A Study Of The Singularities Of The Solution Of A Dirichlet Problem For The Equation Uxyzo

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Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation

Author : Zohar Yosibash
Publisher : Springer Science & Business Media
ISBN 13 : 146141508X
Total Pages : 473 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation by : Zohar Yosibash

Download or read book Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation written by Zohar Yosibash and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations. The book is divided into fourteen chapters, each containing several sections. Most of it (the first nine Chapters) addresses two-dimensional domains, where only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle material on a daily basis. Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, is still a topic of active research and interest, and is addressed herein. Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions. This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.

Singularities in Boundary Value Problems

Author : H.G. Garnir
Publisher : Springer Science & Business Media
ISBN 13 : 9400984340
Total Pages : 390 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Singularities in Boundary Value Problems by : H.G. Garnir

Download or read book Singularities in Boundary Value Problems written by H.G. Garnir and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1980 Maratea NATO Advanced Study Institute (= ASI) followed the lines of the 1976 Liege NATO ASI. Indeed, the interest of boundary problems for linear evolution partial differential equations and systems is more and more acute because of the outstanding position of those problems in the mathematical description of the physical world, namely through sciences such as fluid dynamics, elastodynamics, electro dynamics, electromagnetism, plasma physics and so on. In those problems the question of the propagation of singularities of the solution has boomed these last years. Placed in its definitive mathematical frame in 1970 by L. Hormander, this branch -of the theory recorded a tremendous impetus in the last decade and is now eagerly studied by the most prominent research workers in the field of partial differential equations. It describes the wave phenomena connected with the solution of boundary problems with very general boundaries, by replacing the (generailly impossible) computation of a precise solution by a convenient asymptotic approximation. For instance, it allows the description of progressive waves in a medium with obstacles of various shapes, meeting classical phenomena as reflexion, refraction, transmission, and even more complicated ones, called supersonic waves, head waves, creeping waves, •••••• The !'tudy of singularities uses involved new mathematical concepts (such as distributions, wave front sets, asymptotic developments, pseudo-differential operators, Fourier integral operators, microfunctions, ••• ) but emerges as the most sensible application to physical problems. A complete exposition of the present state of this theory seemed to be still lacking.

Around the Research of Vladimir Maz'ya II

Author : Ari Laptev
Publisher : Springer
ISBN 13 : 9781441913425
Total Pages : 386 pages
Book Rating : 4.9/5 (134 download)

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Book Synopsis Around the Research of Vladimir Maz'ya II by : Ari Laptev

Download or read book Around the Research of Vladimir Maz'ya II written by Ari Laptev and published by Springer. This book was released on 2010-01-04 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics of this volume are close to scientific interests of Professor Maz'ya and use, directly or indirectly, the fundamental influential Maz'ya's works penetrating, in a sense, the theory of PDEs. In particular, recent advantages in the study of semilinear elliptic equations, stationary Navier-Stokes equations, the Stokes system in convex polyhedra, periodic scattering problems, problems with perturbed boundary at a conic point, singular perturbations arising in elliptic shells and other important problems in mathematical physics are presented.

Ginzburg-Landau Vortices

Author : Fabrice Bethuel
Publisher : Birkhäuser
ISBN 13 : 3319666738
Total Pages : 188 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Ginzburg-Landau Vortices by : Fabrice Bethuel

Download or read book Ginzburg-Landau Vortices written by Fabrice Bethuel and published by Birkhäuser. This book was released on 2017-09-21 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ɛ tends to zero. One of the main results asserts that the limit u-star of minimizers uɛ exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized. The material presented in this book covers mostly original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis, partial differential equations, and complex functions. This book is designed for researchers and graduate students alike, and can be used as a one-semester text. The present softcover reprint is designed to make this classic text available to a wider audience.

Singularities: Formation, Structure, and Propagation

Author : J. Eggers
Publisher : Cambridge University Press
ISBN 13 : 1316352390
Total Pages : 471 pages
Book Rating : 4.3/5 (163 download)

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Book Synopsis Singularities: Formation, Structure, and Propagation by : J. Eggers

Download or read book Singularities: Formation, Structure, and Propagation written by J. Eggers and published by Cambridge University Press. This book was released on 2015-09-10 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.

James Serrin. Selected Papers

Author : Patrizia Pucci
Publisher : Birkhäuser
ISBN 13 : 9783034806848
Total Pages : 0 pages
Book Rating : 4.8/5 (68 download)

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Book Synopsis James Serrin. Selected Papers by : Patrizia Pucci

Download or read book James Serrin. Selected Papers written by Patrizia Pucci and published by Birkhäuser. This book was released on 2014-07-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes present the collected works of James Serrin. He did seminal work on a number of the basic tools needed for the study of solutions of partial differential equations. Many of them have been and are being applied to solving problems in science and engineering. Among the areas which he studied are maximum principle methods and related phenomena such as Harnack's inequality, the compact support principle, dead cores and bursts, free boundary problems, phase transitions, the symmetry of solutions, boundary layer theory, singularities and fine regularity properties. The volumes include commentaries by leading mathematicians to indicate the significance of the articles and to discuss further developments along the lines of these articles.

Resolution of Singularities

Author : Steven Dale Cutkosky
Publisher : American Mathematical Soc.
ISBN 13 : 9781470421069
Total Pages : 186 pages
Book Rating : 4.4/5 (21 download)

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Book Synopsis Resolution of Singularities by : Steven Dale Cutkosky

Download or read book Resolution of Singularities written by Steven Dale Cutkosky and published by American Mathematical Soc.. This book was released on 2004 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of singularities by simple algebraic mappings is truly a fundamental problem. It has a complete solution in characteristic zero and partial solutions in arbitrary characteristic. The resolution of singularities in characteristic zero is a key result used in many subjects besides algebraic geometry, such as differential equations, dynamical systems, number theory, the theory of $\mathcal{D}$-modules, topology, and mathematical physics. This book is a rigorous, but instructional, look at resolutions. A simplified proof, based on canonical resolutions, is given for characteristic zero. There are several proofs given for resolution of curves and surfaces in characteristic zero and arbitrary characteristic. Besides explaining the tools needed for understanding resolutions, Cutkosky explains the history and ideas, providing valuable insight and intuition for the novice (or expert). There are many examples and exercises throughout the text. The book is suitable for a second course on an exciting topic in algebraic geometry. A core course on resolutions is contained in Chapters 2 through 6. Additional topics are covered in the final chapters. The prerequisite is a course covering the basic notions of schemes and sheaves.

The Theory of Singularities and Its Applications

Author : Vladimir Igorevich Arnolʹd
Publisher : Cambridge University Press
ISBN 13 : 9780521422802
Total Pages : 88 pages
Book Rating : 4.4/5 (228 download)

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Book Synopsis The Theory of Singularities and Its Applications by : Vladimir Igorevich Arnolʹd

Download or read book The Theory of Singularities and Its Applications written by Vladimir Igorevich Arnolʹd and published by Cambridge University Press. This book was released on 1991-05-31 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, which is based on lectures given in Pisa under the auspices of the Accademia Nazionale dei Lincei, the distinguished mathematician Vladimir Arnold describes those singularities encountered in different branches of mathematics. He avoids giving difficult proofs of all the results in order to provide the reader with a concise and accessible overview of the many guises and areas in which singularities appear, such as geometry and optics; optimal control theory and algebraic geometry; reflection groups and dynamical systems and many more. This will be an excellent companion for final year undergraduates and graduates whose area of study brings them into contact with singularities.

Theory and Applications of Singular Perturbations

Author : W. Eckhaus
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Theory and Applications of Singular Perturbations by : W. Eckhaus

Download or read book Theory and Applications of Singular Perturbations written by W. Eckhaus and published by Lecture Notes in Mathematics. This book was released on 1982-08 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Deformations of singularities

Author : Jan Stevens
Publisher : Springer Science & Business Media
ISBN 13 : 9783540005605
Total Pages : 172 pages
Book Rating : 4.0/5 (56 download)

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Book Synopsis Deformations of singularities by : Jan Stevens

Download or read book Deformations of singularities written by Jan Stevens and published by Springer Science & Business Media. This book was released on 2003 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Typical Singularities of Differential 1-forms and Pfaffian Equations

Author : Mikhail Zhitomirskiĭ
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897423
Total Pages : 196 pages
Book Rating : 4.8/5 (974 download)

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Book Synopsis Typical Singularities of Differential 1-forms and Pfaffian Equations by : Mikhail Zhitomirskiĭ

Download or read book Typical Singularities of Differential 1-forms and Pfaffian Equations written by Mikhail Zhitomirskiĭ and published by American Mathematical Soc.. This book was released on 1992 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularities and the classification of 1-forms and Pfaffian equations are interesting not only as classical problems, but also because of their applications in contact geometry, partial differential equations, control theory, nonholonomic dynamics, and variational problems. In addition to collecting results on the geometry of singularities and classification of differential forms and Pfaffian equations, this monograph discusses applications and closely related classification problems. Zhitomirskii presents proofs with all results and ends each chapter with a summary of the main results, a tabulation of the singularities, and a list of the normal forms. The main results of the book are also collected together in the introduction.

Le Cycles and Hypersurface Singularities

Author : David Massey
Publisher : Springer
ISBN 13 : 3540455213
Total Pages : 141 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Le Cycles and Hypersurface Singularities by : David Massey

Download or read book Le Cycles and Hypersurface Singularities written by David Massey and published by Springer. This book was released on 2006-11-14 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes and gives applications of an important new tool in the study of complex analytic hypersurface singularities: the Lê cycles of the hypersurface. The Lê cycles and their multiplicities - the Lê numbers - provide effectively calculable data which generalizes the Milnor number of an isolated singularity to the case of singularities of arbitrary dimension. The Lê numbers control many topological and geometric properties of such non-isolated hypersurface singularities. This book is intended for graduate students and researchers interested in complex analytic singularities.

Singularities In Geometry And Topology - Proceedings Of The Trieste Singularity Summer School And Workshop

Author : Jean-paul Brasselet
Publisher : World Scientific
ISBN 13 : 9814477044
Total Pages : 917 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Singularities In Geometry And Topology - Proceedings Of The Trieste Singularity Summer School And Workshop by : Jean-paul Brasselet

Download or read book Singularities In Geometry And Topology - Proceedings Of The Trieste Singularity Summer School And Workshop written by Jean-paul Brasselet and published by World Scientific. This book was released on 2007-01-16 with total page 917 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.

New Developments in Singularity Theory

Author : Dirk Wiersma
Publisher : Springer Science & Business Media
ISBN 13 : 9401008345
Total Pages : 470 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis New Developments in Singularity Theory by : Dirk Wiersma

Download or read book New Developments in Singularity Theory written by Dirk Wiersma and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

Introduction to Lipschitz Geometry of Singularities

Author : Walter Neumann
Publisher : Springer Nature
ISBN 13 : 3030618072
Total Pages : 356 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Introduction to Lipschitz Geometry of Singularities by : Walter Neumann

Download or read book Introduction to Lipschitz Geometry of Singularities written by Walter Neumann and published by Springer Nature. This book was released on 2021-01-11 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves. While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category. The book is aimed at graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.

Real and Complex Singularities

Author : James William Bruce
Publisher : CRC Press
ISBN 13 : 9781584881421
Total Pages : 292 pages
Book Rating : 4.8/5 (814 download)

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Book Synopsis Real and Complex Singularities by : James William Bruce

Download or read book Real and Complex Singularities written by James William Bruce and published by CRC Press. This book was released on 1999-08-26 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The boundaries of singularity theory are broad and vague, connecting the most important applications of mathematics and science with more abstract areas. Optics, robotics, computer vision, Hamiltonian mechanics, bifurcation theory and differential equations are among the variety of topics that benefit from developments in the theory. With singularity theory encompassing more and more applications, Real and Complex Singularities provides insight into the future of this expanding field. Comprising refereed contributions to the Fifth Workshop on Real and Complex Singularities, this volume addresses three important areas related to the broad subject of singularities. The first section deals with questions within singularity theory itself, representing the topics currently being investigated. The second explores applications of singularity theory to differential geometry, robotics, and computer vision. The final section consists of applications to bifurcation theory and dynamical systems. With over two-hundred tables that provide quick access to data, this volume is a complete overview of the most current topics and applications of singularity theory. Real and Complex Singularities creates the opportunity for you to stay up-to-date with recent advances and discover promising directions for future research in the field.

Space-Time Methods

Author : Ulrich Langer
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110548488
Total Pages : 262 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Space-Time Methods by : Ulrich Langer

Download or read book Space-Time Methods written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.