Regensburg 2007 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 24: Poster I
DY 24.49: Poster
Wednesday, March 28, 2007, 16:00–18:00, Poster D
Spatiotemporal memory in a one-dimensional reaction-diffusion system — •Knud Zabrocki1, Steffen Trimper1, and Michael Schulz2 — 1Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Deutschland — 2Fachbereich Physik, Universität Ulm, 89069 Ulm, Deutschland
To analyze possible generalizations of reaction-diffusion schemes due to feedback coupling and memory effects we investigate simple scalar evolution equations for the mass density or the probability density where long-range correlations and time delay are coupled. The influence of such a spatiotemperal delay is studied in a reaction-diffusion model. All processes within a sphere of radius R(t) = κ tα around a certain spatial point contribute to the instantaneous reaction and diffusion process. Due to the competition between both processes and the delay the system features a non-trivial stationary state. The resulting concentration profiles are calculated analytically for a ballistic behavior with α = 1 and for an additional local diffusive transport with α=1/2. Moreover the concentration profile offers an anisotropic behavior due to the delay. The model is exactly soluble.