Mathematical Models With Singularities PDF Download
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Author | : Pedro J. Torres |
Publisher | : Springer |
Total Pages | : 130 |
Release | : 2015-01-22 |
Genre | : Mathematics |
ISBN | : 9462391068 |
Download Mathematical Models with Singularities Book in PDF, ePub and Kindle
The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.
Author | : János Kollár |
Publisher | : Cambridge University Press |
Total Pages | : 381 |
Release | : 2013-02-21 |
Genre | : Mathematics |
ISBN | : 1107035341 |
Download Singularities of the Minimal Model Program Book in PDF, ePub and Kindle
An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.
Author | : Michael Griebel |
Publisher | : Springer Science & Business Media |
Total Pages | : 432 |
Release | : 2013-11-18 |
Genre | : Computers |
ISBN | : 3319007866 |
Download Singular Phenomena and Scaling in Mathematical Models Book in PDF, ePub and Kindle
The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop qualitatively new and mathematically challenging methods for various problems from the natural sciences. Ranging from stochastic and geometric analysis over nonlinear analysis and modelling to numerical analysis and scientific computation, the book is divided into the three sections: A) Scaling limits of diffusion processes and singular spaces, B) Multiple scales in mathematical models of materials science and biology and C) Numerics for multiscale models and singular phenomena. Each section addresses the key aspects of multiple scales and model hierarchies, singularities and degeneracies, and scaling laws and self-similarity.
Author | : J. Eggers |
Publisher | : Cambridge University Press |
Total Pages | : 471 |
Release | : 2015-09-10 |
Genre | : Mathematics |
ISBN | : 1316352390 |
Download Singularities: Formation, Structure, and Propagation Book in PDF, ePub and Kindle
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.
Author | : Takashi Suzuki |
Publisher | : World Scientific |
Total Pages | : 414 |
Release | : 2024-01-22 |
Genre | : Mathematics |
ISBN | : 9811287910 |
Download Methods Of Geometry In The Theory Of Partial Differential Equations: Principle Of The Cancellation Of Singularities Book in PDF, ePub and Kindle
Mathematical models are used to describe the essence of the real world, and their analysis induces new predictions filled with unexpected phenomena.In spite of a huge number of insights derived from a variety of scientific fields in these five hundred years of the theory of differential equations, and its extensive developments in these one hundred years, several principles that ensure these successes are discovered very recently.This monograph focuses on one of them: cancellation of singularities derived from interactions of multiple species, which is described by the language of geometry, in particular, that of global analysis.Five objects of inquiry, scattered across different disciplines, are selected in this monograph: evolution of geometric quantities, models of multi-species in biology, interface vanishing of d - δ systems, the fundamental equation of electro-magnetic theory, and free boundaries arising in engineering.The relaxation of internal tensions in these systems, however, is described commonly by differential forms, and the reader will be convinced of further applications of this principle to other areas.
Author | : Dirk Wiersma |
Publisher | : Springer Science & Business Media |
Total Pages | : 470 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401008345 |
Download New Developments in Singularity Theory Book in PDF, ePub and Kindle
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.
Author | : Abul Hasan Siddiqi |
Publisher | : Springer |
Total Pages | : 309 |
Release | : 2015-12-14 |
Genre | : Mathematics |
ISBN | : 9812879730 |
Download Mathematical Models, Methods and Applications Book in PDF, ePub and Kindle
The present volume contains invited talks of 11th biennial conference on “Emerging Mathematical Methods, Models and Algorithms for Science and Technology”. The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.
Author | : Stanley Alama |
Publisher | : American Mathematical Soc. |
Total Pages | : 284 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821873311 |
Download Singularities in PDE and the Calculus of Variations Book in PDF, ePub and Kindle
This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampere functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.
Author | : Bert-Wolfgang Schulze |
Publisher | : Springer-Verlag |
Total Pages | : 299 |
Release | : 2013-12-01 |
Genre | : Technology & Engineering |
ISBN | : 3663115771 |
Download Symposium “Analysis on Manifolds with Singularities”, Breitenbrunn 1990 Book in PDF, ePub and Kindle
The present Teubner-Text contains the contributions from the International Workshop "Analysis in Domains and on Manifolds with Singularities", Breitenbrunn, Germany, 30. April-5. May 1990. In recent years the analysis on manifolds with singularities became more and more interesting, not only because of the progress in solving corresponding singular problems in partial differential equations but also of the new relations to other parts of mathematics such as geometry, topology and mathematical physics. Other motivations come from concrete models in engineering and applied sciences which lead to partial differential equations in domains with a piece-wise smooth geometry (conical points, edges, comers ..., higher singularities), piece-wise smooth data or boundary and transmission conditions, degenerate coefficients, and so on. There are natural relations to the numerical analysis where also the asymptotics of solutions close to the singularities playa role. As for the smooth cases it is necessary to develop structure principles and unified theories that cover as much as possible the huge variety of concrete situations, often being treated by individual papers under very specific assumptions.
Author | : Stanley Alama |
Publisher | : American Mathematical Soc. |
Total Pages | : 267 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9780821843505 |
Download Singularities in PDE and the Calculus of Variations Book in PDF, ePub and Kindle
This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampere functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.