Related papers: Front Propagation in Evanescent Media
We consider a reaction-diffusion equation in narrow random channels. We approximate the generalized solution to this equation by the corresponding one on a random graph. By making use of large deviation analysis we study the asymptotic wave…
A general method for tight focusing of waves, based on compensation of the angular spectrum, is established. We apply the method to monochromatic, polychromatic and diffusive waves. Diffusive and monochromatic waves may form spatially…
We consider reaction-diffusion equations of porous medium type, with different kind of reaction terms, and nonnegative bounded initial data. For all the reaction terms under consideration there are initial data for which the solution…
Interactions between inertia-gravity waves and balanced flows lead to a spectral diffusion of wave action. Prior work has established that this diffusion is weak across constant frequency surfaces in three-dimensional settings, but can be…
We study the behavior of wave propagation in materials for which not all of the principle elements of the permeability and permittivity tensors have the same sign. We find that a wide variety of effects can be realized in such media,…
Frontal polymerization (FP) enables rapid curing of thermosets via a self-sustaining thermal wave, but its propagation mechanism can shift dramatically depending on processing conditions. In this study, we investigate the effect of trigger…
We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, $X_\mathrm{s}(t) = vt$ is the location of the…
Nonlinear stochastic differential equations generating signals with 1/f spectrum have been used so far to describe socio-economical systems. In this paper we consider the motion of a Brownian particle in an inhomogeneous environment such…
Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…
Motivated by recent experiments, the theoretical study of wave propagation in time varying materials is of current interest. Although significant in nearly all such experiments, material dispersion is commonly neglected in theoretical…
We consider Schr\"odinger equations with variable coefficients and the harmonic potential. We suppose the perturbation is short-range type in the sense of [Nakamura 2004]. We characterize the wave front set of the solutions to the equation…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
We explore the nature of the classical propagation of light through media with strong frequency-dependent dispersion in the presence of a gravitational field. In the weak field limit, gravity causes a redshift of the optical frequency,…
In the present article we consider the problem of underwater avalanches propagating over moderate slopes. The main goal of our work is to investigate the avalanche front velocity selection mechanism when it propagates downwards. In…
Highly lossy nature of metals has severely limited the scope of practical applications of plasmonics. The conventional approach to circumvent this limitation has been to search for new materials with more favorable dielectric properties…
Finite propagation speed properties in mathematical elastic and viscoelastic models are fundamental in many applications where the data exhibits propagating fronts. We note particularly that this property is observed in biomechanical…
Detonation propagation in the limit of highly spatially discretized energy sources is investigated. The model of this problem begins with a medium consisting of a calorically perfect gas with a prescribed energy release per unit mass. The…
In its broadest sense the term bent wave rays hints at light or electromagnetic waves bending in a strong gravitational field or in their progress through a transparent medium of nonuniform index of refraction. However, there are instances…
We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of…
Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and…