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 48.8: Talk

Thursday, March 23, 2017, 16:45–17:00, ZEU 118

Traveling Waves in Conserved Systems — •Lisa Rapp, Fabian Bergmann, Markus Hilt, and Walter Zimmermann — Theoretische Physik I, Universität Bayreuth, 95440 Bayreuth, Deutschland

Nonlinear traveling waves are one of the elementary prototype patterns that occur in various systems in nature far from thermal equilibrium. So far, their behavior has mostly been investigated in systems with an unconserved order parameter. In contrast, in systems with conserved order parameter, the Hopf-bifurcation to traveling waves is nearly unexplored (except for a first approach in Ref. [1]). The effects of conservation laws, however, may play a significant role in many pattern forming systems such as the Min protein oscillations during cell division in E.coli bacteria.

In spatially extended conserved systems, there are two distinctly different Hopf-bifurcations from a homogeneous basic state to traveling waves. On the one hand, the transition can occur via a finite wavenumber instability, similar to convection systems. On the other hand, the basic state can also become unstable towards long wavelength modes, comparable to the non-oscillatory Cahn-Hilliard model for potential systems.

We introduce a generalized Swift-Hohenberg model for conserved systems that includes both scenarios as special cases. Exploring this model and its limiting cases, we find interesting types of coarsening behavior and spatio-temporal complexity.

[1] W. Zimmermann, Physica A 237, 575 (1997).