Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 50: Poster: Nonlinear Systems, Patterns, Flows ..

DY 50.24: Poster

Thursday, April 4, 2019, 15:00–18:00, Poster B2

Transition from nonlinear traveling to standing waves in confined systems — •Samuel Grimm, Fabian Bergmann, Lisa Rapp, and Walter Zimmermann — TP1, Universität Bayreuth

In E. coli bacteria, for example, self-organized pole-to-pole oscillations of Min proteins - resembling a short standing wave - ensure correct positioning of the cell division site. The same biochemical reaction leads to traveling protein waves on extended membranes in in vitro experiments. We have shown in [1], that these seemingly contradictory observations can be explained by basic principles of pattern formation: For a complex Swift-Hohenberg model a transition of nonlinear traveling wave patterns in extended systems to reflection-induced standing waves takes place by reducing the system length. We show with this contribution, that the same basic principles of pattern formation cause a transition to standing waves also in the case of a subcritical bifurcation to traveling waves. We also show, how spatiotemporally chaotic traveling wave states can be supressed in favor of standing waves in short systems. We explore this behavior in terms of complex Swift-Hohenberg models with an unconserved and a conserved order-parameter field.

[1] F. Bergmann, L. Rapp, W. Zimmermann, New J. Phys. (Fast track) 20, 072001 (2018)