Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 23: Reaction-Diffusion Systems

DY 23.2: Vortrag

Dienstag, 17. März 2015, 14:45–15:00, BH-N 243

Front propagation in channels with spatially modulated cross-section — •Steffen Martens, Jakob Löber, and Harald Engel — Technische Universität Berlin, Berlin, Germany

The problem of front propagation in a three-dimensional channel with spatially varying cross-section is reduced to an equivalent reaction-diffusion-advection equation with boundary-induced advection term [S. Martens et al.,PRE, in press; arXiv:1406.7516]. Treating the advection term as a weak perturbation, an equation of motion for the front position is derived. We analyze channels whose cross-sections vary periodically with L along the propagation direction of the front. Taking the Schlögl model as representative example, we calculate analytically the nonlinear dependence of the front velocity on the ratio L/l where l denotes the intrinsic front width. Our analytical results agree well with the results obtained by numerical simulations. In particular, the peculiarity of boundary-induced propagation failure for a finite range of L/l values is predicted by analytical calculations. Lastly, we demonstrate that the front velocity is determined by the suppressed diffusivity of the reactants for L ≪ l.