Singularities: Formation, Structure, and Propagation PDF Download
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Author: J. Eggers
Publisher: Cambridge University Press
ISBN: 1316352390
Category : Mathematics
Languages : en
Pages : 471
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Book Description
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: J. Eggers
Publisher: Cambridge University Press
ISBN: 1316352390
Category : Mathematics
Languages : en
Pages : 471
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Book Description
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: Christian Andreas
Publisher: Forschungszentrum Jülich
ISBN: 389336983X
Category :
Languages : en
Pages : 217
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Book Description
Author: Shuxing Chen
Publisher: World Scientific
ISBN: 9814304832
Category : Mathematics
Languages : en
Pages : 207
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Book Description
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: P. A. Davidson
Publisher: Cambridge University Press
ISBN: 1316861953
Category : Science
Languages : en
Pages : 802
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Book Description
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: Kaoru Yamanouchi
Publisher: Springer
ISBN: 3319524313
Category : Science
Languages : en
Pages : 278
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Book Description
This book features chapters based on lectures presented by world-leading researchers of photon science from Russia and Japan at the first “STEPS Symposium on Photon Science” held in Tokyo in March 2015. It describes recent progress in the field of photon science, covering a wide range of interest to experts in the field, including laser-plasma interaction, filamentation and its applications, laser assisted electron scattering, exotic properties of light, ultrafast imaging, molecules and clusters in intense laser fields, photochemistry and spectroscopy of novel materials, laser-assisted material synthesis, and photon technology.
Author: Gadi Fibich
Publisher: Springer
ISBN: 3319127489
Category : Mathematics
Languages : en
Pages : 870
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Book Description
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. “This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.” Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France
Author: Eileen Otte
Publisher: Springer Nature
ISBN: 3030637158
Category : Science
Languages : en
Pages : 184
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Book Description
Structured singular light is an ubiquitous phenomenon. It is not only created when light refracts at a water surface but can also be found in the blue daytime sky. Such light fields include a spatially varying amplitude, phase, or polarization, enabling the occurrence of optical singularities. As structurally stable units of the light field, these singularities are particularly interesting since they determine its topology. In this excellent book, the author presents a pioneering study of structured singular light, thereby contributing many original approaches. Especially in the field of polarization and its rich number of different types of singularities the book defines and drives a completely new field. The work demonstrates how to control complex polarization singularity networks and their propagation. Additionally, the author pioneers tightly focusing vectorial beams, also developing an urgently needed detection scheme for three-dimensional nanoscale polarization structures. She also studies classical spatial entanglement using structured light, introducing entanglement beating and paraxial spin-orbit-coupling. The book is hallmarked by its comprehensive and thorough way of describing a plethora of different approaches to structure light by amplitude, phase and polarization, as well as the important role of optical singularities.
Author: Jean Bernard Lasserre
Publisher: Cambridge University Press
ISBN: 1316240398
Category : Mathematics
Languages : en
Pages : 355
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Book Description
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.
Author: Mark J. Ablowitz
Publisher: Cambridge University Press
ISBN: 110883261X
Category : Mathematics
Languages : en
Pages : 421
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Book Description
An introduction to complex variables that caters for undergraduate students in applied mathematics, science, and engineering.
Author: Michael D. Graham
Publisher: Cambridge University Press
ISBN: 1107024641
Category : Mathematics
Languages : en
Pages : 281
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Book Description
Provides a foundation for understanding complex fluids by integrating fluid dynamics, statistical physics, and polymer and colloid science.
