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Author:
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ISBN:
Category :
Languages : en
Pages :
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Book Description
A Primer of Diffusion Problems A Primer of Diffusion Problems is a concise and lively introduction to diffusion theory in its many guises and to a variety of analytical and numerical methods for the solution of diffusion problems. It discusses the diffusion equation, the steady state, diffusion under external forces, time-dependent diffusion, and similarity, thus bridging mathematical and physical treatments of diffusion. Featured topics include a careful development of the oxidation theory of silicon, properties of the family of error functions, precipitation and phase transformations, a concise introduction to Laplace transforms, and nonlinear boundary conditions. Exercises are found throughout the text, and appendices treat rarely found advanced topics.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
A Primer of Diffusion Problems A Primer of Diffusion Problems is a concise and lively introduction to diffusion theory in its many guises and to a variety of analytical and numerical methods for the solution of diffusion problems. It discusses the diffusion equation, the steady state, diffusion under external forces, time-dependent diffusion, and similarity, thus bridging mathematical and physical treatments of diffusion. Featured topics include a careful development of the oxidation theory of silicon, properties of the family of error functions, precipitation and phase transformations, a concise introduction to Laplace transforms, and nonlinear boundary conditions. Exercises are found throughout the text, and appendices treat rarely found advanced topics.
Author: Richard Ghez
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 268
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Book Description
The only elementary text to provide a complete introduction to diffusion theory and the various analytical and numerical methods of solution. Presents an integrated set of real-life problems taken mainly from metallurgy and device processing, and offers an overview of the solution of diffusion problems in practical cases, with clear explanations of the interrelationships between mathematical solutions, and the underlying physics and chemistry. Covers oxidation theory, error functions, Laplace transforms, and similarity, a topic of current research interest. Also covers Green's functions and integral equations, rarely discussed in introductory texts.
Author: Richard Ghez
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 272
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Book Description
The only elementary text to provide a complete introduction to diffusion theory and the various analytical and numerical methods of solution. Presents an integrated set of real-life problems taken mainly from metallurgy and device processing, and offers an overview of the solution of diffusion problems in practical cases, with clear explanations of the interrelationships between mathematical solutions, and the underlying physics and chemistry. Covers oxidation theory, error functions, Laplace transforms, and similarity, a topic of current research interest. Also covers Green's functions and integral equations, rarely discussed in introductory texts.
Author: Jordan Hristov
Publisher:
ISBN: 9781536183306
Category : Mathematics
Languages : en
Pages : 0
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Book Description
"Diffusion is a principle transport mechanism emerging widely at different scale, from nano to micro and macro levels. This is a contributed book of seventh chapters encompassing local and no-local diffusion phenomena modelled with integer-order (local) and non-local operators. This book collates research results developed by scientists from different countries but with common research interest in modelling of diffusion problems. The results reported encompass diffusion problems related to efficient numerical modelling, hypersonic flows, approximate analytical solutions of solvent diffusion in polymers and wetting of soils. Some chapters are devoted to fractional diffusion problem with operators with singular and non-singular memory kernels. The book content cannot present the entire rich area of problems related to modelling of diffusion phenomena but allow seeing some new trends and approaches in the modelling technologies. In this context, the fractional models with singular and non-singular kernels the numerical methods and the development of the integration techniques related to the integral-balance approach form fresh fluxes of ideas to this classical engineering area of research. The book is oriented to researchers; master and PhD students involved in diffusion problems with a variety of application and could serves as a rich reference source and a collection of texts provoking new ideas"--
Author: Rudy Slingerland
Publisher: Princeton University Press
ISBN: 1400839114
Category : Science
Languages : en
Pages : 246
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Book Description
A concise guide to representing complex Earth systems using simple dynamic models Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. Step-by-step lessons for representing complex Earth systems as dynamical models Explains geologic processes in terms of fundamental laws of physics and chemistry Numerical solutions to differential equations through the finite difference technique A philosophical approach to quantitative problem-solving Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html
Author: Richard Ghez
Publisher: Springer Science & Business Media
ISBN: 1475733615
Category : Science
Languages : en
Pages : 327
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Book Description
This book is a second edition of the one that was published by John Wiley & Sons in 1988. It carries a new title because the former one, A Primer of Diffusion Problems, gave the impression of consisting merely of a set of problems relating to diffusion. Nonetheless, my intention was clearly spelled out and it remains the same, namely, to teach basic aspects and methods of solution for diffusion phenomena through physical examples. Again, I emphasize that the coverage is not encyclopedic. There exist already several outstanding works of that nature, for example, J. Philibert's Atom Movements, Diffusion and Mass Transport in Solids. My emphasis is on modeling and methodology. This book should thus constitute a consistent introduction to diffusion phenomena, whatever their origin or further application. This edition has been largely revised. It contains a completely new chapter and three new appendices. I have added several new exercises stemming from my experience in teaching this material over the last 15 years. I hope that they will be instructive to the reader for they were not chosen perfunctorily. Although they are the bane of authors and of readers, I have retained footnotes if they might help the reader's comprehension. Additional, but nonessential material is collected at the end of chapters, and is indicated in the text by superscripts.
Author: Gale Jay Young
Publisher:
ISBN:
Category :
Languages : en
Pages : 66
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Book Description
Author: Luiz Roberto Evangelista
Publisher: Springer Nature
ISBN: 3031181506
Category : Science
Languages : en
Pages : 411
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Book Description
This book provides a contemporary treatment of the problems related to anomalous diffusion and anomalous relaxation. It collects and promotes unprecedented applications dealing with diffusion problems and surface effects, adsorption-desorption phenomena, memory effects, reaction-diffusion equations, and relaxation in constrained structures of classical and quantum processes. The topics covered by the book are of current interest and comprehensive range, including concepts in diffusion and stochastic physics, random walks, and elements of fractional calculus. They are accompanied by a detailed exposition of the mathematical techniques intended to serve the reader as a tool to handle modern boundary value problems. This self-contained text can be used as a reference source for graduates and researchers working in applied mathematics, physics of complex systems and fluids, condensed matter physics, statistical physics, chemistry, chemical and electrical engineering, biology, and many others.
Author: John Crank
Publisher: Oxford University Press
ISBN: 9780198534112
Category : Mathematics
Languages : en
Pages : 428
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Book Description
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: Merkel H. Jacobs
Publisher: Springer Science & Business Media
ISBN: 3642864147
Category : Science
Languages : en
Pages : 165
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Book Description
A basic tenet of present day biophysics is that flows in biological systems are causally related to forces. A large and growing fraction of membrane biophysics is devoted to an exploration of the quantitative relationship between forces and flows in order to understand both the nature of biological membranes and the processes that take place on and in these membranes. This is why the discussion of the nature of diffusion is so important in any formal development of membrane bio physics. This was equally true twenty years ago when tracers were just beginning to be used for the measurement of m.
