The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid-liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes some of t
he experimental observations of Tyndall stars and a mathematical model for the early stages of their evolution. The modelling is complicated by the strong crystalline anisotropy, which results in an anisotropic kinetic undercooling at the interface; it leads to an interesting class of free boundary problems that treat the melt region as infinitesimally thin.
We develop a version of the pi-calculus, picost, where channels are interpreted as resources which have costs associated with them. Code runs under the financial responsibility of owners; they must pay to use resources, but may profit by providing th
em. We provide a proof methodology for processes described in picost based on bisimulations. The underlying behavioural theory is justified via a contextual characterisation. We also demonstrate its usefulness via examples.
