Seminar

We will consider a variational problem that combines the challenges of designing aesthetically pleasing space curves and constructing area minimizing surfaces. The problem consists of finding energetically preferred equilibrium configurations of a system comprised by a closed, inextensible, unshearable filament with circular cross-section and rectilinear rest configuration that is endowed with elastic resistance to bending and is spanned by a liquid film endowed with uniform surface tension. Aside from presenting results from stability analyses based on the first and second variations of the salient energy functional, we will discuss generalizations that arise if the filament has a noncircular cross-section or a curvilinear rest configuration. We will also present results for the related problem of modeling shape transitions observed in experiments involving nanodiscs and discoidal high-density lipoprotein particles, where it is essential to endow the spanning film with elastic resistance to bending.