Related papers: The discrete Lamb problem: Elastic lattice waves i…
In this article, we report on an exact closed-form solution for the displacement in an elastic homogeneous half-space elicited by a downward vertical point source moving with constant velocity over the surface of the medium. The problem…
Recently, Murthy et al. [2017] and Escande et al. [2020] adopted the Lattice Boltzmann Method (LBM) to model the linear elastodynamic behaviour of isotropic solids. The LBM is attractive as an elastodynamic solver because it can be…
Under periodic boundary conditions, a one-dimensional dispersive medium driven by a Lamb oscillator exhibits a smooth response when the dispersion relation is asymptotically linear or superlinear at large wave numbers, but unusual fractal…
Quantum computers are ideally set up to solve linear systems which are of a form similar to the Schrodinger/Dirac equation of quantum mechanics. In the framework of linear response theory, the propagation and scattering of electromagnetic…
A periodically-uneven (in one horizontal direction) stress-free boundary covering a linear, isotropic, homogeneous, lossless solid half space is submitted to a vertically-propagating shear-horizontal plane, body wave. The rigorous theory of…
In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to compute; we consider the canonical example…
Elastic wave propagation is a century-old problem. Unlike on a flat manifold, analytical solution is not well established for a curved manifold. In this study we take a step towards building an analytical framework for solving the elastic…
The problem of the lattice diffusion of two particles coupled by a contact repulsive interaction is solved by finding analytical expressions of the two-body probability characteristic function. The interaction induces anomalous drift with a…
The study of the scattering of electromagnetic waves by a linear isotropic medium with planar symmetry can be reduced to that of their TE and TM modes. For situations where the medium consists of parallel homogeneous slabs, one may use the…
We consider long longitudinal bulk strain waves in layered waveguides using Boussinesq-type equations. The equations are developed using lattice models, and this is viewed as an extension of the Fermi-Pasta-Ulam problem. We describe…
The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…
Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are…
Within the lattice dynamics formulation, we present an exact solution for anti-plane surface waves in a square lattice strip with a surface row of material particles of two types separated by a linear interface. The considered problem is a…
We consider a simple two-dimemsional harmonic lattice with random, independent and identically distributed masses. Using the methods of stochastic homogenization, we show that solutions with long wave initial data converge in an appropriate…
Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in an open space filled with a homogeneous medium. This paper concerns the mathematical analysis of the coupled two- and three-dimensional…
Simulating the propagation of elastic waves in multi-layered media has many applications. A common approach is to use matrix methods where the elastic wave-field within each material layer is represented by a sum of partial-waves along with…
A one-dimensional wave propagation through elastically asymmetric media is investigated. A class of metamaterials possessing an arbitrary elastic asymmetry is proposed. This asymmetry results in different wave speeds of tensile and…
We investigate thin-slit diffraction problems for two-dimensional lattice waves. The peculiar structure allows us to consider the problems on the semi-infinite triangular lattice, consequently, we study Dirichlet problems for the…
A method is proposed for the analysis of the propagation of electromagnetic waves through a homogeneous slab of a medium with Drude-Lorentz dispersion behavior, and excited by a causal sinusoidal source. An expression of the time dependent…
The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the…