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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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