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Register a new userKinetics of Domain Growth and Aging in a Two-Dimensional Off-lattice System
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We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we have analyzed simulation data on structure, growth and aging for nonequilibrium evolutions in the model. These data were obtained following quenches of well-equilibrated homogeneous configurations, with density close to the critical value, to various temperatures inside the miscibility gap, having vapor-liquid as well as vapor-solid coexistence. For the vapor-liquid phase separation we observe that $ell$, the average domain length, grows with time ($t$) as $t^{1/2}$, a behavior that has connection with hydrodynamics. At low enough temperature, a sharp crossover of this time dependence to a much slower, temperature dependent, growth is identified within the time scale of our simulations, implying solid-like final state of the high density phase. This crossover is, interestingly, accompanied by strong differences in domain morphology and other structural aspects between the two situations. For aging, we have presented results for the order-parameter autocorrelation function. This quantity exhibits data-collapse with respect to $ell/ell_w$, $ell$ and $ell_w$ being the average domain lengths at times $t$ and $t_w$ ($leq t$), respectively, the latter being the age of a system. Corresponding scaling function follows a power-law decay: $~sim (ell/ell_w)^{-lambda}$, for $tgg t_w$. The decay exponent $lambda$, for the vapor-liquid case, is accurately estimated via the application of an advanced finite-size scaling method. The obtained value is observed to satisfy a bound.
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The Chapter is devoted to reviewing the main features of aging in non disordered systems relaxing via domain growth, after an istantaneous temperature quench. Using the autocorrelation and autoresponse functions to gauge the deviation from equilibrium, an hierarchy of processes is obtained by changing the temperature of the quench and the space dimensionality. The special role of the lower critical dimensionality is highlighted. Basic properties like the separation of the time scales and the splitting of degrees of freedom into fast and slow variables are treated in detail, both in general terms and through analytical calculations in solvable models. Though domain growth is believed to be a well understood paradigma of slow relaxation, emphasis of this review is on the non trivial aspects, not yet fully clarified, like the response function scaling behavior.
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We consider an off-lattice liquid crystal pair potential in strictly two dimensions. The potential is purely repulsive and short-ranged. Nevertheless, by means of a single parameter in the potential, the system is shown to undergo a first-order phase transition. The transition is studied using mean-field density functional theory, and shown to be of the isotropic-to-nematic kind. In addition, the theory predicts a large density gap between the two coexisting phases. The first-order nature of the transition is confirmed using computer simulation and finite-size scaling. Also presented is an analysis of the interface between the coexisting domains, including estimates of the line tension, as well as an investigation of anchoring effects.
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We numerically investigate the long-time behavior of the density-density auto-correlation function in driven lattice gases with particle exclusion and periodic boundary conditions in one, two, and three dimensions using precise Monte Carlo simulations. In the one-dimensional asymmetric exclusion process on a ring with half the lattice sites occupied, we find that correlations induce extremely slow relaxation to the asymptotic power law decay. We compare the crossover functions obtained from our simulations with various analytic results in the literature, and analyze the characteristic oscillations that occur in finite systems away from half-filling. As expected, in three dimensions correlations are weak and consequently the mean-field description is adequate. We also investigate the relaxation towards the nonequilibrium steady state in the two-time density-density auto-correlations, starting from strongly correlated initial conditions. We obtain simple aging scaling behavior in one, two, and three dimensions, with the expected power laws.
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