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Rare-event sampling: Occupation-based performance measures for parallel tempering and infinite swapping Monte Carlo methods
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10.1063/1.4765060
/content/aip/journal/jcp/137/20/10.1063/1.4765060
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/20/10.1063/1.4765060

Figures

Image of FIG. 1.
FIG. 1.

Occupation traces for three-temperature PT (top row) and PINS (bottom row) simulations for Ar13. T1 = 30 K and T3 = 40 K for all simulations, while T2 = 35 K for simulations in left column and 39 K for those in right column.

Image of FIG. 2.
FIG. 2.

Plots of the average number of moves required for a round-trip transit of the computational ensemble, ⟨nrt⟩ as function of T2, for extended versions of the three-temperature Ar13 simulations of the type in Fig. 1 .

Image of FIG. 3.
FIG. 3.

Approach of Sf(nmove) (c.f., Eq. (2.3) ) to its uniform limiting value for the three-temperature PINS and PT simulations of Ar13 used in Table I and described in the text. T1 = 30 K, T3 = 40 K, T2 = 35 K or 39 K.

Image of FIG. 4.
FIG. 4.

Plot of ln(Smax − Sf) for the three-temperature Ar13 results of Fig. 3 .

Image of FIG. 5.
FIG. 5.

Plots of C(s) (c.f., Eq. (2.4) ) for the three-temperature Ar13 simulations of Fig. 3 .

Image of FIG. 6.
FIG. 6.

A portion of occupation traces for 66-temperature Ar38 PINS (black) and PT (red) simulations discussed in the text. The vertical axis denotes the temperature index (1–66) as a function of the number of moves in the simulation.

Image of FIG. 7.
FIG. 7.

A histogram of the PINS occupation trace shown in Fig. 6 showing the number of times the various temperature indices are visited, M(n), as a function of n.

Image of FIG. 8.
FIG. 8.

A plot of Sf(nmove) obtained for Ar13 using PINS and PT methods for the various 24-temperature ensembles described in the text. The apparent “break” in the PINS-24a results occurs at an Sf value of roughly 2.5, a value that corresponds to an active number of temperatures (Na) of ∼12.

Image of FIG. 9.
FIG. 9.

Plot of ln(Smax − Sf) for results in Fig. 8 .

Image of FIG. 10.
FIG. 10.

C(s) for the PINS Ar13 results obtained using the three, 24-temperature ensembles described in the text. PT results for ensemble-c are shown for comparison (dashed line near top of plot).

Image of FIG. 11.
FIG. 11.

Brief portions of occupation traces for PINS (top panel) and PT (bottom panel) simulations for Ar13 obtained using 24-temperature ensemble-c (see text for details).

Image of FIG. 12.
FIG. 12.

Plots of the occupation entropy, Sf(nmove), for 66-temperature PINS and PT simulations of the Ar38 system. The two PINS results correspond to simulations that are initiated in the global minimum geometry (black curve) or lowest-lying icosahedral minimum (red curve). The limiting Sf value of ln(66) is shown for reference.

Image of FIG. 13.
FIG. 13.

Plot of ln(Smax − Sf) for results in Fig. 12 .

Image of FIG. 14.
FIG. 14.

A plot of ⟨Q4(T)⟩ for the Ar38 cluster obtained by the PINS simulations described in the text. Results in black (red) are obtained using a simulation initialized using the fcc global minimum (icosahedral local minimum) structure. For clarity and as an aid in comparing the two simulations ⟨Q4(T)⟩ only values for every other (every fourth) temperature are shown for the fcc (icosahedral) results.

Image of FIG. 15.
FIG. 15.

Q4 values for an extended portion of the global minimum initiated occupation trace of Fig. 6 .

Image of FIG. 16.
FIG. 16.

A history of the number of configurations (out of 66) in the two PINS Ar38 simulations described in the text for which Q4 ≤ 0.09.

Image of FIG. 17.
FIG. 17.

Block averages of Q4 for Ar38 for T1 = 10 K, T2 = 14.9350 K for the PINS simulations described in the text.

Image of FIG. 18.
FIG. 18.

Shown are the Q4 values for T = 22.727 K for a short, post warm up portion of the icosahedral minimum initiated Ar38 PINS simulation. Compare with Fig. 11 of Ref. 29 .

Tables

Generic image for table
Table I.

Observed fractions of total moves (fn) spent at each of the ensemble temperatures by two three-temperature Ar13 parallel tempering (PT) and partial swapping (PINS) simulations. In both ensembles, T1 = 30 K and T3 = 40 K, while in one ensemble T2 = 35 K and in the other T2 = 39 K.

Generic image for table
Table II.

The temperatures used in the PINS Ar38 computational ensemble.

Generic image for table
Table III.

Average of Sρ values, ⟨Sρ⟩ , for Ar38 PINS simulation obtained using the computational ensemble shown in Table II . For reference, the maximum values for S ρ correspond to ln(3!) = 1.792 and ln(6!) = 6.579.

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2012-11-27
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Rare-event sampling: Occupation-based performance measures for parallel tempering and infinite swapping Monte Carlo methods
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/20/10.1063/1.4765060
10.1063/1.4765060
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