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Distribution of melting times and critical droplet in kinetic Monte Carlo and molecular dynamics
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10.1063/1.4775773
/content/aip/journal/jcp/138/3/10.1063/1.4775773
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/3/10.1063/1.4775773

Figures

Image of FIG. 1.
FIG. 1.

Number N L of liquid particles versus time t. The solid line gives the results of a molecular dynamics (MD) simulation for a volume fraction ϕ = 0.506 and a total number of particles N = 13 824. The dashed line gives the results of a kinetic Monte Carlo (KMC) simulation for the same total number of particles, the time step Δt = 10−2 and the dynamical parameters n l = 5, n s = 7 and l 0 = 0.8, l 12 = 22, s 0 = 0.5, s 12 = 15.

Image of FIG. 2.
FIG. 2.

(a) Cumulative density function (cdf) of the waiting time τKMC deduced from kinetic Monte Carlo simulations (circles) for an initial configuration with a given initial number of liquid sites N L = 158 and for different seeds of the random number generator. The total number of sites is N = 1728 and the parameters are n l = 7, n s = 8 and l 0 = 1, l 12 = 24, s 0 = 0.6, s 12 = 11. The solid line is the best Weibull-type fit. The inset gives the corresponding probability density function (pdf) for KMC (circles) and the derivative of the cdf fit (solid line). (b) Same caption as (a) for N L = 204. (c) Same caption as (a) for N L = 226. (d) Same caption as (a) for N L = 229.

Image of FIG. 3.
FIG. 3.

(a) Cumulative density function (cdf) of the waiting time τMD deduced from molecular dynamics (circles) for initial configurations with identical particle positions corresponding to an initial number N L = 337 of liquid particles, and different velocities. The total number of particles is N = 1728 and the volume fraction is ϕ = 0.499. The solid line is the best Weibull-type fit. The inset gives the corresponding probability density functions (pdf) for MD (circles) and the derivative of the cdf fit (solid line). (b) Same caption as (a) for a different choice of initial particle positions with N L = 432. (c) Same caption as (b) with N L = 494.

Image of FIG. 4.
FIG. 4.

Snapshot of the initial MD spatial configuration used to obtain Fig. 3(b) . The white particles are solid and the red particles are liquid.

Image of FIG. 5.
FIG. 5.

Cumulative density functions (cdf) of the waiting time τKMC deduced from kinetic Monte Carlo simulations from two configurations containing a single initial spherical drop of N L = 38 liquid sites (dashed line), N L = 68 liquid sites (solid line) and for different seeds of the random number generator. The other parameters are given in the caption of Fig. 2(a) . For the sake of efficiency, the simulations are stopped at time 2000.

Image of FIG. 6.
FIG. 6.

Plateau height h of the cumulative density function of melting time deduced from kinetic Monte Carlo simulations versus number N L of liquid sites in the initial configuration with a single spherical droplet for n l = 7, n s = 8 (circles, solid line), n l = 6, n s = 6 (squares, dashed line) and l 0 = 1, l 12 = 24, s 0 = 0.6, s 12 = 11.

Image of FIG. 7.
FIG. 7.

Plateau height of the cdf of the waiting time τKMC deduced from kinetic Monte Carlo simulations versus droplet anisotropy λ max min for N = 1728, l 0 = 1, l 12 = 24, s 0 = 0.6, s 12 = 11, and an initial droplet of N L = 72 liquid sites. The squares correspond to n l = 6, n s = 7 and the circles to n l = 7, n s = 8. The lines give the plateau height of the cdf corresponding to the spherical droplet for n l = 6 and n s = 7 (solid line) and for n l = 7 and n s = 8 (dashed line).

Image of FIG. 8.
FIG. 8.

Variation of the waiting time before melting with the total number N of sites or particles. All the sites or particles are initially solid. The circles give the results of kinetic Monte Carlo simulations which scale as 1/N (solid line) for the same parameter values as in Fig. 2(a) . The pluses give the results of molecular dynamics simulations for ϕ = 0.499.

Tables

Generic image for table
Table I.

Values of plateau height h of the cumulative density functions given in Figs. 3(a)–3(c) for the three different spatial configurations (a)–(c) and parameters λ l , k l , λ r , and k r of the corresponding Weibull-type fits. The values are given with an uncertainty of 1 on the last significant figure.

Generic image for table
Table II.

Values of the plateau height h of the cumulative density function of melting time for different values of the parameters n l and n s , different droplet sizes N L , and two system sizes N. The value of the parameters l 0, l 12, s 0, s 12 is the same as in Fig. 2(a) .

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/content/aip/journal/jcp/138/3/10.1063/1.4775773
2013-01-18
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Distribution of melting times and critical droplet in kinetic Monte Carlo and molecular dynamics
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/3/10.1063/1.4775773
10.1063/1.4775773
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