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In this paper, we investigate the problem of electromagnetic (EM) wave scattering by one and many small perfectly conducting bodies and present a numerical method for solving it. For the case of one body, the problem is solved for a body of…
Based on the known implicit solution for nonlinear plasma waves, an explicit solution was obtained in the form of decomposition into harmonics. The solution obtained exhibits a mechanism for steepening of nonlinear plasma wave as a result…
Variational turbulence is among the few approaches providing rigorous results in turbulence. In addition, it addresses a question of direct practical interest, namely the rate of energy dissipation. Unfortunately, only an upper bound is…
We describe a simple method to experimentally determine the frequency dependencies of the per-unit-length resistance and conductance of transmission lines. The experiment is intended as a supplement to the classic measurement of the…
Suppose that a plane wave is incident onto an impenetrable grating profile of Dirichlet or Impedance type or a penetrable grating. The grating interface is assumed to be given by a Lipschitz function in two dimensions. We derive stability…
We consider the problem of approximating a function using Herglotz wave functions, which are a superposition of plane waves. When the discrepancy is measured in a ball, we show that the problem can essentially be solved by considering the…
We develop predictive formulas for friction resistance in ducts with complex cross-sectional shape based on the use of the log law and neglect of wall shear stress nonuniformities. The traditional hydraulic diameter naturally emerges from…
The fundamental quadrature governing light rays in a spherically symmetrical medium is first recalled. A rigorous discussion of some qualitative properties of its solutions follows, using the Young-Kattawar diagram which leads to a…
At a horizontally homogeneous isothermal atmosphere approximation, we derive an ordinary six-order differential equation describing linear disturbances with consideration for heat conductivity and viscosity of medium. The wave problem may…
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
An exact series representation of the even frequency moments of the dynamic structure factor is derived. Truncations are proposed that allow to evaluate the explicitly unknown second, fourth and fifth frequency moments for the finite…
This work theoretically and experimentally reports the evanescent connections between propagating bands in periodic acoustic materials. The complex band structures obtained by solving for the $k(\omega)$ problem reveal a complete…
A systematic and full description of the theory for a dissipation mechanism of wind wave energy in a spectral representation is given. As a basis of the theory, the fundamental is stated that the most general dissipation mechanism for wind…
In this paper we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work…
The one dimensional wave equation serves as a basic model for imaging modalities such as seismic which utilize acoustic data reflected back from a layered medium. In 1955 Peterson et al. described a single scattering approximation for the…
A traditional approach to the analysis of mode coupling in a fluctuating underwater waveguide is based on solving the system of coupled equations for the second statistical moments of mode amplitudes derived in the Markov approximation…
Lenses are typically based on refractive index profiles derived from the geometric approximation of high-frequency waves, yet the critical issue of impedance mismatch is often neglected. Mismatched devices suffer from unwanted reflections…
The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the…
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.
This paper describes an investigation of the acoustic properties of a rigid plate with a periodic pattern of holes, in a compressible, ideal, inviscid fluid in the absence of mean flow. Leppington and Levine (J. Fluid Mech., 1973) obtained…