| Sliding-induced creation of phonons is a crucial mechanism of energy dissipation in wearless friction. A major unsolved problem in realistic molecular dynamics simulations of this process is the fact that phonons cannot escape the small simulation cell and are not easily dissipated, unlike the real system, where they can escape in the substrate. Practical solutions to this problem include the use of thermostats to artificially remove Joule heat in the substrate atoms, i.e., adding an arbitrary Langevin damping term to their equations of motion. Besides lacking a fundamental basis, these ad hoc solutions are all the more dubious when the final phononic friction ends up depending on the thermalization or damping parameters, as is often the case. An alternative solution, extensively discussed in the past in other contests, is to include an explicitly designed history-dependent, non markovian Langevin-like term whose aim is to mimick a missing semi-infinite system. Building on this idea we have implemented a scheme where the additional forces, provided by an effective harmonic semi-infinite substrate termination, are attached to substrate atoms. The method will be demonstrated in simple 1D and 2D tribological systems, with a view to pursue future applicability to realistic 3D simulations. |
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