Related papers: Dual Time-Space Model of Wave Propagation
I describe three ways that the spatial properties of a wave propagation medium can cause dispersion, and propose that they should form the basics for correctly understanding and naming phenomena described as "spatial dispersion". In…
In transport phenomena, perturbation waves are a result of interaction of molecules in gases and liquids, charged particles (ions, electrons) in plasma, conduction electrons and phonons in solid bodies. General statistical theory of the…
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…
A covariant formalism for physical perturbations propagating along a string in an arbitrary curved spacetime is developed. In the case of a stationary string in a static background the propagation of the perturbations is described by a…
We present a study of sound wave propagation in a time dependent random medium and an application to imaging. The medium is modeled by small temporal and spatial random fluctuations in the wave speed and density, and it moves due to an…
We study the radial distribution of pressure, density, temperature and flow velocity fields at different times in a two dimensional hard sphere gas that is initially at rest and disturbed by injecting kinetic energy in a localized region…
A theory for multiple scattering of elastic waves is presented in a random medium bounded by two ideal free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. This geometry…
Waves in space-dependent and time-dependent materials obey similar wave equations, with interchanged time- and space-coordinates. However, since the causality conditions are the same in both types of material (i.e., without interchangement…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
The life of a tsunami is usually divided into three phases: the generation (tsunami source), the propagation and the inundation. Each phase is complex and often described separately. A brief description of each phase is given. Model…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
Distributions of wave characteristics of ocean waves, such as wave slope, waveheight or wavelength, are an important tool in a variety of oceanographic applications such as safety of ocean structures or in the study of ship stability, as…
In two space dimensions and one time dimension a wave changes its shape even in the absence of a dispersive medium. However, this anomalous dispersive behavior in empty two-dimensional space does not occur if the wave dynamics is described…
We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…
In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…
An electromagnetic wave-packet propagating in a linear, homogeneous, and isotropic medium changes shape while its envelope travels with different velocities at different points in spacetime. In general, a wave-packet can be described as a…
Ocean surface waves can propagate long distances through regions containing floating ice covers. The impacts ocean waves have on the ice covers are of interest in the climate change era, as the polar regions experience pressure from rising…
The present work investigates some exact solutions of the gravitational wave equation in some widely used cosmological spacetimes. The examples are taken from spatially flat and closed isotropic models as well as Kasner metric which is…
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…
The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or…