David Aristoff's homepage
Shape selection induced by competition between surface and line energy
We will consider a variational problem that consists of finding energetically preferred equilibrium configurations of a system in which a closed, flexible loop is spanned by a soap film. While the loop is modeled by an inextensible, unshearable rod endowed with elastic resistance to bending, the soap film is modeled as a surface endowed with uniform tension. In addition to presenting results from bifurcation and stability analyses based on the first and second variations of the relevant energy functional, we will discuss generalizations of the problem. In particular, we will describe the consequences of extending the model to incorporate elastic resistance to twisting the loop or to bending the spanning film. We will also touch on applications to experiments involving discoidal high-density lipoprotein particles and synthetic nanodiscs.