Kinetic Theory of Response Functions for the Hard Sphere Granular Fluid

The response functions for small spatial perturbations of a homogeneous granular fluid have been described recently. In appropriate dimensionless variables, they have the form of stationary state time correlation functions. Here, these functions are expressed in terms of reduced single particle functions that are expected to obey a linear kinetic equation. The functional assumption required for such a kinetic equation, and a Markov approximation for its implementation are discussed. If, in addition, static velocity correlations are neglected, a granular fluid version of the linearized Enskog kinetic theory is obtained. The derivation makes no a priori limitation on the density, space and time scale, nor degree of inelasticity. As an illustration, recently derived Helfand and Green-Kubo expressions for the Navier-Stokes order transport coefficients are evaluated with this kinetic theory. The results are in agreement with those obtained from the Chapman-Enskog solution to the nonlinear Enskog kinetic equation.Comment: Submitted to J. Stat. Mec

Solidity of viscous liquids. IV. Density fluctuations

This paper is the fourth in a series exploring the physical consequences of the solidity of highly viscous liquids. It is argued that the two basic characteristics of a flow event (a jump between two energy minima in configuration space) are the local density change and the sum of all particle displacements. Based on this it is proposed that density fluctuations are described by a time-dependent Ginzburg-Landau equation with rates in k-space of the form $\Gamma_0+Dk^2$ with $D\gg\Gamma_0a^2$ where $a$ is the average intermolecular distance. The inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian (free energy) may be taken to be ultra local. As an illustration of the theory the case with the simplest non-trivial Hamiltonian is solved to second order in the Gaussian approximation, where it predicts an asymmetric frequency dependence of the isothermal bulk modulus with Debye behavior at low frequencies and an $\omega^{-1/2}$ decay of the loss at high frequencies. Finally, a general formalism for the description of viscous liquid dynamics, which supplements the density dynamics by including stress fields, a potential energy field, and molecular orientational fields, is proposed

Solidity of viscous liquids. V. Long-wavelength dominance of the dynamics

This paper is the fifth in a series exploring the physical consequences of the solidity of glass-forming liquids. Paper IV proposed a model where the density field is described by a time-dependent Ginzburg-Landau equation of the nonconserved type with rates in $k$ space of the form $\Gamma_0+Dk^2$. The model assumes that $D\gg\Gamma_0a^2$ where $a$ is the average intermolecular distance; this inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian (free energy) to a good approximation may be taken to be ultralocal. In the present paper we argue that this is the simplest model consistent with the following three experimental facts: 1) Viscous liquids approaching the glass transition do not develop long-range order; 2) The glass has lower compressibility than the liquid; 3) The alpha process involves several decades of relaxation times shorter than the mean relaxation time. The paper proceeds to list six further experimental facts characterizing equilibrium viscous liquid dynamics and shows that these are readily understood in terms of the model; some are direct consequences, others are quite natural when viewed in light of the model

Therapeutic efficacy of favipiravir against Bourbon virus in mice

Bourbon virus (BRBV) is an emerging tick-borne RNA virus in the orthomyxoviridae family that was discovered in 2014. Although fatal human cases of BRBV have been described, little is known about its pathogenesis, and no antiviral therapies or vaccines exist. We obtained serum from a fatal case in 2017 and successfully recovered the second human infectious isolate of BRBV. Next-generation sequencing of the St. Louis isolate of BRBV (BRBV-STL) showed >99% nucleotide identity to the original reference isolate. Using BRBV-STL, we developed a small animal model to study BRBV-STL tropism in vivo and evaluated the prophylactic and therapeutic efficacy of the experimental antiviral drug favipiravir against BRBV-induced disease. Infection of Ifnar1-/- mice lacking the type I interferon receptor, but not congenic wild-type animals, resulted in uniformly fatal disease 6 to 10 days after infection. RNA in situ hybridization and viral yield assays demonstrated a broad tropism of BRBV-STL with highest levels detected in liver and spleen. In vitro replication and polymerase activity of BRBV-STL were inhibited by favipiravir. Moreover, administration of favipiravir as a prophylaxis or as post-exposure therapy three days after infection prevented BRBV-STL-induced mortality in immunocompromised Ifnar1-/- mice. These results suggest that favipiravir may be a candidate treatment for humans who become infected with BRBV

Phonon-like and single particle dynamics in liquid lithium

The dynamic structure factor, S(Q,E), of liquid lithium (T=475 K) has been determined by inelastic x-ray scattering (IXS) in the momentum transfer region (Q = 1.4-110 nm-1). These data allow to observe how, in a simple liquid, a phonon-like collective mode evolves towards the single particle dynamics. As a function of Q, one finds: i) at low Q's, a sound mode with a positive dispersion of the sound velocity, ii) at intermediate Q's, excitations whose energy oscillates similarly to phonons in the crystal Brillouin zones, and iii) at high Q's, the S(Q,E) approaches a Gaussian shape, indicating that the single particle dynamics has been reached.Comment: 3 pages and 5 figure

Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glass Transition

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.Comment: 34 Pages, Plain TeX, 12 PostScript Figures (not included, available on request

Short-time inertial response of viscoelastic fluids measured with Brownian motion and with active probes

We have directly observed short-time stress propagation in viscoelastic fluids using two optically trapped particles and a fast interferometric particle-tracking technique. We have done this both by recording correlations in the thermal motion of the particles and by measuring the response of one particle to the actively oscillated second particle. Both methods detect the vortex-like flow patterns associated with stress propagation in fluids. This inertial vortex flow propagates diffusively for simple liquids, while for viscoelastic solutions the pattern spreads super-diffusively, dependent on the shear modulus of the medium

Universal divergenceless scaling between structural relaxation and caged dynamics in glass-forming systems

On approaching the glass transition, the microscopic kinetic unit spends increasing time rattling in the cage of the first neighbours whereas its average escape time, the structural relaxation time $\tau_\alpha$, increases from a few picoseconds up to thousands of seconds. A thorough study of the correlation between $\tau_\alpha$ and the rattling amplitude, expressed by the Debye-Waller factor (DW), was carried out. Molecular-dynamics (MD) simulations of both a model polymer system and a binary mixture were performed by varying the temperature, the density $\rho$, the potential and the polymer length to consider the structural relaxation as well as both the rotational and the translation diffusion. The simulations evidence the scaling between the $\tau_\alpha$ and the Debye-Waller factor. An analytic model of the master curve is developed in terms of two characteristic length scales pertaining to the distance to be covered by the kinetic unit to reach a transition state. The model does not imply $\tau_\alpha$ divergences. The comparison with the experiments supports the numerical evidence over a range of relaxation times as wide as about eighteen orders of magnitude. A comparison with other scaling and correlation procedures is presented. The study suggests that the equilibrium and the moderately supercooled states of the glassformers possess key information on the huge slowing-down of their relaxation close to the glass transition. The latter, according to the present simulations, exhibits features consistent with the Lindemann melting criterion and the free-volume model.Comment: 8 pages, 11 figure

Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several CFD approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the Piecewise Parabolic Method) and are found to give good results (about 10% error) for the variances of momentum and energy fluctuations. However, neither of these schemes accurately reproduces the density fluctuations. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce density fluctuations. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS PDE solver are compared with theory, when available, and with molecular simulations using a Direct Simulation Monte Carlo (DSMC) algorithm

Static and Dynamic Properties of a Viscous Silica Melt Molecular Dynamics Computer Simulations

We present the results of a large scale molecular dynamics computer simulation in which we investigated the static and dynamic properties of a silica melt in the temperature range in which the viscosity of the system changes from O(10^-2) Poise to O(10^2) Poise. We show that even at temperatures as high as 4000 K the structure of this system is very similar to the random tetrahedral network found in silica at lower temperatures. The temperature dependence of the concentration of the defects in this network shows an Arrhenius law. From the partial structure factors we calculate the neutron scattering function and find that it agrees very well with experimental neutron scattering data. At low temperatures the temperature dependence of the diffusion constants $D$ shows an Arrhenius law with activation energies which are in very good agreement with the experimental values. With increasing temperature we find that this dependence shows a cross-over to one which can be described well by a power-law, D\propto (T-T_c)^gamma. The critical temperature T_c is 3330 K and the exponent gamma is close to 2.1. Since we find a similar cross-over in the viscosity we have evidence that the relaxation dynamics of the system changes from a flow-like motion of the particles, as described by the ideal version of mode-coupling theory, to a hopping like motion. We show that such a change of the transport mechanism is also observed in the product of the diffusion constant and the life time of a Si-O bond, or the space and time dependence of the van Hove correlation functions.Comment: 30 pages of Latex, 14 figure