Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics

Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics
Title Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics PDF eBook
Author Ferruccio Colombini
Publisher Springer
Pages 313
Release 2017-04-25
Genre Mathematics
ISBN 3319520423

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The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields.

Singularities in Fluids, Plasmas and Optics

Singularities in Fluids, Plasmas and Optics
Title Singularities in Fluids, Plasmas and Optics PDF eBook
Author Russel Caflisch
Publisher Springer
Pages 348
Release
Genre Mathematics
ISBN 9789401120234

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Singularities in Fluids, Plasmas and Optics, which contains the proceedings of a NATO Workshop held in Heraklion, Greece, in July 1992, provides a survey of the state of the art in the analysis and computation of singularities in physical problems drawn from fluid mechanics, plasma physics and nonlinear optics. The singularities include curvature singularities on fluid interfaces, the onset of turbulence in 3-D inviscid flows, focusing singularities for laser beams, and magnetic reconnection. The highlights of the book include the nonlinear Schrödinger equation for describing laser beam focusing, the method of complex variables for the analysis and computation of singularities on fluid interfaces, and studies of singularities for the 3-D Euler equations. The book is suitable for graduate students and researchers in these areas.

Geometric Optics for Surface Waves in Nonlinear Elasticity

Geometric Optics for Surface Waves in Nonlinear Elasticity
Title Geometric Optics for Surface Waves in Nonlinear Elasticity PDF eBook
Author Jean-François Coulombel
Publisher American Mathematical Soc.
Pages 143
Release 2020-04-03
Genre Education
ISBN 1470440377

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This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as “the amplitude equation”, is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions uε to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength ε, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to uε on a time interval independent of ε. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.

Applied Mechanics Reviews

Applied Mechanics Reviews
Title Applied Mechanics Reviews PDF eBook
Author
Publisher
Pages 284
Release 1970
Genre Mechanics, Applied
ISBN

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Singularities and Oscillations

Singularities and Oscillations
Title Singularities and Oscillations PDF eBook
Author Jeffrey Rauch
Publisher Springer Science & Business Media
Pages 161
Release 2012-12-06
Genre Science
ISBN 1461219728

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This volume contains a multiplicity of approaches brought to bear on problems varying from the formation of caustics and the propagation of waves at a boundary, to the examination of viscous boundary layers. It examines the foundations of the theory of high- frequency electromagnetic waves in a dielectric or semiconducting medium. Nor are unifying themes entirely absent from nonlinear analysis: one chapter considers microlocal analysis, including paradifferential operator calculus, on Morrey spaces, and connections with various classes of partial differential equations.

Oscillations and Waves

Oscillations and Waves
Title Oscillations and Waves PDF eBook
Author M.I Rabinovich
Publisher Springer Science & Business Media
Pages 586
Release 2012-12-06
Genre Mathematics
ISBN 9400910339

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'Et mai - ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y semis point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost sheJf next to the dusty canister Iabclled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Self-Exciting Fluid Dynamos

Self-Exciting Fluid Dynamos
Title Self-Exciting Fluid Dynamos PDF eBook
Author Keith Moffatt
Publisher Cambridge University Press
Pages 539
Release 2019-04-25
Genre Mathematics
ISBN 1107065879

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Treats the origin of magnetic fields in planets, stars and galaxies, and the manner of their evolution over time.