Constant pressure-temperature molecular dynamics on a torus

A model of many-body system on the surface of a torus is employed to conduct isothermal-isobaric molecular dynamics. Six independent variables, which are three radius and three angles determining the orientations of the curvatures describe the flexibility of the surface, eliminating the size and the shape of the cell from dynamics. The isotropic and flexible cell motion equations are derived with the help of an approach analogous to the Nosé-Hoover one. Simulations for a temperature-induced structural transformation of a model helium lattice under isotropic applied pressure are used to illustrate the new method. Results of calculations with the usage of time-reversible integrator are compared with the results of the Martyna-Tobias-Klein algorithm.