Thu, 15 Nov 2018

16:00 - 17:30
L3

Self-similarity in boundary layers

Bruno Eckhardt
(Philipps-Universität Marburg)
Abstract

Boundary layers control the transport of momentum, heat, solutes and other quantities between walls and the bulk of a flow. The Prandtl-Blasius boundary layer was the first quantitative example of a flow profile near a wall and could be derived by an asymptotic expansion of the Navier-Stokes equation. For higher flow speeds we have scaling arguments and models, but no derivation from the Navier-Stokes equation. The analysis of exact coherent structures in plane Couette flow reveals ingredients of such a more rigorous description of boundary layers. I will describe how exact coherent structures can be scaled to obtain self-similar structures on ever smaller scales as the Reynolds number increases.

A quasilinear approximation allows to combine the structures self-consistently to form boundary layers. Going beyond the quasilinear approximation will then open up new approaches for controlling and manipulating boundary layers.

Wed, 27 Feb 2013

10:15 - 11:15
OCCAM Common Room (RI2.28)

A model for a protein oscillator in Myxococcus xanthus

Dr Peter Rashkov
(Philipps-Universität Marburg)
Abstract

Cell polarity in the rod-shaped bacterium Myxococcus xanthus is crucial for the direction of movement of individual cells. Polarity is governed by a regulatory system characterized by a dynamic spatiotemporal oscillation of proteins between the opposite cell poles. A mathematical framework for a minimal macroscopic model is presented which produces self-sustained regular oscillations of the protein concentrations. The mathematical model is based on a reaction-diffusion PDE system and is independent of external triggers. Necessary conditions on the reaction terms leading to oscillating solutions are derived theoretically. Possible scenarios for protein interaction are numerically tested for robustness against parameter variation. Finally, possible extensions of the model will be addressed.

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