PDEs and Continuum Models of Phase Transitions PDF Download
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Author: M. Rascle
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 254
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Book Description
In three well-organized sections, this book offers the first detailed survey of dispersion compensating fibers. The sections outline Conventional Dispersion Compensating Fiber, including a chapter on modeling dispersion in optical fibers; Alternative and Emerging Technologies, including control of dispersion in photonic crystal fibers; and Systems experiments and Impacts, featuring a survey of systems experiments demonstrating Dispersion Compensation Technologies.
Author: M. Rascle
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 254
Get Book Here
Book Description
In three well-organized sections, this book offers the first detailed survey of dispersion compensating fibers. The sections outline Conventional Dispersion Compensating Fiber, including a chapter on modeling dispersion in optical fibers; Alternative and Emerging Technologies, including control of dispersion in photonic crystal fibers; and Systems experiments and Impacts, featuring a survey of systems experiments demonstrating Dispersion Compensation Technologies.
Author: Augusto Visintin
Publisher: Springer Science & Business Media
ISBN: 1461240786
Category : Mathematics
Languages : en
Pages : 334
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Book Description
... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/:" "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple ... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX
Author: M. Rascle
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 248
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Book Description
In three well-organized sections, this book offers the first detailed survey of dispersion compensating fibers. The sections outline Conventional Dispersion Compensating Fiber, including a chapter on modeling dispersion in optical fibers; Alternative and Emerging Technologies, including control of dispersion in photonic crystal fibers; and Systems experiments and Impacts, featuring a survey of systems experiments demonstrating Dispersion Compensation Technologies.
Author: Michel Chipot
Publisher: CRC Press
ISBN: 9780582253803
Category : Mathematics
Languages : en
Pages : 244
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Book Description
Presents some recent advances in various important domains of partial differential equations and applied mathematics including harmonic maps, Ginzburg - Landau energy, liquid crystals, superconductivity, homogenization and oscillations, dynamical systems and inertial manifolds. These topics are now part of various areas of science and have experienced tremendous development during the last decades.
Author: Christian Kuehn
Publisher: SIAM
ISBN: 1611975654
Category : Mathematics
Languages : en
Pages : 260
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Book Description
This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.
Author: David Kinderlehrer
Publisher: Springer Science & Business Media
ISBN: 1461383609
Category : Science
Languages : en
Pages : 224
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Book Description
This IMA Volume in Mathematics and its Applications MICROSTRUCTURE AND PHASE TRANSITION is based on the proceedings of a workshop which was an integral part of the 1990-91 IMA program on "Phase Transitions and Free Boundaries." We thank R. Fosdick, M.E. Gurtin, W.-M. Ni and L.A. Peletier for organizing the year-long program and, especially, D. Kinderlehrer, R. James, M. Luskin and J. Ericksen for organizing the meeting and editing these proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, and the National Science Foun dation. A vner Friedman Willard Miller. Jr. PREFACE Much of our traditional knowledge of materials and processes is achievf'd by observa tion and analysis of small departures from equilibrium. Many materials, especially modern alloys, ceramics, and their composites, experience not only larger but more dramatic changes, such as the occurrence of phase transitions and t.he creation of defect structures, when viewed at the microscopic scale. How is this observed, how can it be interpreted, and how does it influence macroscopic behavior? These are the principle concerns of this volume, which constitutes the proceedings of an IMA workshop dedicated to these issues.
Author: S. Friedlander
Publisher: Elsevier
ISBN: 0080472915
Category : Science
Languages : en
Pages : 687
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Book Description
The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
Author: Amir Dembo
Publisher: Springer
ISBN: 3540315373
Category : Mathematics
Languages : en
Pages : 283
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Book Description
This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called \nabla \varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques.
Author: C.M. Dafermos
Publisher: Elsevier
ISBN: 0080931979
Category : Mathematics
Languages : en
Pages : 609
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Book Description
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Author: Mariano Giaquinta
Publisher: Springer Science & Business Media
ISBN: 3662062186
Category : Mathematics
Languages : en
Pages : 717
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Book Description
Non-scalar variational problems appear in different fields. In geometry, for in stance, we encounter the basic problems of harmonic maps between Riemannian manifolds and of minimal immersions; related questions appear in physics, for example in the classical theory of a-models. Non linear elasticity is another example in continuum mechanics, while Oseen-Frank theory of liquid crystals and Ginzburg-Landau theory of superconductivity require to treat variational problems in order to model quite complicated phenomena. Typically one is interested in finding energy minimizing representatives in homology or homotopy classes of maps, minimizers with prescribed topological singularities, topological charges, stable deformations i. e. minimizers in classes of diffeomorphisms or extremal fields. In the last two or three decades there has been growing interest, knowledge, and understanding of the general theory for this kind of problems, often referred to as geometric variational problems. Due to the lack of a regularity theory in the non scalar case, in contrast to the scalar one - or in other words to the occurrence of singularities in vector valued minimizers, often related with concentration phenomena for the energy density - and because of the particular relevance of those singularities for the problem being considered the question of singling out a weak formulation, or completely understanding the significance of various weak formulations becames non trivial.
