Generalized Hydrodynamics and Analysis of Current Correlation Functions

Abstract

A generalization of the Navier-Stokes equation, valid for wavelengths and times of a molecular order of magnitude, is discussed on the basis of viscoelastic behavior of simple classical liquids. In this theory, transport coefficients are replaced by appropriate viscoelastic memory functions. The theory is verified by analyzing the data on current-correlation functions obtained from computer experiments.Three different models for the time dependence of the viscoelastic memory are investigated, namely, a single-exponential decay, a modified-exponential decay, and a Gaussian decay. It is observed that the memory functions are approximately Gaussian, at least for times of the order of one or two relaxation times. This is in agreement with a conjecture of Forster, Martin, and Yip. The wave-number dependence of the half-width of the Gaussian decay, and of the longitudinaland shear-viscosity coefficients, are found from computer experiments. The extrapolated values of these transport coefficients, in the limit k -0, are in good agreement with experiments on liquid argon.

Microscopic dynamics in liquid metals: The experimental point of view

“…This kinematic region lies above the region were collective modes could be expected, so the study mainly deals with the quasielastic spectral component. Generalized hydrodynamics models based upon a single relaxation time were tested against the experimental data utilizing different approximation for the memory function shape (Ailawadi et al, 1971;Lovesey, 1971). Experimental data were then unfolded by instrumental resolution modelling the quasielastic shape as Lorenzian and the resolution as gaussian.…”

Collective dynamics in liquid aluminum near the melting temperature: Theory and computer simulation

“…However, their ratios ξ 5, 4 (k) and ξ 5,6 (k) are close to unity. Therefore, we may assume that (25) In other words, beginning from (k), the high-order frequency parameters virtually coincide.…”

“…Since the quantities reciprocal to the frequency parameters, i.e., 1/ (k), characterize the quadratic time scales of the relaxation processes related to the fluxes of the A j -1 (k) variables [2,31], condition (25) allows us to pass from the infinite set of dynamic variables (9) to the finite set (26) that is, it allows us to decrease the number of variables required for the description of the collective dynamics of particles [11]. As was shown above, the autocorrelation functions of the variables from set (26) are related to the autocorrelators of the longitudinal components of the hydrodynamic variables and their fluxes.…”

“…(i) the transition to the Markovian limit of Van Hove at a certain jth relaxation level, which is performed by introducing the so-called slow time τ = λ 2 t (λ 0) [24]; (ii) the method of model memory functions, where the M j (k, t) function of the jth order is approximated by a certain simplified model function, such as an exponential function, a Gaussian function, or a hyperbolic secant or by their linear combination [25][26][27][28][29];…”

Collective dynamics in noble-gas and other very simple classical fluids

“…Various attempts to theoretically determine the time dependence of the memory function were made in the past mainly by testing different expressions against dynamics simulations [41,42]. It is a matter of fact, however, that in the greatest part of the works that appeared in the literature on the subject, M (Q, t) is given the form of a δ-function and/or a number of exponentials [39].…”