# Presentation: 153147

## Parallel Replica Dynamics

- Arthur F. Voter
- Theoretical Division
- Los Alamos National Laboratory
- Los Alamos, New Mexico  USA
- Work supported by DOE/BES

## Parallel Replica Dynamics

## Parallel Replica Dynamics

- Parallelizes time evolution
- Assumptions:
- 	- infrequent events
- 	- exponential distribution of first-escape times

- AFV, Phys. Rev. B, 57, R13985 (1998)

## Parallel Replica Dynamics Procedure

- Replicate entire system on each of M processors.

## Parallel Replica Dynamics Procedure

- Randomize momenta independently on each processor.

## Parallel Replica Dynamics Procedure

- Run MD for short time (dephase) to dephase the replicas.

## Parallel Replica Dynamics Procedure

- Start clock and run thermostatted MD on each processor.
- Watch for transition...

## Parallel Replica Dynamics Procedure

- Stop all trajectories when first transition occurs on *any* processor.

## Parallel Replica Dynamics Procedure

- Sum the trajectory times over all M processors.  Advance simulation
- clock by this tsum

## Parallel Replica Dynamics Procedure

- On the processor where a transition occurred, continue trajectory for a
- time corr to allow correlated dynamical events.

## Parallel Replica Dynamics Procedure

- Advance simulation clock by corr.

## Parallel Replica Dynamics Procedure

- Replicate the new state and begin procedure again.

## Parallel Replica Dynamics

- The summed time (tsum) obeys the correct exponential distribution, and the system escapes to an appropriate state.
- State-to-state dynamics are thus correct; corr stage even releases the TST assumption  [AFV, Phys. Rev. B, 57, R13985 (1998)].
- Good parallel efficiency if  rxn / M >> dephase+corr
- Applicable to any system with exponential first-event statistics

## Detecting a transition

-    - best method depends on the system
-    - simple method for EAM metal systems:
- 	periodically perform steepest-descent quench; 	see if geometry at basin minimum has changed
-    - other methods:
-    	- change in bond connectivity (Kum, Uberuaga)
- 	- change in local order parameter
- 	- change in energy fluctuations (Pande)

## Parallel-replica dynamics example

- Ag(111) island-on-island decay
- Embedded atom (EAM) potential
- Temperature = 400K
- 5 days on 32 processors
- (1 GHz Pentium-IIIs)
- Upper island decays into lower island via step-edge exchange events.
- For this case, parallel replica is even faster than temperature-accelerated dynamics, since barriers are low relative to T.
- F. Montalenti, T.C. Germann and A.F. Voter

## Parallel replica dynamics for driven systems

- 	Stretching a nanotube on ten processors
- 	On each of the 10 processors, strain rate = 107 s-1
- 	Effective system strain rate = 106 s-1
- State-to-state evolution is valid provided the driving rate on each processor is slow enough that the escape rates at any instant in time are independent of the driving rate.
- (Uberuaga, Stuart and Voter, to be published).
- Notes: 	1) during correlated-event time, use the lower (global) driving rate
- 	2) processors must run at same speed (unnecessary for regular 		    parallel-replica)

## Stretching Nanotubes

- unstretched

- =106/s
- yielded at 15%

- =5x108/s
- yielded at 24%

- .

- - Parallel replica dynamics on 40 processors (1 GHz Pentium IIIs)
- - REBO potential [Brenner et al, J. Phys.: Condensed Matter 14, 783 (2002)]
- - T=2000K
- - One pre-existing vacancy

- slow strain rate

- fast strain rate

- .

- Blas Uberuaga
- Steve Stuart

## Final Structure of

- Nanotubes after Yield

- Lower strain rate (106/s)

- Higher strain rate (5x108/s)

- 5-7
- defect

- Blas Uberuaga
- Steve Stuart

## Energy vs Strain for 

- Energy vs Strain for
- Nanotube with a Vacancy

- 5-7
- defect
- formed

- second defect
- formed

- Blas Uberuaga
- Steve Stuart

- THE END