Geometric Optics For Surface Waves In Nonlinear Elasticity
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Geometric Optics for Surface Waves in Nonlinear Elasticity
Author | : Jean-François Coulombel,Mark Williams |
Publsiher | : American Mathematical Soc. |
Total Pages | : 143 |
Release | : 2020-04-03 |
Genre | : Education |
ISBN | : 9781470440374 |
Download Geometric Optics for Surface Waves in Nonlinear Elasticity Book in PDF, Epub and Kindle
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.
Shocks Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics
Author | : Ferruccio Colombini,Daniele Del Santo,David Lannes |
Publsiher | : Springer |
Total Pages | : 308 |
Release | : 2017-04-25 |
Genre | : Mathematics |
ISBN | : 9783319520421 |
Download Shocks Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics Book in PDF, Epub and Kindle
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.
The Mother Body Phase Transition in the Normal Matrix Model
Author | : Pavel M. Bleher,Guilherme L. F. Silva |
Publsiher | : American Mathematical Soc. |
Total Pages | : 144 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470441845 |
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In this present paper, the authors consider the normal matrix model with cubic plus linear potential.
Affine Flag Varieties and Quantum Symmetric Pairs
Author | : Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang |
Publsiher | : American Mathematical Soc. |
Total Pages | : 123 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470441753 |
Download Affine Flag Varieties and Quantum Symmetric Pairs Book in PDF, Epub and Kindle
The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.
Degree Theory of Immersed Hypersurfaces
Author | : Harold Rosenberg,Graham Smith |
Publsiher | : American Mathematical Soc. |
Total Pages | : 62 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470441852 |
Download Degree Theory of Immersed Hypersurfaces Book in PDF, Epub and Kindle
The authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function.
Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees
Author | : Rodney G. Downey,Keng Meng Ng,Reed Solomon |
Publsiher | : American Mathematical Soc. |
Total Pages | : 90 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470441623 |
Download Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees Book in PDF, Epub and Kindle
First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.
Localization for THH ku and the Topological Hochschild and Cyclic Homology of Waldhausen Categories
Author | : Andrew J. Blumberg,Michael A. Mandell |
Publsiher | : American Mathematical Soc. |
Total Pages | : 100 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470441784 |
Download Localization for THH ku and the Topological Hochschild and Cyclic Homology of Waldhausen Categories Book in PDF, Epub and Kindle
The authors resolve the longstanding confusion about localization sequences in $THH$ and $TC$ and establish a specialized devissage theorem.
Global Smooth Solutions for the Inviscid SQG Equation
Author | : Angel Castro,Diego Cordoba,Javier Gomez-Serrano |
Publsiher | : American Mathematical Soc. |
Total Pages | : 89 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470442149 |
Download Global Smooth Solutions for the Inviscid SQG Equation Book in PDF, Epub and Kindle
In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.