Download or read book Diffusion in Solids written by Helmut Mehrer and published by Springer Science & Business Media. This book was released on 2007-07-24 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the central aspects of diffusion in solids, and goes on to provide easy access to important information about diffusion in metals, alloys, semiconductors, ion-conducting materials, glasses and nanomaterials. Coverage includes diffusion-controlled phenomena including ionic conduction, grain-boundary and dislocation pipe diffusion. This book will benefit graduate students in such disciplines as solid-state physics, physical metallurgy, materials science, and geophysics, as well as scientists in academic and industrial research laboratories.

Download or read book Diffusion written by E. L. Cussler and published by Cambridge University Press. This book was released on 2009-01-15 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This overview of diffusion and separation processes brings unsurpassed, engaging clarity to this complex topic. Diffusion is a key part of the undergraduate chemical engineering curriculum and at the core of understanding chemical purification and reaction engineering. This spontaneous mixing process is also central to our daily lives, with importance in phenomena as diverse as the dispersal of pollutants to digestion in the small intestine. For students, Diffusion goes from the basics of mass transfer and diffusion itself, with strong support through worked examples and a range of student questions. It also takes the reader right through to the cutting edge of our understanding, and the new examples in this third edition will appeal to professional scientists and engineers. Retaining the trademark enthusiastic style, the broad coverage now extends to biology and medicine.

Download or read book Nonlocal Diffusion Problems written by Fuensanta Andreu-Vaillo and published by American Mathematical Soc.. This book was released on 2010 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.

Download or read book Particle Diffusion in the Radiation Belts written by M. Schulz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advent of artificial earth satellites in 1957-58 opened a new dimension in the field of geophysical exploration. Discovery of the earth's radiation belts, consisting of energetic electrons and ions (chiefly protons) trapped by the geomagnetic field, followed almost immediately [1,2]' This largely unexpected development spurred a continuing interest in magnetospheric exploration, which so far has led to the launching of several hundred carefully instrumented spacecraft. Since their discovery, the radiation belts have been a subject of intensive theoretical analysis also. Over the years, a semiquantitative understanding of the governing dynamical processes has gradually evol ved. The underlying kinematical framework of radiation-belt theory is given by the adiabatic theory of charged-particle motion [3J, and the interesting dynamical phenomena are associated with the violation of one or more of the kinematical invariants of adiabatic motion. Among the most important of the operative dynamical processes are those that act in a stochastic manner upon the radiation-belt particles. Such stochastic processes lead to the diffusion of particle distributions with respect to the adiabatic invariants. The observational data indicate that some form of particle diffusion plays an essential role in virtually every aspect of the radiation belts.

Download or read book Diffusion Processes and Related Topics in Biology written by Luigi M. Ricciardi and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a one-quarter course given at the Department of Biophysics and Theoretical Biology of the University of Chicago in 1916. The course was directed to graduate students in the Division of Biological Sciences with interests in population biology and neurobiology. Only a slight acquaintance with probability and differential equations is required of the reader. Exercises are interwoven with the text to encourage the reader to play a more active role and thus facilitate his digestion of the material. One aim of these notes is to provide a heuristic approach, using as little mathematics as possible, to certain aspects of the theory of stochastic processes that are being increasingly employed in some of the population biol ogy and neurobiology literature. While the subject may be classical, the nov elty here lies in the approach and point of view, particularly in the applica tions such as the approach to the neuronal firing problem and its related dif fusion approximations. It is a pleasure to thank Professors Richard C. Lewontin and Arnold J.F. Siegert for their interest and support, and Mrs. Angell Pasley for her excellent and careful typing. I . PRELIMINARIES 1. Terminology and Examples Consider an experiment specified by: a) the experiment's outcomes, ~, forming the space S; b) certain subsets of S (called events) and by the probabilities of these events.

Download or read book Policy Diffusion Dynamics in America written by Graeme Boushey and published by Cambridge University Press. This book was released on 2010-11-01 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Policy Diffusion Dynamics in America integrates research from agenda setting and epidemiology to model factors that shape the speed and scope of public policy diffusion. Drawing on a data set of more than 130 policy innovations, the research demonstrates that the 'laboratories of democracy' metaphor for incremental policy evaluation and emulation is insufficient to capture the dynamic process of policy diffusion in America. A significant subset of innovations trigger outbreaks - the extremely rapid adoption of innovation across states. The book demonstrates how variation in the characteristics of policies, the political and institutional traits of states, and differences among interest group carriers interact to produce distinct patterns of policy diffusion.

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 Diffusion Processes and their Sample Paths written by Kiyosi Itô and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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 Diffusion MRI written by Heidi Johansen-Berg and published by Academic Press. This book was released on 2013-11-04 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion MRI remains the most comprehensive reference for understanding this rapidly evolving and powerful technology and is an essential handbook for designing, analyzing, and interpreting diffusion MR experiments. Diffusion imaging provides a unique window on human brain anatomy. This non-invasive technique continues to grow in popularity as a way to study brain pathways that could never before be investigated in vivo. This book covers the fundamental theory of diffusion imaging, discusses its most promising applications to basic and clinical neuroscience, and introduces cutting-edge methodological developments that will shape the field in coming years. Written by leading experts in the field, it places the exciting new results emerging from diffusion imaging in the context of classical anatomical techniques to show where diffusion studies might offer unique insights and where potential limitations lie. Fully revised and updated edition of the first comprehensive reference on a powerful technique in brain imaging Covers all aspects of a diffusion MRI study from acquisition through analysis to interpretation, and from fundamental theory to cutting-edge developments New chapters covering connectomics, advanced diffusion acquisition, artifact removal, and applications to the neonatal brain Provides practical advice on running an experiment Includes discussion of applications in psychiatry, neurology, neurosurgery, and basic neuroscience Full color throughout

Download or read book Diffusion in Nanoporous Materials 2 Volumes written by Jörg Kärger and published by John Wiley & Sons. This book was released on 2012-10-29 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: Atoms and molecules in all states of matter are subject to continuous irregular movement. This process, referred to as diffusion, is among the most general and basic phenomena in nature and determines the performance of many technological processes. This book provides an introduction to the fascinating world of diffusion in microporous solids. Jointly written by three well-known researchers in this field, it presents a coherent treatise, rather than a compilation of separate review articles, covering the theoretical fundamentals, molecular modeling, experimental observation and technical applications. Based on the book Diffusion in Zeolites and other Microporous Solids, originally published in 1992, it illustrates the remarkable speed with which this field has developed since that time. Specific topics include: new families of nanoporous materials, micro-imaging and single-particle tracking, direct monitoring of transient profiles by interference microscopy, single-file diffusion and new approaches to molecular modeling.

Download or read book Nonlocal Diffusion and Applications written by Claudia Bucur and published by Springer. This book was released on 2016-04-08 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.

Download or read book The Nonlinear Diffusion Equation written by J.M. Burgers and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the 'Introduction' to the main text gives an account of the way in which the problems treated in the following pages originated, this 'Preface' may be limited to an acknowledgement of the support the work has received. It started during the pe riod when I was professor of aero- and hydrodynamics at the Technical University in Delft, Netherlands, and many discussions with colleagues ha ve in:fluenced its devel opment. Oftheir names I mention here only that ofH. A. Kramers. Papers No. 1-13 ofthe list given at the end ofthe text were written during that period. Severa! ofthese were attempts to explore ideas which later had to be abandoned, but gradually a line of thought emerged which promised more definite results. This line began to come to the foreground in pa per No. 3 (1939}, while a preliminary formulation ofthe results was given in paper No. 12 (1954}. At that time, however, there still was missing a practica! method for manipulating a certain distribution function of central interest. A six months stay at the Hydrodynamics Laboratories ofthe California Institute of Technology, Pasadena, California (1950-1951}, was supported by a Contract with the Department of the Air F orce, N o. AF 33(038}-17207. A course of lectures was given during this period, which were published in typescript under the title 'On Turbulent Fluid Motion', as Report No. E-34. 1, July 1951, of the Hydrodynamics Laboratory.

Download or read book Diffusion and Mass Transfer written by James S. Vrentas and published by CRC Press. This book was released on 2016-04-19 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: A proper understanding of diffusion and mass transfer theory is critical for obtaining correct solutions to many transport problems. Diffusion and Mass Transfer presents a comprehensive summary of the theoretical aspects of diffusion and mass transfer and applies that theory to obtain detailed solutions for a large number of important problems. Par

Download or read book Shock Waves and Reaction Diffusion Equations written by Joel Smoller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.

Download or read book Thermodynamics Diffusion and the Kirkendall Effect in Solids written by Aloke Paul and published by Springer. This book was released on 2014-07-16 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book basic and some more advanced thermodynamics and phase as well as stability diagrams relevant for diffusion studies are introduced. Following, Fick’s laws of diffusion, atomic mechanisms, interdiffusion, intrinsic diffusion, tracer diffusion and the Kirkendall effect are discussed. Short circuit diffusion is explained in detail with an emphasis on grain boundary diffusion. Recent advances in the area of interdiffusion will be introduced. Interdiffusion in multi-component systems is also explained. Many practical examples will be given, such that researches working in this area can learn the practical evaluation of various diffusion parameters from experimental results. Large number of illustrations and experimental results are used to explain the subject. This book will be appealing for students, academicians, engineers and researchers in academic institutions, industry research and development laboratories.

Download or read book Diffusion in Gases and Porous Media written by Roberto Cunningham and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world we live in exhibits, on different scales, many phenomena related to the diffusion of gases. Among them are the movement of gases in earth strata, the aeration of soils, the drying of certain materials, some catalytic reactions, purification by adsorption, isotope separation, column chro matography, cooling of nuclear reactors, and the permeability of various packing materials. The evolution of the understanding of this subject has not always been straightforward and progressive-there has been much confusion and many doubts and misunderstandings, some of which remain to this day. The main reason for the difficulties in the development of this subject is, we now know, the lack of an understanding of the effects of walls on diffusing systems. Textbooks usually treat diffusion on two levels: at the physicochemi cal or molecular level, making use of the kinetic theory of gases (which while a very rigorous and well-founded theory nevertheless is valid only for systems without walls), or at the level of a transport phenomenon, a level geared toward applications. The influence of walls is usually disregarded or is treated very briefly (for example, by taking account of the Knudsen regime or by introducing a transition regime of limited validity) in a way unconnected with previous studies. As a consequence, the extensive, gener alized, and well-founded knowledge of systems without walls has often been applied without sound basis to real situations, i.e., to systems with walls.