Related papers: Reaction-diffusion waves of blood coagulation
In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of…
The propagation of microwaves across a turbulent plasma density layer is investigated with full-wave simulations. To properly represent a fusion edge-plasma, drift-wave turbulence is considered based on the Hasegawa-Wakatani model.…
Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or with a Gaussian distributed…
Centrifugation is a commonly performed laboratory procedure that helps to separate blood cells such as $RBCs$, $WBCs$, and platelets from plasma or serum. Although centrifugation is a routine procedure in most medical laboratories, the…
The response of the living tissue to the effects of strong heating or cooling can cause the blood flow rate to vary by an order of magnitude. A mathematical model for the freezing of living tissue is formulated which takes into account the…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
We consider the evolution of a tight binding wave packet propagating in a time dependent potential. If the potential evolves according to a stationary Markov process, we show that the square amplitude of the wave packet converges, after…
Turbulence, left unforced, decays and invades the surrounding quiescent fluid. Though ubiquitous, this simple phenomenon has proven hard to capture within a simple and general framework. Experiments in conventional turbulent flow chambers…
In this paper, the one-dimensional time-fractional diffusion-wave equation with the fractional derivative of order $1 \le \alpha \le 2$ is revisited. This equation interpolates between the diffusion and the wave equations that behave quite…
Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable,…
Many systems in life sciences have been modeled by reaction-diffusion equations. However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release, fire events,…
We determine the spectrum of particles accelerated at shocks with arbitrary speed and arbitrary scattering properties for different choices of the equation of state of the downstream plasma. More specifically we consider the effect of…
We investigate in detail two models describing how stresses propagate and fluctuate in granular media. The first one is a scalar model where only the vertical component of the stress tensor is considered. In the continuum limit, this model…
Analysis of signal fluctuations of a locally fixed probe, caused by molecules diffusing under the probe, can be used to determine diffusion coefficients. Theoretical treatments so far have been limited to point-like particles or to…
The structure of steady plane-parallel radiative shock waves propagating through the hydrogen gas undergoing partial ionization and excitation of bound atomic states is investigated in terms of the self-consistent solution of the equations…
We study travelling-wave solutions for a reaction-diffusion system arising as a model for host-tissue degradation by bacteria. This system consists of a parabolic equation coupled with an ordinary differential equation. For large values of…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
This paper is concerned with pulsating waves for multi-dimensional reaction-diffusion equations in spatially periodic media. First, assuming the existence of pulsating waves connecting two linearly stable steady states, we study the…
This paper concerns wave propagation in a class of scalar reaction-diffusion-convection equations with $p$-Laplacian-type diffusion and monostable reaction. We introduce a new concept of a non-smooth traveling wave profile, which allows us…
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to…