Title: Shape transition in some systems involving surface and line energy

Title: Shape transition in some systems involving surface and line energy

Abstract:

Abstract:

We will present a variational problem that combines the challenges of constructing aesthetically pleasing space curves and area minimizing surfaces. The problem consists of finding energetically preferred equilibrium configurations of a system consisting of a closed, inextensible, unshearable loop endowed with elastic resistance to bending that is spanned by a liquid film endowed with constant surface tension. Aside from 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 incorporating elastic resistance to twisting the bounding loop and bending the spanning film. We will also mention applications to experiments involving discoidal high-density lipoprotein particles and synthetic nanodiscs.

We will present a variational problem that combines the challenges of constructing aesthetically pleasing space curves and area minimizing surfaces. The problem consists of finding energetically preferred equilibrium configurations of a system consisting of a closed, inextensible, unshearable loop endowed with elastic resistance to bending that is spanned by a liquid film endowed with constant surface tension. Aside from 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 incorporating elastic resistance to twisting the bounding loop and bending the spanning film. We will also mention applications to experiments involving discoidal high-density lipoprotein particles and synthetic nanodiscs.