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Surface Tension-Induced Dynamics of Networked Droplets
14 May
14. May 2019
Oberseminar Analysis und Theoretische Physik

Surface Tension-Induced Dynamics of Networked Droplets

Motivated by the defense mechanism of a leaf beetle (Hemisphaerota cyanea), we present and analyze a dynamical system modeling surface tension-induced flows of liquids in networks of interconnected channels. These channel flows are driven by volume scavenging where fluid droplets of varying sizes leech off one another to increase in volume. Volume exchange arises by pressure (curvature) differences that drive liquid from one to another droplet along the network of channels.

The underlying physics-based model is given by a large gradient system of ordinary differential equations on a simple, connected graph. It generalizes an earlier Newtonian model by van Lengerich, Vogel and Steen. The presentation will report about previously unknown equilibrium solutions, a (surprisingly) complete, rigorous classification of their stability in dependence on the relevant bifurcation parameters as well as related results on forward invariant sets and hierarchies of equilibria. The stability discussion is complicated by the (potential) non-hyperbolicity of the equilibria. The nonlinear dynamics will be demonstrated with some animations. “The infinite-droplet limit” will be obtained via Sobolev regularization for certain networks. This is joint work with Paul H. Steen (Cornell).

Speaker

Prof. Dr. Thomas Hagen (University of Memphis)

Organiser

Institut für Angewandte Mathematik
Welfengarten 1
30167 Hannover

Date

14. May 2019
15:00 o'clock - 17:00 o'clock

Public contact

Antje Günther
Institut für Angewandte Mathematik
Welfengarten 1
30167 Hannover
Tel.: 0511/762-3251
Fax: 0511/762-3988
guenther@ifam.uni-hannover.de

Location

Leibniz Universität Hannover
Building: 1101
Room: c311
Welfengarten 1
30167 Hannover
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