相关论文: Whispering gallery modes for a transmission proble…

We present a fully three-dimensional theoretical study of the extraordinary transmission of light through subwavelength hole arrays in optically thick metal films. Good agreement is obtained with experimental data. An analytical minimal…

The Laplace operator is considered for waveguides perturbed by a periodic structure consisting of N congruent obstacles spanning the waveguide. Neumann boundary conditions are imposed on the periodic structure, and either Neumann or…

We observe that the Laplacian of a random graph G on N vertices represents and explicitly solvable model in the limit of infinitely increasing N. Namely, we derive recurrent relations for the limiting averaged moments of the adjacency…

A general class of wireless relay networks with a single source-destination pair is considered. Intermediate nodes in the network employ an amplify-and-forward scheme to relay their input signals. In this case the overall input-output…

We consider the problem of the numerical approximation of the linear controllability of waves. All our experiments are done in a bounded domain \Omega of the plane, with Dirichlet boundary conditions and internal control. We use a Galerkin…

We study whispering gallery modes in triple microdisks of equilateral and isosceles triangular configurations. The characteristic properties of resonant modes in three microdisks on vertices of an equilateral triangle are explained by…

The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is…

In this paper we demonstrate that using a mathematical physics approach (focusing the attention to the physics and using mathematics as a tool) it is possible to visualize the formation of the transverse modes inside a cylindrical…

Sensors based on whispering gallery mode resonators can detect single nanoparticles and even single molecules. Particles attaching to the resonator induce a doublet in the transmission spectrum which provides a self-referenced detection…

A random surface scattering in a one-mode waveguide is studied in the case when the surface profile has long-range correlations along the waveguide. Analytical treatment of this problem shows that with a proper choice of the surface, one…

We investigate the scattering of elastic waves off a disordered region described by a one-dimensional random-phase sine-Gordon model. The collective pinning results in an effective static disorder potential with universal and non-Gaussian…

This paper investigates the inverse source problem with a single propagating mode at multiple frequencies in an acoustic waveguide. The goal is to provide both theoretical justifications and efficient algorithms for imaging extended sources…

We theoretically study the propagation of sound waves in GaAs/AlAs superlattices focussing on periodic modes in the vicinity of the band gaps. Based on analytical and numerical calculations, we show that these modes are the product of a…

We consider a generalization of the diffusion equation on graphs. This generalized diffusion equation gives rise to both normal and superdiffusive processes on infinite one-dimensional graphs. The generalization is based on the $k$-path…

We predict and study theoretically a new nonlinear electromagnetic phenomenon in a sample of layered superconductor of finite length placed in a waveguide with ideal walls. Two geometries are considered here: when the superconducting layers…

All metamaterial applications are based upon the idea that extreme material properties can be achieved through appropriate dynamic homogenization of composites. This homogenization is almost always done for infinite domains and the results…

Discontinuity of dielectric constants at the interface is a common feature of all nanostructures and semiconductor heterostructures. Near such interfaces, a charged particle creates a singular self-interaction potential which may be…

This work addresses the Galerkin isogeometric discretization of the one-dimensional Laplace eigenvalue problem subject to homogeneous Dirichlet boundary conditions on a bounded interval. We employ GLT theory to analyze the behavior of the…

The inherent coupling of optical and mechanical modes in high finesse optical microresonators provide a natural, highly sensitive transduction mechanism for micromechanical vibrations. Using homodyne and polarization spectroscopy…

The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a ``transmission`` system. A transmission system is a mathematical representation of a means of transmitting…