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A spatial averaging approach to rare-event sampling
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10.1063/1.3220629
/content/aip/journal/jcp/131/10/10.1063/1.3220629
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/10/10.1063/1.3220629

Figures

Image of FIG. 1.
FIG. 1.

Plots of the asymptotic convergence parameters, , and acceptance probabilities (red curves) as functions of the Metropolis box size, , for the harmonic oscillator using the Metropolis method for ( maximum at smaller value, more steeply decaying acceptance probability) and for

Image of FIG. 2.
FIG. 2.

As in Fig. 1, except for the quartic oscillator. Note the qualitative similarity to the results of Fig. 1.

Image of FIG. 3.
FIG. 3.

Plots of the asymptotic convergence parameters, , and acceptance probabilities (red curves) as functions of the Metropolis box size, , for the double-well potential using the Metropolis method for (lower curve, more steeply decaying acceptance probability) and for

Image of FIG. 4.
FIG. 4.

Plots of the asymptotic convergence parameters, , and acceptance probabilities (red curves) as functions of the Metropolis box size, , for the triple-well potential using the Metropolis method for , 0.32, and 0.64. For the range shown in the plot, (the acceptance probability) is an increasing (decreasing) function of the temperature.

Image of FIG. 5.
FIG. 5.

Shown are plots of the natural log of the asymptotic convergence parameter for the triple-well potential as a function of the reciprocal temperature obtained using the Metropolis method using different values of , the sampling box size. The results (in order of decreasing activation energy) correspond to , 0.50, 0.75, 1.00, and 1.50.

Image of FIG. 6.
FIG. 6.

Plot of for the double-well potential for and for (solid line), (longer dashes), and (shorter dashes). The modified densities are obtained by numerically averaging the original, classical density over a Gaussian distribution of the appropriate width.

Image of FIG. 7.
FIG. 7.

A plot of for the triple-well model potential. Other system parameters are and . Conventional Metropolis sampling corresponds to .

Image of FIG. 8.
FIG. 8.

A plot of for the triple-well model potential for (from bottom to top in the graph) , 0.08, 0.16, 0.32, 0.64. The value for all results is . [Note the linear scale for used here vs the logarithmic scale in Fig. 7].

Tables

Generic image for table
Table I.

The apparent activation energies as computed from the slopes of the curves shown in Fig. 5.

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/content/aip/journal/jcp/131/10/10.1063/1.3220629
2009-09-10
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A spatial averaging approach to rare-event sampling
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/10/10.1063/1.3220629
10.1063/1.3220629
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