twitter data are included in the book: one describing the social movement in Twitter during the Egyptian revolution in 2011 and another predicting influenza prevalence. The new approach advocates a paradigm shift for modeling information diffusion in online social networks and lays the theoretical groundwork for many spatio-temporal modeling problems in the big-data era.
Author : Glenn Fulford,Philip Broadbridge
Publisher : Cambridge University Press
Page : 220 pages
File Size : 54,7 Mb
Release : 2002
Category : Mathematics
ISBN : 0521001811
An undergraduate text focussing on mathematical modelling stimulated by contemporary industrial problems.
Author : Kiyosi Itô,Henry P. Jr. McKean
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642620256
Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.
Author : Digby Macdonald
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461341451
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.
Author : Susumu Mori,J-Donald Tournier
Publisher : Academic Press
Page : 140 pages
File Size : 40,5 Mb
Release : 2013-08-02
Category : Medical
ISBN : 9780123984074
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
Author : J. Crank
Publisher : Unknown
Page : 414 pages
File Size : 55,6 Mb
Release : 1975
Category : Electronic
ISBN : OCLC:474214568
Author : P. C. Fife
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 45,9 Mb
Release : 2013-03-08
Category : Mathematics
ISBN : 9783642931116
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.