Related papers: Wave propagation in waveguides with random boundar…
In this paper we review the results of the author on the theory of scalar and vector wave scattering by small bodies of an arbitrary shape with the emphasis on practical applicability of the formulas obtained and on the mathematical rigor…
Transport properties of a single-mode waveguide with rough boundary are studied by discrimination between two mechanisms of surface scattering, the amplitude and square-gradient ones. Although these mechanisms are generically mixed, we show…
We study the effect of surface scattering on transport properties in many-mode conducting channels (electron waveguides). Assuming a strong roughness of the surface profiles, we show that there are two independent control parameters that…
In shallow-water waveguides a propagating field can be decomposed over three kinds of modes: the propagating modes, the radiating modes and the evanescent modes. In this paper we consider the propagation of a wave in a randomly perturbed…
In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…
We consider the propagation of gravitational waves in the late time Universe with the presence of structure. Before detection, gravitational waves emitted from distant sources have to traverse through regions of spacetime which are far from…
We demonstrate experimentally that long-range intensity correlation for light propagating inside random photonic waveguides can be modified by changing the shape of the waveguide. The functional form of spatial correlation is no longer…
Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water…
The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful in various fields of applied mathematics. To be more…
A new method of path averaging for waves propagating in a random dilute system of identical scatterers is developed. The scattering matrix of such a system is calculated. The method systematically takes into account repeating scatterings on…
Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small…
A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wavefunction is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The case of transmission (interface) boundary…
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…
The analytical study of long wave scattering in a canal with a rapidly varying cross-section is presented. It is assumed that waves propagate on a stationary current with a given flow rate. Due to the fixed flow rate, the current speed is…
We analyze radiation from a bunch that uniformly moves in a circular waveguide and crosses the boundary between two areas: with a corrugated wall and with a smooth wall. It is assumed that the corrugation period is much less than the…
We study chaotic properties of eigenstates for periodic quasi-1D waveguides with "regular" and "random" surfaces. Main attention is paid to the role of the so-called "gradient scattering" which is due to large gradients in the scattering…
We study wave propagation in linear arrays composed of pairs of conjugate waveguides with balanced gain and loss, i.e. arrays of the PT-symmetric couplers, where the linear spectrum is known to feature high-frequency and low-frequency…
A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only…
In underwater acoustic waveguides a pressure field can be decomposed over three kinds of modes: the propagating modes, the radiating modes and the evanescent modes. In this paper, we analyze the effects produced by a randomly perturbed free…