Related papers: An introduction to spatial dispersion: revisiting …

Dispersive shock waves are fascinating phenomena occurring when nonlinearity overwhelms linear effects, such as dispersion and diffraction. Many features of shock waves are still under investigation, as the interplay with noninstantaneity…

This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and…

In this article, we investigate the wave equation in spiral geometry and study the modes of vibrations of a one-dimensional (1-D) string in spiral shape. Here we show that the problem of wave propagation along a spiral can be reduced to…

Wave scattering is considered in a medium in which many small particles are embedded. Equations for the effective field in the medium are derived when the number of particles tends to infinity.

Disease outbreaks, such as those of Severe Acute Respiratory Syndrome in 2003 and the 2009 pandemic A(H1N1) influenza, have highlighted the potential for airborne transmission in indoor environments. Respirable pathogen-carrying droplets…

The evolution of acoustic waves can be evaluated in two ways: either as a temporal, or a spatial propagation. Propagating in space provides the considerable advantage of being able to handle dispersion and propagation across interfaces with…

We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive…

Time variable delays due to radio wave propagation in the ionized interstellar medium are a substantial source of error in pulsar timing array efforts. We describe the physical origin of these effects, discussing dispersive and scattering…

Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental…

We review various methods for the analysis of initial-value problems for integrable dispersive equations in the weak-dispersion or semiclassical regime. Some methods are sufficiently powerful to rigorously explain the generation of…

Waves are propagating disturbances that redistribute energy across space. Previous studies have shown that for waves propagating through an inhomogeneously moving mean flow, the conserved quantity is wave action rather than wave energy,…

Pattern dynamics on curved surfaces are found everywhere in nature. The geometry of surfaces have been shown to influence dynamics and play a functional role, yet a comprehensive understanding is still elusive. Here, we report for the first…

Different approaches are presented to investigate diffusion from a point source in a slab delimited by two absorbing boundaries consisting of parallel infinite planes. These approaches enable to consider the effect of absorption at the…

Various properties of fluids consisting of platelike particles differ from the corresponding ones of fluids consisting of spherical particles because interactions between platelets depend on their mutual orientations. One of the main issues…

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…

Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with…

In these last years, many studies have focalized on the design of reliable underwater acoustic communication systems. However, the ocean acoustic communication channel exhibits strong amplitude and phase fluctuations and the phenomena of…

We investigate different mechanical effects which accompany the nerve pulse propagation by using mathematical modeling. The propagation process is composed by three connected phenomena: (i) the action potential (electrical signal) which is…

We consider principal properties of various wave regimes in two selected excitable systems with linear cross-diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope…

Starting from the wave equation for a medium with material properties that vary periodically, we study a system of recurrence relations that describe propagation of wave packets that oscillate on the microscale (i.e. on lengths of the order…