Biomaterial Database

Analyzing critical propagation in a reaction-diffusion-advection model using unstable slow waves. 2015

Frederike Kneer, and Klaus Obermayer, and Markus A Dahlem

Department of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, Ernst-Reuter-Platz 7, D-10587, Berlin, Germany, fkneer@ni.tu-berlin.de.

The effect of advection on the propagation and in particular on the critical minimal speed of traveling waves in a reaction-diffusion model is studied. Previous theoretical studies estimated this effect on the velocity of stable fast waves and predicted the existence of a critical advection strength below which propagating waves are not supported anymore. In this paper, an analytical expression for the advection-velocity relation of the unstable slow wave is derived. In addition, the critical advection strength is calculated taking into account the unstable slow wave solution. We also analyze a two-variable reaction-diffusion-advection model numerically in a wide parameter range. Due to the new control parameter (advection) we can find stable wave propagation in the otherwise non-excitable parameter regime, if the advection strength exceeds a critical value. Comparing theoretical predictions to numerical results, we find that they are in good agreement. Theory provides an explanation for the observed behaviour.

UI	MeSH Term	Description	Entries
D008956	Models, Chemical	Theoretical representations that simulate the behavior or activity of chemical processes or phenomena; includes the use of mathematical equations, computers, and other electronic equipment.	Chemical Models,Chemical Model,Model, Chemical
D010507	Periodicity	The tendency of a phenomenon to recur at regular intervals; in biological systems, the recurrence of certain activities (including hormonal, cellular, neural) may be annual, seasonal, monthly, daily, or more frequently (ultradian).	Cyclicity,Rhythmicity,Biological Rhythms,Bioperiodicity,Biorhythms,Biological Rhythm,Bioperiodicities,Biorhythm,Cyclicities,Periodicities,Rhythm, Biological,Rhythmicities,Rhythms, Biological
D004058	Diffusion	The tendency of a gas or solute to pass from a point of higher pressure or concentration to a point of lower pressure or concentration and to distribute itself throughout the available space. Diffusion, especially FACILITATED DIFFUSION, is a major mechanism of BIOLOGICAL TRANSPORT.	Diffusions
D057446	Hydrodynamics	The motion of fluids, especially noncompressible liquids, under the influence of internal and external forces.	Fluid Dynamics,Dynamic, Fluid,Dynamics, Fluid,Fluid Dynamic,Hydrodynamic