Related papers: On the parabolic equation method in internal wave …
A study of the diffusion of a passive Brownian particle on the surface of a sphere and subject to the effects of an external potential, coupled linearly to the probability density of the particle's position, is presented through a numerical…
We attempt to gain some insight into the modeling of the generation of internal waves produced by submarines traveling in the littoral regions of the ocean with the use of high fidelity numerical simulations. These numerical simulations are…
A 3D singular integral equation is derived for electromagnetic wave scattering by bodies of arbitrary shape. Its numerical solution by a projection method is outlined.
Three-dimensional numerical models for underwater sound propagation are popular in computational ocean acoustics. For horizontally slowly varying waveguide environments, an adiabatic mode-parabolic equation hybrid theory can be used for…
We present an explicit numerical scheme to solve the variable coefficient wave equation in one space dimension with minimal restrictions on the coefficient and initial data.
The cubic nonlinear Helmholtz equation with third and fourth order dispersion and non-Kerr nonlinearity like the self steepening and the self frequency shift is considered. This model describes nonparaxial ultrashort pulse propagation in an…
Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the…
Assuming that a formal approximation of multiple waves has been obtained by matched asymptotic methods, we derive a {\em Spatial Shadowing lemma} to construct exact solutions near the formal approximation. In Part I, we consider a general…
We give a detailed analysis of long range cumulative scattering effects from rough boundaries in waveguides. We assume small random fluctuations of the boundaries and obtain a quantitative statistical description of the wave field. The…
The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a first verification of the validity of these equations, a two-layer rigid frame porous system considered as one single porous…
A heat equation with uncertain domains is thoroughly investigated. Statistical moments of the solution is approximated by the counterparts of the shape derivative. A rigorous proof for the existence of the shape derivative is presented.…
Molecular dynamical (MD) simulations are performed to simulate two dimensional vibrofluidized granular materials in this work. Statistics on simulation results indicate that there exist shocks propagating upward in each vibrating cycle.…
In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is investigated via the method of multiple scales. Commonly employed to the investigate the effect of weakly nonlinear interactions on the free wave…
We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated…
We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation,…
We discuss the propagation of harmonic and transient waves for systems governed by a wave equation with memory whose integral kernel involves ratios of modified Bessel functions of the first kind in the Laplace domain. In particular, the…
When the electromagnetic wave is incident on the periodic structures, in addition to the scattering field, some guided modes that are traveling in the periodic medium could be generated. In the present paper, we study the calculation of…
Internal waves are believed to be of primary importance as they affect ocean mixing and energy transport. Several processes can lead to the breaking of internal waves and they usually involve non linear interactions between waves. In this…
The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…