Dew drops on spider webs: A symmetry breaking bifurcation for a parabolic differential-algebraic equation

摘要

Lines of dew drops on spider webs are frequently observed on cold mornings. In this paper we present a simple model explaining their generation. Although dew is supposed to condense 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 has some interesting mathematical challenges. In fact, we analyse bifurcations for a degenerate parabolic differential-algebraic equation employing a combination of analytical and numerical tools.