Equilibrium configurations for a floating drop

Equilibrium Configurations for a Territorial Model

We consider a territorial model based on Voronoi tessellations, which form a partition of a planar region by enclosing each agent in a polygon such that every point within the polygon is closest to that agent instead of any other. Equilibria for this model correspond to centroidal Voronoi tessellations. For rectangular domains and for small population sizes, we show that there can be distinct c...

Floating Bodies of Equilibrium

A long cylindrical body of circular cross-section and homogeneous density may float in all orientations around the cylinder axis. It is shown that there are also bodies of non-circular cross-sections which may float in any direction. Apart from those found by Auerbach for ρ = 1/2 there are one-parameter families of cross-sections for ρ 6= 1/2 which have a p-fold rotation axis. For given p they ...

Floating Bodies of Equilibrium I

A long cylindrical body of circular cross-section and homogeneous density may float in all orientations around the cylinder axis. It is shown that there are also bodies of non-circular cross-sections which may float in any direction. Apart from those found by Auerbach for ρ = 1/2 there are one-parameter families of cross-sections for ρ = 1/2 which have a p-fold rotation axis. For given p they e...

Equilibrium configurations of defective crystals

Floating Bodies of Equilibrium II

In a previous paper (physics/0203061) ”Floating bodies of equilibrium” we have shown that there exist two-dimensional non-circular crosssections of bodies of homogeous density ρ 6= 1/2 which can float in any orientation in water, which have a p-fold rotation axis. For given p they exist for p− 2 different densities. However, this was found only in a Taylor-expansion in a parameter which describ...