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Stochastic boundary conditions

In some cases it is desirable to study approach of initially non-equilibrium system to equilibrium. Examples of such simulations include the impact problems when a particle with large kinetic energy hits a surface or calculation of friction force between two surfaces sliding with respect to each other. As shown in Ref. [83], this type of problems can be studied using the stochastic boundary conditions (SBC) derived from generalized Langevin equation by Kantorovich and Rompotis [75]. In this approach, the system of interest is divided into three regions: (a) fixed atoms, (b) the internal (Newtonian) atoms moving according to Newtonian dynamics, and (c) a buffer region of Langevin atoms (i.e. atoms governed by Langevin equations of motion, see eq. 6.33) located between (a) and (b). The role of Langevin atoms is to dissipate heat, while the fixed atoms are needed solely to create the correct potential well for the Langevin atoms to move in. The Newtonian region should include all atoms relevant to the process under study: in the case of the impact problem, for instance, the Newtonian region should contain atoms of the molecule hitting the surface and several uppermost layers of the material forming the surface. Performing molecular dynamics with such a setup guarantees that the system (possibly out of equilibrium initially) arrives at the appropriate canonical distribution.

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