Regensburg 2019 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 15: Pattern Formation

DY 15.5: Vortrag

Dienstag, 2. April 2019, 11:00–11:15, H3

Simulation of surface evolution beyond the small gradient approximation — •Christoph Kabelitz and Stefan Jakob Linz — Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster

Apart from three-dimensional and discrete models the evolution of surfaces is usually described by spatially two-dimensional PDEs. These models are often derived from small gradient approximations, but the studied surfaces do not fulfill this requirement in all cases. We will explain how to overcome the small gradient approximation. Therefore, we will introduce a method to simulate the evolution of surfaces with respect to local geometric properties. In contrast to traditional PDEs, the resulting geometric PDEs do not depend on the parametrization of the surface [1]. This allow us to simulate surface evolution not only on almost flat surfaces but also on more complex shaped objects. For small gradients the studies of simple model equations show similar results compared to the related PDEs (like the Kuramoto-Sivashinsky equation [2, 3]). For large gradients the results differ fundamentally.

[1] M. Marsili et al, Rev. Mod. Phys., 68, 963 (1996).

[2] Y. Kuramoto and T. Tsuzuki, Progress of Theoretical Physics, 55, 356 (1976).

[3] G. Sivashinsky, Acta Astronautica, 4, 1177 (1977).