Author: Morton E. Gurtin Publisher: Oxford University Press on Demand ISBN: 9780198536949 Category : Mathematics Languages : en Pages : 148
Book Description
This book is one of the very first on the subject of mathematical materials science and presents a view different from that prevalent in the physical literature. Issues foundational in nature are stressed with the emphasis on the interplay between mathematics and physics. It discusses thedynamics of two-phase systems within the framework of modern continuum thermodynamics. Two general theories are considered and the resulting equations exhibit unstable growth patterns. The free boundary problems that form the basis of the subject should be of great interest to mathematicians andphysical scientists.
Author: Augusto Visintin Publisher: Springer Science & Business Media ISBN: 1461240786 Category : Mathematics Languages : en Pages : 334
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: Grard A. Maugin Publisher: World Scientific ISBN: 9789810233754 Category : Science Languages : en Pages : 398
Book Description
In this invaluable book, macroscopic irreversible thermodynamics is presented in its realm and its splendor by appealing to the notion of internal variables of state. This applies to both fluids and solids with or without microstructures of mechanical or electromagnetic origin. This unmatched richness of essentially nonlinear behaviors is the result of the use of modern mathematical techniques such as convex analysis in a clear-cut framework which allows one to put under the umbrella of ?irreversible thermodynamics? behaviors which until now have been commonly considered either not easily covered, or even impossible to incorporate into such a framework.The book is intended for all students and researchers whose main concern is the rational modeling of complex and/or new materials with physical and engineering applications, such as those accounting for coupled-field, hysteresis, fracture, nonlinear-diffusion, and phase-transformation phenomena.
Author: Yoshikazu Giga Publisher: Springer Science & Business Media ISBN: 3764373911 Category : Mathematics Languages : en Pages : 270
Book Description
This book presents a self-contained introduction to the analytic foundation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in many applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Moreover, structures of level set equations are studied in detail. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set approach. Although most of the results in this book are more or less known, they are scattered in several references, sometimes without proofs. This book presents these results in a synthetic way with full proofs. The intended audience are graduate students and researchers in various disciplines who would like to know the applicability and detail of the theory as well as its flavour. No familiarity with differential geometry or the theory of viscosity solutions is required. Only prerequisites are calculus, linear algebra and some basic knowledge about semicontinuous functions.
Author: Paul Baird Publisher: Birkhäuser ISBN: 3034879687 Category : Mathematics Languages : en Pages : 158
Book Description
This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. There are introductory survey articles as well as papers presenting the latest research results. Among the topics covered are blow-up theory for second order elliptic equations; bubbling phenomena in the harmonic map heat flow; applications of scans and fractional power integrands; heat flow for the p-energy functional; Ricci flow and evolution by curvature of networks of curves in the plane.
Author: Dominic D. Joyce Publisher: OUP Oxford ISBN: 9780198506010 Category : Mathematics Languages : en Pages : 460
Book Description
This is a combination of a graduate textbook on Reimannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It contains much new research and many new examples.
Author: William Mark Goldman Publisher: Oxford University Press ISBN: 9780198537939 Category : Mathematics Languages : en Pages : 342
Book Description
This is the first comprehensive treatment of the geometry of complex hyperbolic space, a rich area of research with numerous connections to other branches of mathematics, including Riemannian geometry, complex analysis, symplectic and contact geometry, Lie groups, and harmonic analysis.
Author: Charles J. Colbourn Publisher: Oxford University Press ISBN: 9780198535768 Category : Computers Languages : en Pages : 582
Book Description
Among the simplest combinatorial designs, triple systems have diverse applications in coding theory, cryptography, computer science, and statistics. This book provides a systematic and comprehensive treatment of this rich area of mathematics.
Author: Johann Boos Publisher: Clarendon Press ISBN: 9780198501657 Category : Mathematics Languages : en Pages : 616
Book Description
Summability is a mathematical topic with a long tradition and many applications in, for example, function theory, number theory, and stochastics. It was originally based on classical analytical methods, but was strongly influenced by modern functional analytical methods during the last seven decades. The present book aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used. Part I contains a short general introduction to summability, the basic classical theory concerning mainly inclusion theorems and theorems of the Silverman-Toeplitz type, a presentation of the most important classes of summability methods, Tauberian theorems, and applications of matrix methods. The proofs in Part I are exclusively done by applying classical analytical methods. Part II is concerned with modern functional analytical methods in summability, and contains the essential functional analytical basis required in later parts of the book, topologization of sequence spaces as K- and KF-spaces, domains of matrix methods as FK-spaces and their topological structure. In this part the proofs are of functional analytical nature only. Part III of the present book deals with topics in summability and topological sequence spaces which require the combination of classical and modern methods. It covers investigations of the constistency of matrix methods and of the bounded domain of matrix methods via Saks space theory, and the presentation of some aspects in topological sequence spaces. Lecturers, graduate students, and researchers working in summability and related topics will find this book a useful introduction and reference work.
Author: Gerald W. Johnson Publisher: Clarendon Press ISBN: 0191546267 Category : Mathematics Languages : en Pages : 790
Book Description
This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results.
Author: Morton E. Gurtin
Author: Augusto Visintin
Author: Grard A. Maugin
Author: Yoshikazu Giga
Author: Paul Baird
Author: Dominic D. Joyce
Author: William Mark Goldman
Author: Charles J. Colbourn
Author: Johann Boos
Author: Gerald W. Johnson