Dresden 2017 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 48: Pattern Formation / Reaction-Diffusion II (joint session DY/BP)

DY 48.7: Talk

Thursday, March 23, 2017, 16:30–16:45, ZEU 118

Size matters for Nonlinear Waves and Min Protein Patterns — •Fabian Bergmann, Lisa Rapp, and Walter Zimmermann — Theoretische Physik I, Universität Bayreuth, 95440 Bayreuth, Germany

Self-organization is a fundamental strategy in nature. In E. coli bacteria, for example, self-organized pole-to-pole oscillations of the Min proteins have an important function within the cell division machinery. Such pole-to-pole oscillations in living cells behave like standing waves (SW) in very small (confined) systems. In extended in vitro experiments, Min oscillations develop into nonlinear traveling waves (TW). TW patterns are also known from many other nonequilibrium systems. But is the transition from traveling waves in extended to standing waves in strongly confined systems a specific property of the Min oscillation pattern? Or is it a generic and robust universal principle of all nonlinear traveling waves that just also applies to the Min oscillations in cells?

We address this central question by imposing strong spatial confinement to a generic model for nonlinear traveling waves. Using simulations, analytical and symmetry considerations, we conclude that traveling waves inevitably change into standing waves in sufficiently small confined systems.