(a) Probability density function (pdf) of the interparticle distance (solid line). The vertical solid line gives the chosen cutoff radius r c . The dashed-dotted, dashed, and dotted lines correspond to the first-, second-, and third-neighbor peaks. (b) Pdf of S for a metastable solid at ϕ = 0.506 (solid line), a stable solid at ϕ m = 0.55 (dotted line), and a stable liquid at ϕ s = 0.49 (dashed line). (c) Pdf of the number n cn of connected neighbors per particle for the same parameters as in (b).
(a) Number N L of liquid particles versus time t for the three different descriptions. The solid line gives the results of one 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 one KMC simulation for the same total number of particles and the time step Δt = 10−2. The dotted line gives the two stable stationary states of the mean-field model. In the two last approaches, the dynamical parameters are n l = 5, n s = 7 and l 0 = 0.8, l 12 = 22, s 0 = 0.5, s 12 = 15. (b) Time evolution of the global order parameter Q 6 in the same MD simulation as in (a).
Variation of deduced from molecular dynamics with the volume fraction ϕ for different total number of particles N = 576 (circles), N = 1728 (crosses), and N = 13 824 (plus). In the inset, the probability density function of the waiting time τMD (circle) for different initial particle velocities and its best fit dW/dτ with λ = 25 000 and k = 1.1 (solid line) are shown for N = 576 and ϕ = 0.497.
Variation of the mean waiting time before melting occurs ⟨τMD⟩ deduced from molecular dynamics with the total number N of particles for a volume fraction ϕ = 0.499.
Finite size effects on coexistence at equilibrium in molecular dynamics. (a) Time evolution of the global order parameter Q 6 for a total number of particles N = 110 592 at the volume fraction ϕ = 0.504 (solid line) and for N = 13 824 at ϕ = 0.499 (dashed line). The last value of ϕ is chosen such that the mean waiting times compare in both cases. (b) Pdf of S for coexistent liquid and solid at equilibrium at ϕ = 0.504 for N = 110 592 (solid line), a stable solid at ϕ m = 0.55 for N = 110 592 (dotted line), and an equilibrated liquid at ϕ = 0.504 for N = 13 824 (dashed line).
Molecular dynamics results for a volume fraction ϕ = 0.506, a total number of particles N = 13 824, and the threshold values S tr = 0.4 and n tr = 4: Scaled probabilities l n = P n (S → L)/Δt MD for a solid particle surrounded by n liquid neighbors to become liquid during Δt MD versus n for two values of the time interval Δt MD = 10−3 (solid line) and Δt MD = 10−4 (dashed line). Same results for s n = P n (L → S)/Δt MD for a liquid particle surrounded by n solid neighbors to become solid, for Δt MD = 10−3 (dashed-dotted line) and Δt MD = 10−4 (dotted line).
Same caption as in Fig. 6 for l n (a), s n (b), Δt MD = 10−3, and different threshold values: S tr = 0.2 for n tr = 7 (solid line) and n tr = 8 (dotted line), S tr = 0.3 for n tr = 6 (solid line) and n tr = 7 (dotted line), S tr = 0.4 for n tr = 4 (solid line) and n tr = 5 (dotted line). Lines become bolder as S tr increases.
Variation of the mean waiting time before melting occurs ⟨τKMC⟩ deduced from the KMC simulations for different values of the boundaries n s and n l and the same other parameter values as in Fig. 2.
Article metrics loading...
Full text loading...