Related papers: Spectral gaps in a double-periodic perforated Neum…
We will study the spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder with contains periodic arrangement of inclusions. On the boundary of the waveguide we…
We study the spectral linear elasticity problem in an unbounded periodic waveguide, which consists of a sequence of identical bounded cells connected by thin ligaments of diameter of order $ h >0$. The essential spectrum of the problem is…
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…
At the example of two coupled waveguides we construct a periodic second order differential operator acting in a Euclidean domain and having spectral gaps whose edges are attained strictly inside the Brillouin zone. The waveguides are…
In this paper, we provide uniform bounds for convergence rates of the low frequencies of a parametric family of problems for the Laplace operator posed on a rectangular perforated domain of the plane of height $H$. The perforations are…
In this note we investigate spectral properties of a periodic waveguide $\Omega^\varepsilon$ ($\varepsilon$ is a small parameter) obtained from a straight strip by attaching an array of $\varepsilon$-periodically distributed identical…
It is proved that small periodic singular perturbation of a cylindrical waveguide surface may open a gap in the continuous spectrum of the Dirichlet problem for the Laplace operator. If the perturbation period is long and the caverns in the…
We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. For a given number $N$ we construct periodic (i.e. covering) manifolds such that the essential spectrum of the corresponding…
In this paper we investigate via an asymptotic method the opening of gaps in the spectrum of a stiff problem for the Laplace operator $-\Delta$ in $\mathbb{R}^2$ perforated by contiguous circular holes. The density and the stiffness…
We consider Laplacians on periodic metric graphs with unit-length edges. The spectrum of these operators consists of an absolutely continuous part (which is a union of an infinite number of non-degenerated spectral bands) plus an infinite…
We investigate spectral properties of the Neumann Laplacian $\mathscr{A}_\varepsilon$ on a periodic unbounded domain $\Omega_\varepsilon$ depending on a small parameter $\varepsilon>0$. The domain $\Omega_\varepsilon$ is obtained by…
The spectral problem on a periodic domain with cracks is studied. An asymptotic form of dispersion relations is calculated under assumption that the opening of the cracks is small.
The article deals with a convergence of the spectrum of the Neumann Laplacian in a periodic unbounded domain $\Omega^\varepsilon$ depending on a small parameter $\varepsilon>0$. The domain has the form…
We consider spectral problems for Laplace operator in 3D rod structures with a small cross section of diameter $O(\varepsilon)$, $\varepsilon$ being a positive parameter. The boundary conditions are Dirichlet (Neumann, respectively) on the…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
We study the Neumann Laplacian $-\Delta^N$ restricted to a periodic waveguide. In this situation its spectrum $\sigma(-\Delta^N)$ presents a band structure. Our goal and strategy is to get spectral information from an analysis of the…
We investigate the band-gap structure of the frequency spectrum for elastic waves in a high-contrast, two-component periodic elastic medium. We consider two-dimensional phononic crystals consisting of a background medium which is perforated…
We consider a periodic strip in the plane and the associated quantum waveguide with Dirichlet boundary conditions. We analyse finite segments of the waveguide consisting of $L$ periodicity cells, equipped with periodic boundary conditions…
This paper studies the size of the minimal gap between any two consecutive eigenvalues in the Dirichlet and in the Neumann spectrum of the standard Laplace operator on the Sierpinski gasket. The main result shows the remarkable fact that…
We analyze a family of singular Schr\"odinger operators describing a Neumann waveguide with a periodic array of singular traps of a $\delta'$ type. We show that in the limit when perpendicular size of the guide tends to zero and the…