Nonlinear hydrodynamics and the liquid-glass transition: A numerical study

Nonequilibrium dynamics of four-point correlations of collective density fluctuations in a supercooled liquid

In this paper we study the four-point correlation function χ(4) of collective density fluctuations in a nonequilibrium liquid. The equilibration is controlled by a modified stretched exponential behavior (exp[-(t(w)/τ)(β)]) having the relaxation time τ dependent on the aging time t(w). Similar aging behavior has been seen experimentally in supercooled liquids. The basic equations of fluctuating nonlinear hydrodynamics are solved here numerically to obtain χ(4) for equilibrium and non equilibrium states. We also identify a dynamic length scale ξ from the equilibrated function. ξ(T) grows with fall of temperature T. From a broader perspective, we demonstrate here that the characteristic signatures of dynamical heterogeneities in a supercooled liquid, observed previously in computer simulations of the dynamics of a small number of particles, are also present in the coarse grained equations of generalized hydrodynamics.

Time dependent stretching of aging dynamics in a generalized hydrodynamic model for supercooled liquids

The nonequilibrium dynamics and aging behavior of a supercooled liquid is investigated from an analysis of the correlation of density fluctuations at two different times. The dynamic correlation functions are computed by solving numerically the equations of nonlinear fluctuating hydrodynamics. The aging time dependence follows a modified stretched exponential form with a relaxation time which is dependent on the aging time. This is similar to the behavior seen in the aging data of dielectric response functions of a typical glass forming liquid.

Time-dependent correlations in a supercooled liquid from nonlinear fluctuating hydrodynamics

We solve numerically the equations of nonlinear fluctuating hydrodynamics (NFH). A coarse graining of the density field is applied at each time step to avoid instabilities which otherwise plague the algorithm at long times. The equilibrium correlation of the density fluctuations at different times obtained directly from the solutions of the NFH equations are shown here to be in quantitative agreement with corresponding molecular dynamics simulation data. Low-order perturbative treatment of the these NFH equations obtains the mode coupling model. The latter has been widely studied for understanding the slow dynamics characteristic of the supercooled state. A crucial aspect of this theory is a rounded version of a possible ergodic-nonergodic transition in the supercooled liquid at a temperature T(c) between melting point T(m) and the glass transition temperature T(g). In the present work we demonstrate numerically the role of strongly coupled density fluctuations in giving rise to slow dynamics and how the 1/ρ nonlinearity in the NFH equations of motion is essential in restoring the ergodic behavior in the liquid. The relaxation data indicate that at moderate supercooling near T(c), the time temperature superposition holds. The relaxation gets increasingly stretched with increased supercooling. The relaxation time τ shows an initial power-law divergence approaching a transition temperature T(c) generally identified as the mode coupling temperature. From the direct solutions we obtain a value for T(c) much lower than that typically estimated from solution of low-order integral equations of mode coupling theory. This is in agreement with the trend seen in computer simulations.