arXiv subjects

James W. Dufty

Publications and source records attributed to James W. Dufty.

44 records · Page 3Linked to original sources

arXiv2001

Shear Stress Correlations in Hard and Soft Sphere Fluids

The shear stress autocorrelation function has been studied recently by molecular dynamics simulation using the 1/q^n potential for very large n. The results are analyzed and interpreted here by comparing them to the shear stress response function for hard spheres. It is shown that the hard sphere response function has a singular contribution and that this is reproduced accurately by the simulations for large n. A simple model for the stress autocorrelation function at finite n is proposed, based on the required hard sphere limiting form.

cond-mat.stat-mech↗

arXiv2001

Kinetic Theory and Hydrodynamics for a Low Density Gas

Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to calculate properties of interest. The domain of validity for such methods is a priori uncertain due to the inelasticity, but recent systematic studies continue to support the utility of kinetic theory and hydrodynamics as both qualitative and quantitative descriptions for many physical states. The basis for kinetic theory and hydrodynamic descriptions is discussed briefly for the special case of a low density gas.

cond-mat.stat-mech↗

arXiv2001

Nonequilibrium Phase Transition for a Heavy Particle in a Granular Fluid

It is shown that the homogeneous cooling state (HCS) for a heavy impurity particle in a granular fluid supports two distinct phases. The order parameter $ϕ$ is the mean square velocity of the impurity particle relative to that of a fluid particle, and the control parameter $ξ$ is the fluid cooling rate relative to the impurity collision rate. For $ξ<1$ there is a ``normal'' phase for which $ϕ$ scales as the fluid/impurity mass ratio, just as for a system with elastic collisions. For $ξ>1$ an ``ordered'' phase occurs in which $ϕ$ is finite even for vanishingly small mass ratio, representing an extreme violation of energy equipartition. The phenomenon can be described in terms of a Landau-like free energy for a second order phase transition. The dynamics leading to the HCS is studied in detail using an asymptotic analysis of the Enskog-Lorentz kinetic equation near each phase and the critical domain. Critical slowing is observed with a divergent relaxation time at the critical point. The stationary velocity distributions are determined in each case, showing a crossover from Maxwellian in the normal phase to an exponential quartic function of the velocity that is sharply peaked about the non-zero $ϕ$ for the ordered phase. It is shown that the diffusion coefficient in the normal phase diverges at the critical point and remains so in the ordered phase. This is interpreted as a transition from diffusive to ballistic dynamics between the normal and ordered phases.

cond-mat.stat-mech↗

arXiv2001

Kinetic Theory and Hydrodynamics for Rapid Granular Flow - A Perspective

These are notes prepared for presentation at the workshop "Challenges in Granular Matter" at the Abdus Salam Institute for Theoretical Physics, Trieste, August 2001. Revisions and figures will be added at a later date. Many features of real granular fluids under rapid flow are replicated by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to calculate properties of interest. The domain of validity for such methods is a priori uncertain due to the inelasticity, but recent systemmatic studies continue to support the utility of kinetic theory and hydrodynamics as both qualitative and quantitative descriptions for many physical states. The current status of kinetic theory and hydrodynamics is reviewed and interpreted, with the optimistic conclusion that much existing phenomenology can be placed on firm grounds for further understanding of complex states observed in rapid granular flow.

cond-mat.stat-mech↗

arXiv2001

Critical Behavior of a Heavy Particle in a Granular Fluid

Behavior analogous to a second order phase transition is observed for the homogeneous cooling state of a heavy impurity particle in a granular fluid. The order parameter $ϕ$ is the ratio of impurity mean square velocity to that of the fluid, with a conjugate field $h$ proportional to the mass ratio. A parameter $β$, measuring the fluid cooling rate relative to the impurity--fluid collision rate, is the analogue of the inverse temperature. For $β<1$ the fluid is ``normal'' with $ϕ=0$ at $h=0$, as in the case of a system with elastic collisions. For $β>1$ an ``ordered'' state with $ϕ\neq 0$ occurs at $h=0$, representing an extreme breakdown of equipartition. Critical slowing and qualitative changes in the velocity distribution function for the impurity particle near the transition are noted

cond-mat.stat-mech↗

arXiv1997

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.

cond-mat↗

arXiv1997

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.

cond-mat.stat-mech↗

arXiv1996

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.

cond-mat↗