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In the present contribution we investigate some features of dynamical lattice systems near periodic traveling waves. First, following the formal averaging method of Whitham, we derive modulation systems expected to drive at main order the…
We investigate elastic periodic structures characterized by topologically nontrivial bandgaps supporting backscattering suppressed edge waves. These edge waves are topologically protected and are obtained by breaking inversion symmetry…
The two-dimensional propagation of small-amplitude waves through an infinite periodic array of freely-floating rectangular floes is considered under the assumptions of inviscid linearised wave theory. Fluid gaps between adjacent floes allow…
This paper concerns the existence of generalized solitary waves (solitary waves with small ripples at infinity) for a diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. It is proved that the FPUT lattice problem has a generalized…
Plasmonic lattices consisting of nanoparticles in a homogeneous environment are well known fortheir support of so-called lattice plasmon resonances. They are associated with localized surfaceplasmons coupled to each other via free…
Bloch wavefunctions are used to derive dispersion relations for water wave propagation in the presence of an infinite array of periodically arranged surface scatterers. For one dimensional periodicity (stripes), band gaps for wavevectors in…
This article delves into the intricate dynamics of Rayleigh wave propagation within a nonlocal orthotropic medium, where the presence of void and diffusion adds an intriguing layer to the analysis. Grounded in Eringen nonlocal elasticity…
For general anisotropic linear elastic solids with smooth boundaries, Rayleigh-type surface waves are studied. Using spectral factorizations of matrix polynomials, a self-contained exposition of the case of a homogeneous half-space is given…
The physical processes taking place at the surface and near the surface of solids is so rich and versatile that sometimes they seem to be the inexhaustible subject of fundamental research. In particular, since the discovery by Lord Rayleigh…
A periodic assembly of acoustically-rigid blocks (termed 'grating'), situated between two half spaces occupied by fluid-like media, lends itself to a rigorous theoretical analysis of its response to an acoustic homogeneous plane wave. This…
We present a comprehensive analysis of wavenumber resonances or leaky modes associated with the Rayleigh operator in a half space containing a heterogeneous slab, being motivated by seismology. To this end, we introduce Jost solutions on an…
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions:…
The study of wave propagation outside bounded obstacles uncovers the existence of resonances for the Laplace operator, which are complex-valued generalized eigenvalues, relevant to estimate the long time asymptotics of the wave. In order to…
In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…
We report on the observation of emerging beam resonances, well known as Rayleigh-Wood anomalies and threshold resonances in photon and electron diffraction, respectively, in an atom-optical diffraction experiment. Diffraction of He atom…
Motivated by research in metamaterials, we consider the challenging problem of acoustic wave scattering by a doubly periodic quadrant of sound-soft scatterers arranged in a square formation, which we have dubbed the quarter lattice. This…
This work focuses on the interaction of an acoustical quasi-Gaussian beam centered on a rigid immovable sphere, during which at least three physical phenomena arise, namely, the (axial) acoustic scattering, the instantaneous force, and the…
The standard Bloch oscillation normally refers to the oscillatory tunneling dynamics of quantum particles in a periodic lattice plus a linear gradient. In this work we theoretically investigate the generalized form of the Bloch oscillation…
We consider wave propagation across an infinite waveguide of an arbitrary bounded cross-section, whose interior is blocked by two identical thick barriers with holes. When the holes are small, the waves over a broad range of frequencies are…
This work presents a mathematical theory for electromagnetic scattering resonances in a subwavelength annular hole embedded in a metallic slab, with the annulus width $h\ll1$. The model is representative among many 3D subwavelength hole…