Related papers: Local gaps in three-dimensional periodic media
We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the…
We consider acoustic wave propagation through a periodic array of the inclusions of arbitrary shape. The inclusion size is much smaller than the array period while the wavelength is fixed. We derive and rigorously justify the dispersion…
We study acoustic propagation in one dimensional water ducts containing many air-filled blocks. The acoustic band structures for the periodic arrangements of the blocks is calculated, whereas the transmission for various random…
We consider the linear water-wave problem in a periodic channel which consists of infinitely many identical containers connected with apertures of width $\epsilon$. Motivated by applications to surface wave propagation phenomena, we study…
We study the propagation of one-dimentional optical beams in a weakly nonlocal medium exhibiting cubic-quintic nonlinearity. A nonlinear equation governing the evolution of the beam intensity in the nonlocal medium is derived thereby which…
We investigate the behavior of waves in a periodic medium containing small soft inclusions or cavities of arbitrary shape, such that the homogeneous Dirichlet conditions are satisfied at the boundary. The leading terms of Bloch waves, their…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the…
We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the…
We rigorously calculate the propagation and scattering of electromagnetic waves by rectangular and random arrays of dielectric cylinders in a uniform medium. For regular arrays, the band structures are computed and complete bandgaps are…
We consider $k$ intervals on the real line whose images under a continuous map $f$ contain themselves. It's conjectured that there exists a periodic point of period not bigger than $k$ in these intervals. We prove the conjecture for $k=5$…
In this paper, we prove global regularity, scattering, and the non-existence of small traveling waves for the $3D$ finite depth capillary waves system for small initial data. The non-existence of small traveling waves shows a fundamental…
It is found that there exist composite media that exhibit strong spatial dispersion even in the very large wavelength limit. This follows from the study of lattices of ideally conducting parallel thin wires (wire media). In fact, our…
In this paper, the phenomenon of band gaps and Anderson localization of water waves over one-dimensional periodic and random bottoms is investigated by the transfer matrix method. The results indicate that the range of localization in…
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 is dedicated to the study of a one-dimensional congestion model, consisting of two different phases. In the congested phase, the pressure is free and the dynamics is incompressible, whereas in the non-congested phase, the fluid…
The present paper deals with the wave propagation in a particular two dimensional structure, obtained from a localized perturbation of a reference periodic medium. This reference medium is a ladder like domain, namely a thin periodic…
This paper is devoted to existence and non-existence results for generalized tran-sition waves solutions of space-time heterogeneous Fisher-KPP equations. When the coefficients of the equation are periodic in space but otherwise depend in a…
We prove global in time dispersion for the wave and the Klein-Gordon equation inside the Friedlander domain by taking full advantage of the space-time localization of caustics and a precise estimate of the number of waves that may cross at…
We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the…
Our interest itself of this paper is strongly inspired from an open problem in the paper [1] published by D'Abbicco. In this article, we would like to study the Cauchy problem for a weakly coupled system of semi-linear structurally damped…