Simultaneously Resolved Bifurcation Diagrams: A Novel Global Approach Applied to Liquid Figures of Equilibrium

A new approach to the computation of bifurcation diagrams is illustrated on axi-symmetric equilibria of liquid droplets and bridges. The new technique has an architecture that solves boundary-value problems in parallel and delivers a global bifurcation diagram, capturing isolated branches. In contrast, conventional techniques deliver solutions in sequence using local path continuation. A suitable mathematical formulation for the classical problem of predicting shapes of droplet and bridge equilibria is introduced and it its shown how the new technique yields global diagrams. Properties of these diagrams allow families of equilibria to be organized in a way that reveals common structures.