M. J. Ruiz-Montero

Numerical calculation of the rate of crystal nucleation in a Lennard‐Jones system at moderate undercooling

We report a computer‐simulation study of the rate of homogeneous crystal nucleation and the structure of crystal nuclei in a Lennard‐Jones system at moderate undercooling. The height of the nucleation barrier has been determined using umbrella sampling, whereas the barrier crossing rate is calculated using molecular dynamics simulation. The simulations clearly show that the barrier crossing is a diffusive process. Nevertheless, the kinetic prefactor in the nucleation rate is found to be some two orders of magnitude larger than predicted by classical nucleation theory. The height of the barrier is in good agreement with the theoretical prediction. Although the Lennard‐Jones system has a stable face‐centered cubic (fcc) phase below the melting line, the precritical nuclei are found to be mainly body‐centered cubic (bcc) ordered. As they grow to their critical size, they become more fcc ordered in the core. However, the critical and postcritical nuclei retain a high degree of bcc ordering in the interface. F...

Numerical calculation of the rate of homogeneous gas-liquid nucleation in a Lennard-Jones system

We report a computer-simulation study of the absolute rate of homogeneous gas–liquid nucleation in a Lennard-Jones system. The height of the barrier has been computed using umbrella sampling, whereas the kinetic prefactor is calculated using molecular dynamics simulations. The simulations show that the nucleation process is highly diffusive. We find that the kinetic prefactor is a factor of 10 larger than predicted by classical nucleation theory.

Simulation of homogeneous crystal nucleation close to coexistence

We discuss a numerical scheme to study homogeneous crystal nucleation. Using this approach, it is possible to compute the height of the free energy barrier that separates the solid from the liquid phase and the rate at which this barrier is crossed. We point out that there is a fundamental difference between the use of a global- and a local-order parameter to measure the degree of crystallinity. Using a global-order parameter, precritical nuclei may break up spontaneously for entropic reasons. Near the top of the barrier the nuclei combine to form a relatively large cluster. The transition from many small clusters to one large cluster is discussed in some detail. Finally we present a new method that allows us to avoid this entropic cluster break up.

Efficient schemes to compute diffusive barrier crossing rates

The formulation of the classical barrier-crossing problem is reviewed in the context of numerical simulations, with the focus on barrier crossing problems where the reaction coordinate depends in a non-trivial way on the Cartesian coordinates of many particles. Often it is convenient to measure the barrier height using constrained dynamics. Such a calculation requires a knowledge of the Jacobian for the coordinate transformation between Cartesian and generalized (‘reaction’) coordinates, and it is shown that the calculation of this Jacobian can be simplified. The conventional expression for the crossing rate is found to become computationally inefficient when the barrier crossing is diffusive. An alternative formulation of the barrier-crossing rate is given that leads to much better statistical accuracy in the computed crossing rates.

Self-diffusion in freely evolving granular gases

A self-diffusion equation for a freely evolving gas of inelastic hard disks or spheres is derived starting from the Boltzmann–Lorentz equation, by means of a Chapman–Enskog expansion in the density gradient of the tagged particles. The self-diffusion coefficient depends on the restitution coefficient explicitly, and also implicitly through the temperature of the system. This latter introduces also a time dependence of the coefficient. As in the elastic case, the results are trivially extended to the Enskog equation. The theoretical predictions are compared with numerical solutions of the kinetic equation obtained by the direct simulation Monte Carlo method, and also with molecular dynamics simulations. An excellent agreement is found, providing mutual support to the different approaches.

Energy partition and segregation for an intruder in a vibrated granular system under gravity.

The difference of temperatures between an impurity and the surrounding gas in an open vibrated granular system is studied. It is shown that, in spite of the high inhomogeneity of the state, the temperature ratio remains constant in the bulk of the system. The lack of energy equipartition is associated to the change of sign of the pressure diffusion coefficient for the impurity at certain values of the parameters of the system, leading to a segregation criterium. The theoretical predictions are consistent with previous experimental results, and also in agreement with molecular dynamics simulation results reported in this Letter.

Velocity distribution of fluidized granular gases in the presence of gravity.

The velocity distribution of a fluidized dilute granular gas in the direction perpendicular to the gravitational field is investigated by means of molecular dynamics simulations. The results indicate that the velocity distribution can be exactly described neither by a Gaussian nor by a stretched exponential law. Moreover, it does not exhibit any kind of scaling. In fact, the actual shape of the distribution depends on the number of monolayers at rest, on the restitution coefficient and on the height at what it is measured. The role played by the number of particle-particle collisions as compared with the number of particle-wall collisions is discussed.

Transversal inhomogeneities in dilute vibrofluidized granular fluids

The spontaneous symmetry breaking taking place in the direction perpendicular to the energy flux in a dilute vibrofluidized granular system is investigated, using both a hydrodynamic description and simulation methods. The latter include molecular dynamics and direct Monte Carlo simulation of the Boltzmann equation. A marginal stability analysis of the hydrodynamic equations, carried out in the WKB approximation, is shown to be in good agreement with the simulation results. The shape of the hydrodynamic profiles beyond the bifurcation is discussed.

Instability and spatial correlations in a dilute granular gas

Direct Monte Carlo simulation is used to investigate the stability of a dilute freely evolving granular gas of hard disks. The boundary between stability and instability in the plane (α,L), where α is the restitution coefficient and L the size of the system, has been delineated. Instability is associated with the buildup of spatial correlations, which describes the formation of velocity vortices in the system. The simulation results are compared with theoretical predictions presented recently, and a good agreement is found.

Hydrodynamic modes, Green–Kubo relations, and velocity correlations in dilute granular gases

It is shown that the hydrodynamic modes of a dilute granular gas of inelastic hard spheres can be identified, and calculated in the long wavelength limit. Assuming they dominate at long times, formal expressions for the Navier–Stokes transport coefficients are derived. They can be expressed in a form that generalizes the Green–Kubo relations for molecular systems, and it is shown that they can also be evaluated by means of N-particle simulation methods. The form of the hydrodynamic modes to zeroth order in the gradients is used to detect the presence of inherent velocity correlations in the homogeneous cooling state, even in the low density limit. They manifest themselves in the fluctuations of the total energy of the system. The theoretical predictions are shown to be in agreement with molecular dynamics simulations. Relevant related questions deserving further attention are pointed out.