Dynamics on a torus.
The dynamics of atoms on the surface of a torus is considered. The simple illustration of motion with regard to rotating and fixed space gives a model of a four-dimensional (4D) torus. Two different schemes including rotation and shear in angular frame are used to take into account shears of the surface. In general, a variable-cell-shape molecular dynamics method analogous to the Parrinello-Raman one is developed. The six dynamical variables, the three radiuses and the three angles, specifying the deformations of the surface describe the cell dynamics. The new equations of motion contain no vectors of translations of the cell making its shape irrelevant for the structural and thermodynamical description of the system. The new method was tested on two problems concerning structure transformations of two-dimensional lattices.
Ryabov
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Federal State Scientific Centre, Institute of Physics and Power Engineering, 249020 Obninsk, Russia.