# Dresden 2006 – wissenschaftliches Programm

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# SYSS: Structure Formation and Self-Organization in non-equilibrium Systems

## SYSS 2: Structure Formation and Self-Organization in non-equilibrium Systems II

### SYSS 2.2: Vortrag

### Donnerstag, 30. März 2006, 14:45–15:00, BAR Sch\"o

**Nonlinear competition between patterns in filament-motor-systems** — •Falko Ziebert and Walter Zimmermann — Theoretische Physik Ia, Universität Bayreuth

Biopolymer systems have various mechanisms for pattern formation. One is the interplay of polymerization and demixing

[1] . Interaction via molecular motors is a second way and modelled here by a Smoluchowski equation approach. It is shown that the homogeneous distribution of filaments, such as actin or microtubules, may become either unstable with respect to a homogeneous nematic state, to an orientational instability of a finite wave number or with respect to modulations of the filament density, where long wavelength modes are amplified as well. In the stationary case above threshold nonlinear interactions select either stripe patterns or periodic asters

[2] . The existence and stability ranges of each pattern close to threshold are predicted in terms of a weakly nonlinear perturbation analysis and confirmed by numerical simulations of the basic model equations. Also oscillatory solutions exist and existence and stability of 1D and 2D wave solutions are discussed.

[1] F. Ziebert and W. Zimmermann, Phys. Rev. E **70**, 022902 (2004)

[2] F. Ziebert and W. Zimmermann, Europhys. J. E **18**, 41 (2005)