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DY: Dynamik und Statistische Physik

DY 5: Strukturbildung in dissipativen Systemen III

DY 5.2: Talk

Monday, March 17, 1997, 17:15–17:30, R4

Stability of Current Filaments in a Semiconductor Model on Two-dimensional Spatial Domains — •P. Rodin^2,3, A. Alekseev¹, S. Bose², and E. Schöll ² — ¹Institute for Theoretical Physics, Uppsala University, Sweden — ²Institut für Theoretische Physik, Technische Universität Berlin,10623 Berlin — ³Alexander von Humboldt fellow on leave of absence from Ioffe Institute, St.Petersburg, Russia

We study a reaction-diffusion model of a bistable semiconductor system on a two-dimensional spatial domain with Neumann boundary conditions. It is shown analytically that for any convex domain the presence of a global constraint given by the external circuit is a necessary condition of steady filament stability. With global constraint, the instability with respect to the translation mode is proved for a certain class of current distributions, which includes a small filament inside the domain and a radially symmetrical filament of arbitrary size in the center of a circular domain. On the basis of analytical considerations we conjecture that a boundary always attracts current filaments. This conclusion is confirmed by detailed numerical simulation of transient processes for circular and rectangular domains. Hysteresis of two different stable filament configurations and exponentially slow transient processes have been observed numerically.