The surface evolver and the stability of liquid surfaces

The Surface Evolver is an interactive program for studying the shapes of liquid surfaces. Recently added features permit the calculation of the Hessian matrix of second derivatives of the energy. The Hessian can be used for fast convergence to an equilibrium, and eigenvalue analysis of the stability of that equilibrium. This paper describes the use of the Hessian by the Surface Evolver, presents some sample stability analyses, and gives some numerical results on the accuracy and convergence of the methods. It is also shown how one can evolve unstable surfaces.