Parallel replica

Keywords infrequent events transition-state theory accelerated dynamics hyperdynamics parallel-replica dynamics temperature-accelerated dynamics molecular dynamics bond-boost hyperdynamics parallel-accelerated dynamics Cu(100)... 

The parallel-replica method [5] is perhaps the least glamorous of the AMD methods, but is, in many cases, the most powerful. It is also the most accurate AMD method, assuming only first-order kinetics (exponential decay) i.e., for any trajectory that has been in a state long enough to have lost its memory of how it entered the state (longer than the correlation time icorr, the time after which the system is effectively sampling a stationary distribution restricted to the current state), the probability distribution function for the time of the next escape from that state is given by... 

The parallel-replica method also correctly accounts for correlated dynamical events (there is no requirement that the system obeys TST), unlike the other AMD methods. This is accomplished by allowing the trajectory that made the transition to continue for a further amount of time Afcorr > Tcorr, during which recrossings or follow-on events may occur. The simulation clock is then advanced by Afcorr, the new state is replicated on all processors, and the whole process is repeated. 

Figure 1 Schematic illustration of the parallel-replica method. The four steps, described in the text, are (A) replication of the system into M copies, (B) dephasing of the replicas, (C) propagation of independent trajectories until a transition is detected in any of the replicas, and (D) brief continuation of the transitioning trajectory to allow for correlated events such as recrossings or follow-on transitions to other states. The resulting configuration is then replicated, beginning the process again. Reprinted, with permission, from ref. 6. Copyright 2002 by Annual Reviews, www.annualreviews.org...

An extension to parallel-replica allows the method to be applied to driven systems. To result in valid dynamics, the drive rate must be slow enough that at any given time the rates for the different pathways in the system depend only on the instantaneous configuration of the system [7]. 

Figure 4 Left Distribution of hopping times for an adatom at a solid-liquid interface at 600 K for conventional molecular dynamics and for superstate parallel-replica dynamics. Right Temperature dependence of the hopping rate for an adatom at a dry interface and at a wet interface as obtained using superstate parallel-replica dynamics.

Voter, A.F. Parallel replica method for dynamics of infrequent events. Phys. Rev. B 1998, 57, 13985-88. 

Kum, O., Dickson, B.M., Stuart, S.J., Uberuaga, B.P., Voter, A.F. Parallel replica dynamics with a heterogeneous distribution of barriers application to n-hexadecane pyrolysis. J. Chem. Phys. 2004, 121(20), 9808-19. 

Among the methods utilizing the TST, the parallel replica method is the simplest and most accurate dynamics techniques, because the only assumption for the method is that of infrequent events obeying first-order kinetics (exponential decay). In practice, replicated MD simulations are started in a particular basin state in search for a transition to an adjacent basin state on M non-correlated processors. Whenever a transition is detected on any processor, the... 

Panel d illustrates parallel replica dynamics (PRD). First, a system A is replicated on a large number p of processors running in parallel (here, p=4). Ater randomization of momenta and equilibration, the dynamics of all p uncorrelated replicas are monitored at the same temperature. The simulation clock stops when the first transition of interest is detected in any of replicas. After that, the simulation clock is advanced by the accumulated trajectory time summed over all replicas, the detected configuration (B) is replicated on all processors, and the whole process is restarted. 

Prominent among the methods for exploring the atomic scale dynamics of a system, including relaxation and rare events, are temperature-accelerated dynamics (TAD) [39], hyperdynamics [40] and parallel replica [41], all developed by Voter and coworkers. These techniques build on statistical mechanics principles for infrequent event systems, and as such do not make any prior assumptions regarding the atomistic mechanisms. They are designed to simply allow the system to evolve more quickly from state to state than they would in normal MD, provided that the barriers are relatively high compared to kT. 

Very recently, Uberuaga employed both TAD and parallel replica simulations to study the formation of fullerene and graphene from carbon nanotube fragments [46]. Using 39 processors, they obtained a boost factor of 28 in the parallel replica simulations, whereas the TAD simulations resulted in boost factors in the range 10-1400 (depending on the exact structure simulated). While the boost factor of parallel replica is typically the lowest of the three methods, it is important to realize that the boost can be trivially increased by increasing the number of processors. 

Voter A (1998) Parallel replica method for dynamics of infi-e-quent events. Phys Rev B Condens Matter 57(22) 13985-13988... 

For systems in which the dynamics consist of long stays in the basins around potential energy minima interrupted by swift hops between them passing through saddle points, the assumptions of TST are often obeyed and the long time dynamics can be studied with the accelerated MD methods [20] discussed in Sect. 4. hi these approaches, which include parallel replica dynamics, hyperdynamics, and temperature-accelerated dynamics, the rate of esct ie from the minima is artificially enhanced in one way or another. The natural dynamics on long time scales is then reconstructed from such boosted simulations and often dramatic speed-ups can be achieved. 

In the parallel replica dynamics method the time scale of MD simulations is extended by distributing the computation on many processors in a way that requires only tittle information exchange between them yielding almost linear speed-up in many cases. This method is applicable whenever the distribution of escape times t from a potential (or free) energy basin is exponential, ... 

The parallel replica formalism has been generalized to non-exponential escape time distributions. In this case, the calculation of the advanced time becomes more involved [146],... 

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