192 research outputs found
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.
Nonlinear response of electrons to a positive ion
Electric field dynamics at a positive ion imbedded in an electron gas is
considered using a semiclassical description. The dependence of the field
autocorrelation function on charge number is studied for strong ion-electron
coupling via MD simulation. The qualitative features for larger charge numbers
are a decreasing correlation time followed by an increasing anticorrelation.
Stopping power and related transport coefficients determined by the time
integral of this correlation function result from the competing effects of
increasing initial correlations and decreasing dynamical correlations. An
interpretation of the MD results is obtained from an effective single particle
model showing good agreement with the simulation results.Comment: To be published in the proceedings of the International Workshop on
Strongly Coupled Coulomb Systems, Journal of Physics
Theoretical Description of Coulomb Balls - Fluid Phase
A theoretical description for the radial density profile of a finite number
of identical charged particles confined in a harmonic trap is developed for
application over a wide range of Coulomb coupling (or, equivalently,
temperatures) and particle numbers. A simple mean field approximation
neglecting correlations yields a density profile which is monotonically
decreasing with radius for all temperatures, in contrast to molecular dynamics
simulations and experiments showing shell structure at lower temperatures. A
more complete theoretical description including charge correlations is
developed here by an extension of the hypernetted chain approximation,
developed for bulk fluids, to the confined charges. The results reproduce all
of the qualitative features observed in molecular dynamics simulations and
experiments. These predictions are then tested quantitatively by comparison
with new benchmark Monte Carlo simulations. Quantitative accuracy of the theory
is obtained for the selected conditions by correcting the hypernetted chain
approximation with a representation for the associated bridge functions.Comment: 10 figures, submitted to Physical Review
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
Continuum simulations of shocks and patterns in vertically oscillated granular layers
We study interactions between shocks and standing-wave patterns in vertically
oscillated layers of granular media using three-dimensional, time-dependent
numerical solutions of continuum equations to Navier-Stokes order. We simulate
a layer of grains atop a plate that oscillates sinusoidally in the direction of
gravity. Standing waves form stripe patterns when the accelerational amplitude
of the plate's oscillation exceeds a critical value. Shocks also form with each
collision between the layer and the plate; we show that pressure gradients
formed by these shocks cause the flow to reverse direction within the layer.
This reversal leads to an oscillatory state of the pattern that is subharmonic
with respect to the plate's oscillation. Finally, we study the relationship
between shocks and patterns in layers oscillated at various frequencies and
show that the pattern wavelength increases monotonically as the shock strength
increases.Comment: 12 pages, 9 figure
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
Gaussian Kinetic Model for Granular Gases
A kinetic model for the Boltzmann equation is proposed and explored as a
practical means to investigate the properties of a dilute granular gas. It is
shown that all spatially homogeneous initial distributions approach a universal
"homogeneous cooling solution" after a few collisions. The homogeneous cooling
solution (HCS) is studied in some detail and the exact solution is compared
with known results for the hard sphere Boltzmann equation. It is shown that all
qualitative features of the HCS, including the nature of over population at
large velocities, are reproduced semi-quantitatively by the kinetic model. It
is also shown that all the transport coefficients are in excellent agreement
with those from the Boltzmann equation. Also, the model is specialized to one
having a velocity independent collision frequency and the resulting HCS and
transport coefficients are compared to known results for the Maxwell Model. The
potential of the model for the study of more complex spatially inhomogeneous
states is discussed.Comment: to be submitted to Phys. Rev.
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 is the ratio of impurity mean square velocity to that
of the fluid, with a conjugate field proportional to the mass ratio. A
parameter , measuring the fluid cooling rate relative to the
impurity--fluid collision rate, is the analogue of the inverse temperature. For
the fluid is ``normal'' with at , as in the case of a
system with elastic collisions. For an ``ordered'' state with occurs at , representing an extreme breakdown of equipartition.
Critical slowing and qualitative changes in the velocity distribution function
for the impurity particle near the transition are notedComment: 4 pages (4 figures included
Rental Discrimination in the Multi-ethnic Metropolis: Evidence from Sydney
© 2016 Editorial Board, Urban Policy and Research. Investigating differential treatment in rental housing markets is important to ensure that renters are not discriminated against based on their personal characteristics. However, little Australian research has focused systematically on this question. This paper reports the results of a study that used paired tests to estimate the extent of differential treatment of Anglo, Indian, and Muslim Middle Eastern renters in the Sydney metropolitan housing market. We find statistically significant differences in treatment on several measures, including the likelihood an agent will offer an individual appointment, will provide additional information about other housing, will provide additional information about completing the application form, and will contact a prospective renter after an inspection
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