Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 83: Pattern Formation II

DY 83.2: Talk

Friday, March 16, 2018, 10:15–10:30, BH-N 333

Wave propagation in spatially modulated domains — •Steffen Martens, Alexander Ziepke, and Harald Engel — Technische Universität Berlin, Institut für Theoretische Physik, 10623 Berlin, Germany

Propagation of traveling wave patterns plays in crucial role in various technological and biophysical processes such as catalysis, CO₂ sequestration, chemical computing, neural information processing, and self-organized pattern formation in cells. Often, the medium supporting wave propagation exhibits an irregular shape and/or is limited in size, leading to complex wave phenomena.

Recently [S. Martens et al., PRE 91, 022902; JCP 145, 094108], we have provided a first systematic treatment by applying asymptotic perturbation analysis leading to an approximate description that involves a reduction of dimensionality; the 3D RD equation with spatially dependent no-flux boundary conditions on the reactants reduces to a 1D reaction-diffusion-advection equation. 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.

Proofing the assumptions made in our analytic approach, we perform experiments on the propagation of traveling pulses in the Belousov-Zhabotinsky reaction through sinusoidal modulated channels being milled into acryl glas.