| Motivated by observations regarding collective motion and rippling patterns of gliding myxobacteria on a substrate, we have derived various mathematical models to de-scribe these phenomena. The talk starts with a short recollection of rippling patterns and their explanation by mathematical modelling. Most models of rippling patterns assume, however, perfect orientational ordering which is not completely in line with experimental findings. Therefore, we present results on two models describing emergence of orientational order in rod-shaped self-propelled particles in the main part of our contribution. We demonstrate that orientational order is a result of self-assembly, i. e. achieved by minimization of the free energy given by the interaction energy of the moving rods and their entropy. In contrast, other patterns found in the models such as rippling patterns [1] and clustering phenomena [2] result genuinely from the active motion of the self-propelled rods and should therefore be considered as self-organization phenomena. [1] U. Börner et al., Phys. Biol. 3, 138 (2006). [2] F. Peruani et al., Phys. Rev. E 74, 030904 (2006). |
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