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| Author | : J. Eggers |
| Publisher | : Cambridge University Press |
| Total Pages | : 471 |
| Release | : 2015-09-10 |
| Genre | : Mathematics |
| ISBN | : 1107098416 |
This book explores a wide range of singular phenomena, providing mathematical tools for understanding them and highlighting their common features.
| Author | : J. Eggers |
| Publisher | : Cambridge University Press |
| Total Pages | : 471 |
| Release | : 2015-09-10 |
| Genre | : Mathematics |
| ISBN | : 1316352390 |
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 | : Valeria Banica |
| Publisher | : SMF |
| Total Pages | : 162 |
| Release | : 2012 |
| Genre | : Capillarity |
| ISBN | : 9782856297698 |
| Author | : Lars Garding |
| Publisher | : Springer |
| Total Pages | : 129 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540472169 |
These lecture notes stemming from a course given at the Nankai Institute for Mathematics, Tianjin, in 1986 center on the construction of parametrices for fundamental solutions of hyperbolic differential and pseudodifferential operators. The greater part collects and organizes known material relating to these constructions. The first chapter about constant coefficient operators concludes with the Herglotz-Petrovsky formula with applications to lacunas. The rest is devoted to non-degenerate operators. The main novelty is a simple construction of a global parametrix of a first-order hyperbolic pseudodifferential operator defined on the product of a manifold and the real line. At the end, its simplest singularities are analyzed in detail using the Petrovsky lacuna edition.
| Author | : Andreas Martin |
| Publisher | : |
| Total Pages | : 27 |
| Release | : 2002 |
| Genre | : |
| ISBN | : 9783887225339 |
| Author | : A. Bove |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 1983-04-01 |
| Genre | : Mathematics |
| ISBN | : 9783540122852 |
| Author | : P. A. Davidson |
| Publisher | : Cambridge University Press |
| Total Pages | : 802 |
| Release | : 2016-12-22 |
| Genre | : Science |
| ISBN | : 1316861953 |
Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite.
| Author | : Christian Andreas |
| Publisher | : Forschungszentrum Jülich |
| Total Pages | : 217 |
| Release | : 2014 |
| Genre | : |
| ISBN | : 389336983X |
| Author | : Shuxing Chen |
| Publisher | : World Scientific |
| Total Pages | : 207 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 9814304832 |
The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs). It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation of singularities of solutions to nonlinear equations, singularity index and formation of shocks.
| Author | : Jean Bernard Lasserre |
| Publisher | : Cambridge University Press |
| Total Pages | : 355 |
| Release | : 2015-02-19 |
| Genre | : Mathematics |
| ISBN | : 1316240398 |
This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains how to use relatively recent results from real algebraic geometry to provide a systematic numerical scheme for computing the optimal value and global minimizers. Indeed, among other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided.
