Transport Far From Equilibrium --- Uniform Shear Flow

The BGK model kinetic equation is applied to spatially inhomogeneous states near steady uniform shear flow. The shear rate of the reference steady state can be large so the states considered include those very far from equilibrium. The single particle distribution function is calculated exactly to first order in the deviations of the hydrodynamic field gradients from their values in the reference state. The corresponding non-linear hydrodynamic equaitons are obtained and the set of transport coefficients are identified as explicit functions of the shear rate. The spectrum of the linear hydrodynamic equation is studied in detail and qualitative differences from the spectrum for equilibrium fluctuations are discussed. Conditions for instabilities at long wavelengths are identified and disccused.Comment: 32 pages, 1 figure, RevTeX, submitted to Phys. Rev.

Kinetic Theory for Electron Dynamics Near a Positive Ion

A theoretical description of time correlation functions for electron properties in the presence of a positive ion of charge number Z is given. The simplest case of an electron gas distorted by a single ion is considered. A semi-classical representation with a regularized electron - ion potential is used to obtain a linear kinetic theory that is asymptotically exact at short times. This Markovian approximation includes all initial (equilibrium) electron - electron and electron - ion correlations through renormalized pair potentials. The kinetic theory is solved in terms of single particle trajectories of the electron - ion potential and a dielectric function for the inhomogeneous electron gas. The results are illustrated by a calculation of the autocorrelation function for the electron field at the ion. The dependence on charge number Z is shown to be dominated by the bound states of the effective electron - ion potential. On this basis, a very simple practical representation of the trajectories is proposed and shown to be accurate over a wide range including strong electron - ion coupling. This simple representation is then used for a brief analysis of the dielectric function for the inhomogeneous electron gas.Comment: 30 pages, 5 figures, submitted to Journal of Statistical Mechanics: Theory and Experimen

Linear Response for Granular Fluids

The linear response of an isolated, homogeneous granular fluid to small spatial perturbations is studied by methods of non-equilibrium statistical mechanics. The long wavelength linear hydrodynamic equations are obtained, with formally exact expressions for the susceptibilities and transport coefficients. The latter are given in equivalent Einstein-Helfand and Green-Kubo forms. The context of these results and their contrast with corresponding results for normal fluids are discussed.Comment: Submitted to PR

Hydrodynamic Modes for Granular Gases

The eigenfunctions and eigenvalues of the linearized Boltzmann equation for inelastic hard spheres (d=3) or disks (d=2) corresponding to d+2 hydrodynamic modes, are calculated in the long wavelength limit for a granular gas. The transport coefficients are identified and found to agree with those from the Chapman-Enskog solution. The dominance of hydrodynamic modes at long times and long wavelengths is studied via an exactly solvable kinetic model. A collisional continuum is bounded away from the hydrodynamic spectrum, assuring a hydrodynamic description at long times. The bound is closely related to the power law decay of the velocity distribution in the reference homogeneous cooling state

Stability of Uniform Shear Flow

The stability of idealized shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at any finite shear rate for sufficiently long wavelength perturbations. The analysis is extended to larger shear rates using a low density model kinetic equation. Direct Monte Carlo Simulation of this equation is computed with a hydrodynamic description including non Newtonian rheological effects. The hydrodynamic description of the instability is in good agreement with the direct Monte Carlo simulation for $t < 50t_0$, where $t_0$ is the mean free time. Longer time simulations up to $2000t_0$ are used to identify the asymptotic state as a spatially non-uniform quasi-stationary state. Finally, preliminary results from molecular dynamics simulation showing the instability are presented and discussed.Comment: 25 pages, 9 figures (Fig.8 is available on request) RevTeX, submitted to Phys. Rev.

Aging to non-Newtonian hydrodynamics in a granular gas

The evolution to the steady state of a granular gas subject to simple shear flow is analyzed by means of computer simulations. It is found that, regardless of its initial preparation, the system reaches (after a transient period lasting a few collisions per particle) a non-Newtonian (unsteady) hydrodynamic regime, even at strong dissipation and for states where the time scale associated with inelastic cooling is shorter than the one associated with the irreversible fluxes. Comparison with a simplified rheological model shows a good agreement.Comment: 6 pages, 4 figures; v2: improved version to be published in EP

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

Long Wavelength Instability for Uniform Shear Flow

Uniform Shear Flow is a prototype nonequilibrium state admitting detailed study at both the macroscopic and microscopic levels via theory and computer simulation. It is shown that the hydrodynamic equations for this state have a long wavelength instability. This result is obtained first from the Navier-Stokes equations and shown to apply at both low and high densities. Next, higher order rheological effects are included using a model kinetic theory. The results are compared favorably to those from Monte Carlo simulation.Comment: 12 pages, including 2 figure

Body Condition and the Adrenal Stress Response in Captive American Kestrel Juveniles

We examined the adrenal response to handling stress of birds in different body conditions. In order to affect the birds’ body condition, young (73-d old) female American kestrels (Falco sparverius) were maintained for 6 wk on one of three diets: a control diet (fed ad lib.) and two calorically restricted diets. To invoke a stress response, we removed birds from their cages and took repeated blood samples over the course of an hour. All birds responded to handling stress with an increase in plasma corticosterone, but control birds (in good body condition) showed a more rapid increase to maximum corticoste rone levels, followed by a decrease. Both groups of food-restricted birds had a slower rate of increase to maximum corticosterone levels and then maintained high corticosterone levels through 60 min. These results suggest that birds in good physical condition respond more quickly to stressors and adapt physiologically to stressful situations more rapidly than do birds in poor physical condition. This difference may reflect the ability of birds in good condition to mobilize fat for energy, while birds in poor condition must mobilize protein (i.e., muscle)