Phase transitions cusp catastrophe

Another example is provided by pressure-induced phase transitions in which a cusp catastrophe transforms a double-well of the potential energy curve into a single-well and vice versa. In a wide pressure range, between 10 and 100 GPa, stishovite is the stable modification of silica. At about 100 GPa, a phase transition from PA2/mnm. (rutile) to Pmnm(CaCl2) occurs which corresponds to the twinning of the initial tetragonal cell... 

Fig. 39. The liquid-vapour phase transition on the surface of the cusp catastrophe (A3).

The first important conclusion which can be drawn from the above construction is a structural stability of phenomena described by the van der Waals equation. The conclusion is consistent with an observation that the reduced van der Waals equation (3.18) describes the critical transition for a number of gases. The liquid-vapour phase transition may thus be describred on the surface of the cusp catastrophe, see Fig. 39, in which a projection on the control parameters plane and the isotherm T = const are also shown. 

We may notice here that time and/or space are here the bifurcation parameters. We could also say that we have here a non-equilibrium phase transition figured by a cusp catastrophe [l5]. 

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