Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 26: Poster II

DY 26.19: Poster

Donnerstag, 26. März 2009, 16:00–18:00, P1A

Velocity of Fronts in Periodic-Heterogeneous Reaction Diffusion Systems — •Jakob Löber and Harald Engel — Institut für Theoretische Physik, TU Berlin

Heterogeneities affect the pulse and front dynamics in excitable and bistable media. The velocity of travelling front solutions of the Schlögl model in a one-dimensional infinite medium has been calculated analytically for a spatially-periodic variation of the excitation threshold. The front velocity was found to display a maximum for a certain value of the spatial period. In a certain parameter range the maximum velocity exceeds the velocity in the effective homogeneous medium. Previously, a similar dependence of the pulse velocity on the size of the heterogeneity had been found in numerical simulations with a modified Oregonator model for the light-sensitive Belousov-Zhabotinskii reaction, where the local excitation threshold depends on the intensity of applied illumination [1]. The analytical results have been obtained for the Schlögl model by a second order perturbation approach that is based on the averaging method and uses the size of the heterogeneity as a small parameter [2]. These results agree qualitatively with direct numerical simulations.

[1] I. Schebesch and H. Engel, Wave propagation in heterogeneous excitable media, Phys. Rev. E 57, 3905(1998).

[2] J.P. Keener, Propagation of Waves in an Excitable Medium with Discrete Release Sites, SIAM 61, 317(2000).