Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 83: Pattern Formation II

DY 83.5: Talk

Friday, March 16, 2018, 11:15–11:30, BH-N 333

Influence of additive noise on spatially one- and two-dimensional localized structures in the Kuramoto-Sivashinsky-Verhulst equation — •Christoph Kabelitz and Stefan Jakob Linz — Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster

In the past years, spatially localized structures in physical systems and mathematical models became popular [1, 2]. While mathematical models are usually deterministic, experiments suffers from noise. We present an analysis concerning the Kuramoto-Sivashinsky-Verhulst equation with additive noise. The model equation is representative for stochastic partial differential equations whose deterministic versions have stable localized structures as solutions. In both, the spatially one- and the spatially two-dimensional case, the localized structures become unstable due to noise. We will show that the average time till a structural change occurs depends primarily on the strength of noise and the distance to the pinning border of the localized structures in the equation's deterministic variant in parameter space.

[1] E. Knobloch, Annu. Rev. Cond. Matter Phys., 6, 325 (2015).

[2] D. J. B. Lloyd et al., SIAM J. on Appl. Dyn. Sys., 7, 1049 (2008).