Related papers: On Resonant Waves in Lattices
This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lam\'{e} parameters and density. Our contributions are fourfold. First, we construct an…
We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices of point masses connected by Voigt elements, under an antiplane concentrated loading. The emphasis is on obtaining analytical estimates for…
We consider a lattice equation modelling one-dimensional metamaterials formed by a discrete array of nonlinear resonators. We focus on periodic travelling waves due to the presence of a periodic force. The existence and uniqueness results…
Our goal is to study statistical properies of "dielectric resonances" which are poles of conductance of a large random $LC$ network. Such poles are a particular example of eigenvalues $\lambda_n$ of matrix pencils ${\bf H}-\lambda {\bf W}$,…
We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the…
This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout the…
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of…
Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…
The electromagnetic modes and the resonances of homogeneous, finite size, two-dimensional bodies are examined in the frequency domain by a rigorous full wave approach based on an integro-differential formulation of the electromagnetic…
Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…
We study free surface water waves in a 2-D symmetric triangular channel with sides that have a 45o slope. We develop models for small amplitude nonlinear waves, extending earlier studies that have considered the linearized problem. We see…
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the…
We show a novel kind of nonlinear waves in two-dimensional photonic lattices. This waves take the form of light clusters that may fill an arbitrary number of lattice sites. We have demonstrated by numerical simulations that stable…
The multi-wave exact resonance condition is a fundamental principle for understanding energy transfer in condensed matter systems, yet the dynamical evolution of waves satisfying this condition remains unexplored. Here, we reveal that the…
In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…
Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
The propagation of waves through transmission eigenchannels in complex media is emerging as a new frontier of condensed matter and wave physics. A crucial step towards constructing a complete theory of eigenchannels is to demonstrate their…
We study a simple 2-d model representing two fields with different mass and a 3-point coupling term. The phase shift in the resonating 2-particle channel is determined from the energy spectrum obtained in Monte Carlo simulations on finite…