Related papers: Rayleigh and Stoneley Waves in Linear Elasticity
Complex elastic media such as biological membranes, in particular, blood vessels, may be described as fiber-reinforced solids in the framework of nonlinear hyperelasticity. Finite axially symmetric anti-plane shear displacements in such…
A linear theory of whistler wave is developed wihtin the paradigm of a two dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for a small amplitude whistler wave that exhibit magnetic…
We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…
This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. We consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic…
Multitime evolution PDEs for Rayleigh waves are considered, using geometrical ingredients capable to build an ultra-parabolic-hyperbolic differential operator. Their soliton solutions are found based on appropriate hypotheses and specific…
In this work, we experimentally and numerically investigate the propagation and attenuation of vertically polarized surface waves in an unconsolidated granular medium equipped with small-scale metabarriers of different depths, i.e., arrays…
In this paper the small-amplitude motion of multiple superposed viscous fluids is studied as a linearized initial-value problem. The analysis results in a closed set of equations for the Laplace transformed amplitudes of the interfaces that…
Linearly polarized elastic waves propagating in a linear path have been extensively explored in numerous applications from biomedical imaging to structural health monitoring. However, elastic waves propagating in a circularly polarized…
In this short note, we prove a refinement of bilinear local smoothing estimate to Airy solutions, when the frequency support of two wave are separated. As an application we prove a smoothing property of a bilinear form.
Evolved late-type stars are frequently identified as photometric and spectroscopic variables, such as Mira-type or semi-regular variable objects. These stars can also be polarimetrically variable, an indicator of non-spherical geometry for…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
We consider in a simple and general way elastic waves in isotropic and anisotropic media, their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. Reflection of quasi transverse waves in anisotropic…
We study the interaction between gravitational waves and elastic bodies within the framework of relativistic elasticity. Starting from the Lagrangian formulation of relativistic elasticity, we derive the linearized equations governing the…
We derive sharp decay estimates and prove holomorphic extensions for the solutions of a class of semilinear nonlocal elliptic equations with linear part given by a sum of Fourier multipliers with finitely smooth symbols at the origin.…
Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…
In this paper we study the reflective properties of a 2D interface separating a homogeneous solid from a band-gap metamaterial by modeling it as an interface between a classical Cauchy continuum and a relaxed micromorphic medium. We show…
We study the motion of an interface between two irrotational, incompressible fluids, with elastic bending forces present; this is the hydroelastic wave problem. We prove a global bifurcation theorem for the existence of families of…
We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.
Mathematical ambiguities in partial-wave analysis present a significant challenge to the extraction of resonance properties in hadronic reactions. Recent work has shown that while linear photon polarization can resolve continuous…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…