A series of experiments for steady state rotation of water in vessels of various geometries is presented. The experiments focus on the geometrical characteristics of the rotating liquids and the change in their surface topology, from that akin to a sphere to that of a torus (i.e., from genus 0 to 1), for sufficiently large angular speeds. Cylindrical, planar rectangular, cubic, spherical, and conical containers are considered. The cone is an exception as some liquid always remains in its apex, no matter how fast the spin. It is shown also that for any amount of liquid within, there exists a critical angular speed above which the liquid can no longer be confined and is therefore expelled from the cone spontaneously breaking the symmetry. This instability is investigated experimentally. V

We describe a semi-analytic model to predict the triaxial shapes of dark matter halos utilizing the sequences of random merging events captured in merger trees to follow the evolution of each halo's energy tensor. When coupled with a simple model for relaxation toward a spherical shape, we find that this model predicts distributions of halo axis length ratios which approximately agree with those measured from cosmological N-body simulations in their medians and inter-quartile ranges. We demonstrate the predictive and explanatory power of this model by considering conditioned distributions of axis length, and the mass-dependence of halo shapes, finding these to be in excellent agreement with N-body results. This model provides both insight into the physics driving the evolution of halo triaxial shapes, and rapid quantitative predictions for the statistics of triaxiality connected directly to the formation history of the halo.

We describe a semi-analytic model to predict the triaxial shapes of dark matter haloes utilizing the sequences of random merging events captured in merger trees to follow the evolution of each halo’s energy tensor. When coupled with a simple model for relaxation toward a spherical shape, we find that this model predicts distributions of halo axis length ratios which approximately agree with those measured from cosmological N-body simulations once constrained to match the median axial ratio at a single halo mass. We demonstrate the predictive and explanatory power of this model by considering conditioned distributions of axis length ratios, and the mass-dependence of halo shapes, finding these to be in good agreement with N-body results. This model provides both insight into the physics driving the evolution of halo triaxial shapes, and rapid quantitative predictions for the statistics of triaxiality connected directly to the formation history of the halo.