Related papers: Reaction-diffusion waves of blood coagulation
The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the…
The reaction-diffusion waves of proteins are known to be involved in fundamental cellular functions, such as cell migration, cell division, and vesicular transportation. In some of these phenomena, pattern formation on the membranes is…
A Smoluchowski type model of coagulation in a turbulent fluid is given, first expressed by means of a stochastic model, then in a suitable scaling limit as a deterministic model with enhanced diffusion in the velocity component. A precise…
This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trival steady state for the…
We develop a general method for calculating statistical properties of the speckle pattern of coherent waves propagating in disordered media. In some aspects this method is similar to the Boltzmann-Langevin approach for the calculation of…
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 various combinations of active diffusion with branching, as an extension of standard reaction-diffusion processes. We concentrate on the selection of the asymptotic wavefront speed for thermal run-and-tumble and for thermal active…
We describe a formal procedure to obtain and specify the general form of a marginal distribution for the Lagrangian acceleration of fluid particle in developed turbulent flow using Langevin type equation and the assumption that velocity…
The effect of advection on the critical minimal speed of traveling waves is studied. Previous theoretical studies estimated the effect on the velocity of stable fast waves and predicted the existence of a critical advection strength below…
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…
Laser-induced breakdown has shown many potential applications in the various field of science and engineering. As the breakdown occurs in gas or aerosol, a rapid hydrodynamic expansion as shock (blast) wave initiated from the deposition…
Rayleigh-B\'enard convection, i.e. the flow of a fluid between two parallel plates that is driven by a temperature gradient, is an idealised setup to study thermal convection. Of special interest are the statistics of the turbulent…
We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e. on the time evolution of the reaction product, M(t). At…
Presented here is the mathematical model describing the phenomenon of shock waves. The underlying concept is based on the time-space model of wave propagation.
Living cells employ excitable reaction-diffusion waves for internal cellular functions, in which curvature-inducing proteins are often involved. However, the role of their mechanochemical coupling is not well understood. Here, we report the…
We perform numerical simulations to examine particle diffusion at steady shear in a model granular material in two dimensions at the jamming density and zero temperature. We confirm findings by others that the diffusion constant depends on…
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…
Direct numerical simulations and mean-field theory are used to model reactive front propagation in a turbulent medium. In the mean-field approach, memory effects of turbulent diffusion are taken into account to estimate the front speed in…
In this paper, we numerically show and discuss the existence and characteristics of rogue heat and diffusion waves. More specifically, we use two different nonlinear heat (diffusion) models and show that modulation instability leads to the…
The dispersion of small amplitude, impulsively excited wave trains propagating along a magnetic flux tube is investigated. The initial disturbance is a localized transverse displacement of the tube that excites a fast kink wave packet. The…