Geometric Optics for Surface Waves in Nonlinear Elasticity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Optics for Surface Waves in Nonlinear Elasticity write by Jean-François Coulombel. This book was released on 2020-04-03. Geometric Optics for Surface Waves in Nonlinear Elasticity available 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.
Filtrations and Buildings
Filtrations and Buildings - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Filtrations and Buildings write by Christophe Cornut. This book was released on 2020-09-28. Filtrations and Buildings available in PDF, EPUB and Kindle. The author constructs and studies a scheme theoretical version of the Tits vectorial building, relates it to filtrations on fiber functors, and uses them to clarify various constructions pertaining to affine Bruhat-Tits buildings, for which he also provides a Tannakian description.
Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics
Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics write by Ferruccio Colombini. This book was released on 2017-04-25. Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics available 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.
Current Progress in Hyperbolic Systems: Riemann Problems and Computations
Current Progress in Hyperbolic Systems: Riemann Problems and Computations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Current Progress in Hyperbolic Systems: Riemann Problems and Computations write by W. Brent Lindquist. This book was released on 1989. Current Progress in Hyperbolic Systems: Riemann Problems and Computations available in PDF, EPUB and Kindle. Contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Current Progress in Hyperbolic Systems: Riemann Problems and Computations, held at Bowdoin College in July 1988.
Nonlinear Elastic Waves in Materials
Nonlinear Elastic Waves in Materials - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Elastic Waves in Materials write by Jeremiah J. Rushchitsky. This book was released on 2014-04-23. Nonlinear Elastic Waves in Materials available in PDF, EPUB and Kindle. The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professionally interesting in waves. But mechanics is understood in the broad sense, when it includes mechanical and other engineering, material science, applied mathematics and physics and so forth. The genesis of this book can be found in author’s years of research and teaching while a head of department at SP Timoshenko Institute of Mechanics (National Academy of Sciences of Ukraine), a member of Center for Micro and Nanomechanics at Engineering School of University of Aberdeen (Scotland) and a professor at Physical-Mathematical Faculty of National Technical University of Ukraine “KPI”. The book comprises 11 chapters. Each chapter is complemented by exercises, which can be used for the next development of the theory of nonlinear waves.
