Nonlinear hydrodynamics of a hard-sphere fluid near the glass transition

Abstract

We conduct a numerical study of the dynamic behavior of a dense hard sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through stretched exponential decay and two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wavenumber dependence of the kinetics is extensively explored. The connection of our results with experiment, mode coupling theory, and molecular dynamics results is discussed. 1992 PACS numbers: 64.70Pf, 61.20Ja, 61.20Lc 2

Time scales for transitions between free-energy minima of a dense hard-sphere system

“…The other runs yielded only lower bounds τ 1 > 120,000 MCS, that is, the system remained in the domain of attraction of the initial minimum. We did not need to calculate τ 1 for n * ≤ 0.93 because our previous studies 17,18 showed that for such densities, a system initially prepared in the liquid state, remains in the vicinity of the uniform liquid minimum for all time scales accessible in our Langevin simulations. We see from Fig.…”

“…In our previous work, [17][18][19][20] we have studied the dynamical properties of this model by introducing the appropriate Langevin dynamics. Briefly, one introduces the additional current field g(r) and the total free energy:…”

“…The Langevin dynamics used in our previous studies [17][18][19] is used (in conjunction with the free energy minimization routine, as described above) only in the determination of the initial configurations to be used in the Monte Carlo simulations. Since our goal in the present study is to estimate the characteristic time for thermally activated transitions from shallow glassy minima to deeper, more ordered ones, a proper choice of the initial state is important.…”

“…Although a different Langevin simulation method could in principle be developped to study the dynamics in this density range, the methods of Refs. (17)(18)(19)(20), which are based on a liquid-like formulation, are not physically appropriate for such a study. In practice, attempts to use these methods at higher densities lead to numerical instabilities associated with large-scale density fluctuations present at the inhomogeneous minima.…”

“…This scenario, however, remains speculative because the existence of such a phase transition has not yet been demonstrated convincingly for any physically realistic system. Recently, we have carried out a number of investigations [17][18][19][20] which suggest that elements of these two apparently dissimilar descriptions of the glass transition should be combined for the development of a full understanding of the observed phenomena. This conclusion was based on the results of a numerical study of a set of Langevin equations which describe the nonlinear fluctuating hydrodynamics of a dense hard sphere liquid.…”