Dresden 2017 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 24: Pattern Formation / Reaction-Diffusion I

DY 24.3: Vortrag

Dienstag, 21. März 2017, 15:00–15:15, ZEU 147

Propagation and Boundary Mediated Control of Reaction-Diffusion Waves in Modulated Tubes — •Alexander Ziepke, Steffen Martens, and Harald Engel — Institut für Theoretische Physik, Technische Universität Berlin, Germany

Propagation of traveling front and pulse solutions to reaction-diffusion equations within periodically modulated tubes is investigated. In the fashion of our recent paper [1], we apply asymptotic analysis for a small changing rate of the tube’s cross-section to reduce the dimensionality of the problem. Within this approach, the no-flux condition at the tube’s boundary translates into a boundary-induced advection term. Treating the latter as a weak perturbation, we derive an equation of motion for the wave position [2]. Numerical simulations demonstrate that our analytical results predict properly the nonlinear dependence of the propagation velocity on the ratio of the period of the cross-section’s spatial modulation to the intrinsic width of the wave solution. As a main feature, we observe finite intervals of propagation failure of waves induced by the tube’s modulation. Further, using the derived equation of motion, the inverse problem of calculating the cross-section profile for a given protocol of motion is treated. This allows a geometry based control of chemical wave propagation. Additionally, we discuss the effects of a single bottleneck on periodic pulse trains.

[1] A. Ziepke, S. Martens, and H. Engel, J. Chem. Phys., 145, 094108 (2016).

[2] J. Löber and H. Engel, Phys. Rev. Lett., 112, 148305 (2014).