Geometric Optics For Surface Waves In Nonlinear Elasticity

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Geometric Optics For Surface Waves In Nonlinear Elasticity

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Author : Jean-François Coulombel
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-04-03

Geometric Optics For Surface Waves In Nonlinear Elasticity written by Jean-François Coulombel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Education categories.

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

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Author : Ferruccio Colombini
language : en
Publisher: Springer
Release Date : 2017-04-25

Shocks Singularities And Oscillations In Nonlinear Optics And Fluid Mechanics written by Ferruccio Colombini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-25 with Mathematics categories.

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.

Degree Theory Of Immersed Hypersurfaces

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Author : Harold Rosenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Degree Theory Of Immersed Hypersurfaces written by Harold Rosenberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.

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.

Localization For Thh Ku And The Topological Hochschild And Cyclic Homology Of Waldhausen Categories

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Author : Andrew J. Blumberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Localization For Thh Ku And The Topological Hochschild And Cyclic Homology Of Waldhausen Categories written by Andrew J. Blumberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.

The authors resolve the longstanding confusion about localization sequences in $THH$ and $TC$ and establish a specialized devissage theorem.

Conformal Graph Directed Markov Systems On Carnot Groups

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Author : Vasileios Chousionis
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Conformal Graph Directed Markov Systems On Carnot Groups written by Vasileios Chousionis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.

The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.

Affine Flag Varieties And Quantum Symmetric Pairs

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Author : Zhaobing Fan
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Affine Flag Varieties And Quantum Symmetric Pairs written by Zhaobing Fan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.

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 $A$.

Explicit Arithmetic Of Jacobians Of Generalized Legendre Curves Over Global Function Fields

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Author : Lisa Berger
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Explicit Arithmetic Of Jacobians Of Generalized Legendre Curves Over Global Function Fields written by Lisa Berger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.

The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $mathbb F_p(t)$, when $p$ is prime and $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.

The Mother Body Phase Transition In The Normal Matrix Model

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Author : Pavel M. Bleher
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

The Mother Body Phase Transition In The Normal Matrix Model written by Pavel M. Bleher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.

In this present paper, the authors consider the normal matrix model with cubic plus linear potential.

Dynamics Near The Subcritical Transition Of The 3d Couette Flow I Below Threshold Case

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Author : Jacob Bedrossian
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Dynamics Near The Subcritical Transition Of The 3d Couette Flow I Below Threshold Case written by Jacob Bedrossian and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.

The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.

Global Smooth Solutions For The Inviscid Sqg Equation

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Author : Angel Castro
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Global Smooth Solutions For The Inviscid Sqg Equation written by Angel Castro and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.

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.