Dresden 2017 – scientific programme
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BP: Fachverband Biologische Physik
BP 53: Pattern Formation (Joint Session DY/BP)
BP 53.4: Talk
Thursday, March 23, 2017, 15:45–16:00, ZEU 118
Control of competing patterns in anti-symmetrically coupled Swift-Hohenberg equations — •Maximilian Becker1, Sina Reichelt2, Thomas Niedermayer1, Thomas Frenzel2, Alexander Mielke2, and Markus Bär1 — 1Physikalisch-Technische Bundesanstalt (PTB), Berlin, Germany — 2Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Berlin, Germany
The Swift-Hohenberg equation (SHE) provides a generic formulation for non-equilibrium pattern formation at a characteristic length scale. We present analytical and numerical investigations of two anti-symmetrically coupled 1d SHEs with cubic nonlinearities. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the Turing instability of uncoupled SHEs. Weakly nonlinear analysis has been performed in the vicinity of the codimension-2-point of the Turing-wave instability, resulting in a set of coupled amplitude equations for Turing patterns and left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict a mutual suppression of the amplitudes. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific control mechanisms for these interfaces which allow for global pattern selection. Extensive simulations of the underlying SHEs confirm our results.