Mathematicians are developing new algorithms for modelling complex physical and biological two-phase systems such as turbulent gas flows, melting-evaporation processes and tumour growth.
Processes in which matter transitions from one phase to another (e.g. solid to liquid when ice melts) can be mathematically modelled using partial differential equations (PDEs). The heat equation, for example, is a PDE describing the distribution of heat (or variation in temperature) in a given region over time.
Further details: New mathematical models for tumour growth