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Related papers: Rayleigh and Stoneley Waves in Linear Elasticity

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Bi-periodic patterns of waves that propagate in the x direction with amplitude variation in the y direction are generated in a laboratory. The amplitude variation in the y direction is studied within the framework of the vector (vNLSE) and…

Fluid Dynamics · Physics 2021-08-19 D. M. Henderson , J. D. Carter , M. E. Catalano

This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the…

Soft Condensed Matter · Physics 2017-09-21 Davide Riccobelli , Pasquale Ciarletta

We establish a connection between the general equations of nonlinear elastodynamics and the nonlinear ordinary differential equation of Pinney [Proc. Amer. Math. Soc. 1 (1950) 681]. As a starting point, we use the exact travelling wave…

Soft Condensed Matter · Physics 2013-02-08 Michel Destrade , Giuseppe Saccomandi

We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…

Analysis of PDEs · Mathematics 2021-01-19 Heinrich Freistühler , Jan Fuhrmann

The propagation of surface acoustic waves in a rotating anisotropic crystal is studied. The crystal is monoclinic and cut along a plane containing the normal to the symmetry plane; this normal is also the axis of rotation. The secular…

Soft Condensed Matter · Physics 2013-04-26 Michel Destrade

We derive a linearized version of the monotonicity method for shape reconstruction using time harmonic elastic waves. The linearized method provides an efficient version of the method, drastically reducing computation time. Here we show…

Analysis of PDEs · Mathematics 2024-10-01 Sarah Eberle-Blick , Valter Pohjola

This study analyzes steady periodic hydroelastic waves propagating on the water surface of finite depth beneath nonlinear elastic membranes. Unlike previous work \cite{BaldiT,BaldiT1,Toland,Toland1}, our formulation accommodates rotational…

Analysis of PDEs · Mathematics 2025-08-07 Yong Zhang

Rayleigh-type surface waves correspond to the characteristic variety, in the elliptic boundary region, of the displacement-to-traction map. In this paper, surface quasimodes are constructed for the reduced elastic wave equation, anisotropic…

Analysis of PDEs · Mathematics 2012-02-13 Sönke Hansen

We show that solutions for a specifically scaled nonlinear wave equation of nonlinear elasticity converge to solutions of a linear Euler-Bernoulli beam system. We construct an approximation of the solution, using a suitable asymptotic…

Analysis of PDEs · Mathematics 2022-07-27 Helmut Abels , Tobias Ameismeier

We consider closed planar curves with fixed length and arbitrary winding number whose elastic energy depends on an additional density variable and a spontaneous curvature. Working with the inclination angle, the associated $L^2$-gradient…

Analysis of PDEs · Mathematics 2024-02-16 Anna Dall'Acqua , Leonie Langer , Fabian Rupp

In this work, we study the nonlinear traveling waves in density stratified fluids with depth varying shear currents. Beginning the formulation of the water-wave problem due to [1], we extend the work of [4] and [18] to examine the interface…

Fluid Dynamics · Physics 2017-08-30 K. L. Oliveras , C. W. Curtis

We investigate the elastic normal modes of two-dimensional media with broken time-reversal and parity symmetries due to a Lorentz term. Our starting point is an elasticity theory that captures the low-energy physics of a diverse range of…

Soft Condensed Matter · Physics 2022-07-27 Filip Marijanović , Sergej Moroz , Bhilahari Jeevanesan

A relativistic analysis of the polarization properties of light elastically scattered by atomic hydrogen is performed, based on the Dirac equation and second order perturbation theory. The relativistic atomic states used for the…

The existence of surface elastic waves at a mechanically free surface of granular phononic crystals is studied. The granular phononic crystals are made of spherical particles distributed periodically on a simple cubic lattice. It is assumed…

Efforts at modelling the propagation of seismic waves in half-spaces with continuously varying properties have been mostly focused on shear-horizontal waves. Here a sagittaly polarized (Rayleigh type) wave travels along a symmetry axis (and…

Geophysics · Physics 2007-11-29 Michel Destrade

Pressure-driven flow of a dilute polymer solution has been numerically observed to possess a form of elastic turbulence which is organised around the interactions of localised versions of 2-dimensional `arrowhead' travelling waves (Page et…

Fluid Dynamics · Physics 2026-04-22 Theo A. Lewy , Rich R. Kerswell

We study stationary points of the bending energy of curves $\gamma\colon[a,b]\to\mathbb{R}^n$ subject to constraints on the arc-length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the…

Differential Geometry · Mathematics 2025-08-05 Oliver Gross , Ulrich Pinkall , Moritz Wahl

Existence and bifurcation results are derived for quasi periodic traveling waves of discrete nonlinear Schrodinger equations with nonlocal interactions and with polynomial type potentials. Variational tools are used. Several concrete…

Pattern Formation and Solitons · Physics 2009-09-11 Michal Feckan , Vassilis Rothos

We introduce Rayleigh functional for nonlinear systems. It is defined using the energy functional and the normalization properties of the variables of variation. The key property of the Rayleigh quotient for linear systems is preserved in…

Pattern Formation and Solitons · Physics 2007-05-23 Valery S. Shchesnovich , Solange B. Cavalcanti

Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of…

Pattern Formation and Solitons · Physics 2011-12-30 Philippe Beltrame , Edgar Knobloch , Peter Hänggi , Uwe Thiele