Research Colloquium Wednesday, October 24, 2012
Dew drops on spider webs: a symmetry breaking bifurcation for a parabolic differential-algebraic equationDr. Klaus Boehmer
Department of Mathematics and Information
Philipps-Universitat Marburg, Germany
This lecture is an appetizer for my two books in OUP: Numerical Methods for Nonlinear Elliptic Differential Equations, A Synopsis, and Numerical Methods for Bifurcation and Center Manifolds in Nonlinear Elliptic and Parabolic Differential Equations, 2010 and 2011.
Lines of dew drops on spider webs are frequently observed on cold mornings. In this lecture we present a model explaining their generation. Although dew is supposed to condense somehow evenly along the thread, only lines of drops are observed along the spider thread. What are the reasons for this difference? We try to give an explanation by concentrating on some essential aspects only. This every-day observation is an example of one of the fascinating scenarios of nonlinear problems, symmetry breaking bifurcation. Despite many simplifications the model still provides very interesting mathematical challenges. In fact the necessary mathematical model and the corresponding numerical methods for this problem are so complicated that in its full complexity it has never been studied before. We analyse and numerically study symmetry breaking bifurcations for a degenerate parabolic differential-algebraic equation employing a combination of analytical and numerical tools.