Parallel replica dynamics for driven systems: Derivation and application to strained nanotubes

We show that parallel replica dynamics can be extended to driven systems (e.g., systems with time-dependent boundary conditions). Each processor simulates a replica at a driving rate that is M times faster than the desired rate, where M is the number of processors. As in regular parallel replica dynamics, when a transition to a new state is detected on any processor, the times are summed and every processor is restarted in the new state. The state-to-state dynamics are shown to be correct if the processors run at the same speed and the system is driven slowly enough (on each processor) so that the escape rates do not depend on the time history of the drive. We demonstrate the algorithm by stretching a carbon nanotube with a preexisting vacancy, noting a significant dependence of the nature of nanotube yield on the strain rate. In particular, we are able to achieve strain rates slow enough such that the time scale for vacancy diffusion is faster than that for mechanical yield at a temperature of 2000 K. We thus observe vacancy-induced morphological changes in the nanotube structure, providing some insight into previously unexplained experimental features.