Regensburg 2019 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 15: Pattern Formation
DY 15.9: Talk
Tuesday, April 2, 2019, 12:15–12:30, H3
Nonlinear analysis of dissipative systems with a conservation law — •Tobias Frohoff-Hülsmann1 and Uwe Thiele1,2 — 1Institute of Theoretical Physics, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster — 2Center of Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, 48149 Münster
We investigate the coupled dynamics of a conserved and a non-conserved order parameter field using the generic example of a Cahn-Hilliard equation coupled to a Swift-Hohenberg equation. Uncoupled, both equations have a gradient dynamics structure and we employ couplings that may preserve or violate this structure. In both cases, the coupled system can show short- and long-scale instabilities. We analytically examine the types of linear instability and the weakly nonlinear behaviour deriving amplitude equations which are generically influenced by the conservation law. The weakly nonlinear results are compared to fully nonlinear bifurcation diagrams obtained with numerical path continuation. Finally, we discuss the generic consequences of a conservation law in variational and nonvariational systems.