Related papers: Diffraction of Elastic Waves by Edges
We consider the localization of elastic waves in thin elastic structures with spatially varying curvature profiles, using a curved rod and a singly curved shell as concrete examples. Previous studies on related problems have broadly focused…
We consider the non-monotone degenerate diffusion equation with time delay. Different from the linear diffusion equation, the degenerate equation allows for semi-compactly supported traveling waves. In particular, we discover…
The action functional for a linear elastic medium with dislocations is given. The equations of motion following from this action reproduce the Peach-K\"{o}hler and Lorentzian forces experienced by dislocations. The explicit expressions for…
Surface waves on liquids act as a dynamical phase grating for incident light. In this article, we revisit the classical method of probing such waves (wavelengths of the order of mm) as well as inherent properties of liquids and liquid films…
Particles such as microplastics and phytoplankton suspended in the water column in the natural environment are often subject to the action of surface gravity waves. By modelling such anisotropic particles as small spheroids that slowly…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…
We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order…
In this work we further advance theoretical investigation of radiation by the electric dipole under the assumption that wavelength is much smaller than charge separation distance of an electric dipole, which in turn is much smaller than a…
We prove a dispersive estimate for the solutions of the linearized Water-Waves equations in dimension 1 in presence of a flat bottom. We prove a decay with respect to time t of order 1/3 for solutions with initial data in weighted Sobolev…
We introduce a numerical strategy to study the evolution of 2D water waves in the presence of a plunging jet. The free-surface Navier-Stokes solution is obtained with a finite but small viscosity. We observe the formation of a surface…
This paper presents a comprehensive analysis of two-dimensional water waves characterized by a significant adverse constant vorticity over flows without stagnation points. Surprisingly, we discover qualitative distinctions between this…
We establish a decoupling result for the $P$ and $S$ waves of linear, isotropic elasticity, in the setting of twice-differentiable Lam\'e parameters. Precisely, we show that the $P\leftrightarrow S$ components of the wave propagation…
We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the…
In the context of elastic wave propagation in damaged solids, an analytical approach for scattering of antiplane waves by two-dimensional periodic arrays of cracks is developed. Before considering the study of arrays of cracks, the…
A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine…
We propose wave and ray approaches for modelling mid- and high- frequency structural vibrations through smoothed joints on thin shell cylindrical ridges. The models both emerge from a simplified classical shell theory setting. The ray model…
Recent advances in electron microscopy allowed the generation of high-energy electron wave packets of ultrashort duration. Here we present a non-perturbative S-matrix theory for scattering of ultrashort electron wave packets by atomic…
In this work, we are concerned with the inverse scattering by interfaces for the linearized and isotropic elastic model at a fixed frequency. First, we derive complex geometrical optic solutions with linear or spherical phases having a…
This study investigates the interaction of a shock wave with a fixed layer of particles in cylindrical geometries using particle-resolved large eddy simulations. The curvature radius of the particle layer is varied and the resulting flow…
We investigate the reflection and refraction behaviors of electromagnetic waves at the interface between an isotropic material and the anisotropic medium with a unique dispersion relation. We show that the refraction angle of whether phase…