Related papers: On Resonant Waves in Lattices
Semiconductor superlattices may display dispersions that are degenerate either at the zone center or zone boundary. We show that they are linear upon the wave-vector in the vicinity of the crossing point. This establishes a realisation of…
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…
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…
The resonance modes and the related effects to the transmission of elastic waves in a two dimensional phononic crystal formed by periodic arrangements of a two blocks unit cell in one direction are studied. The unit cell consists of two…
Linear wave equations on Hamiltonian lattices with translational invariance are characterized by an eigenvalue band structure in reciprocal space. Flat band lattices have at least one of the bands completely dispersionless. Such bands are…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
The paper presents new results on localisation and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, surface waves are identified and studied at the interface…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
We study the optical response of a 2D square lattice of atoms using classical electrodynamics. Due to dipole-dipole interactions, the lattice atoms polarize as if the lattice were an atom with up to three resonance frequencies, with…
We study 4 problems in the area of scattering of time harmonic acoustic or electromagnetic waves by unbounded rough surfaces/inhomogeneous layers. Specifically we study: i) a boundary value problem (BVP) for the Helmholtz equation, in both…
We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with 2 commensurate frequencies. The spatio-temporal behavior of 4 qualitatively different types of superlattice…
We discuss an idea whether spherical blast waves can amplify by a non-local resonant hydrodynamic mechanism inhomogeneities formed by turbulence or phase segregation in the interstellar medium. We consider the problem of a…
In rotating stars and planets, excitation of inertial waves in convective envelopes provides an important channel for tidal dissipation, but the dissipation rate due to inertial waves depends erratically on the tidal frequency. Tidal…
Robustly manipulating waves on subwavelength scales can be achieved by, firstly, designing a structure with a subwavelength band gap and, secondly, introducing a defect so that eigenfrequencies fall within the band gap. Such frequencies are…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…
The paper deals with the generic problem of two waveguides coupled by perforations, which can be perforated tube mufflers without or with partitions, possibly with absorbing materials. Other examples are ducts with branched resonators of…
Solitons in the fractional space, supported by lattice potentials, have recently attracted much interest. We consider the limit of deep one- and two-dimensional (1D and 2D) lattices in this system, featuring finite bandgaps separated by…
Starting from the wave equation for a medium with material properties that vary periodically, we study a system of recurrence relations that describe propagation of wave packets that oscillate on the microscale (i.e. on lengths of the order…