806 research outputs found
A causal statistical family of dissipative divergence type fluids
In this paper we investigate some properties, including causality, of a
particular class of relativistic dissipative fluid theories of divergence type.
This set is defined as those theories coming from a statistical description of
matter, in the sense that the three tensor fields appearing in the theory can
be expressed as the three first momenta of a suitable distribution function. In
this set of theories the causality condition for the resulting system of
hyperbolic partial differential equations is very simple and allow to identify
a subclass of manifestly causal theories, which are so for all states outside
equilibrium for which the theory preserves this statistical interpretation
condition. This subclass includes the usual equilibrium distributions, namely
Boltzmann, Bose or Fermi distributions, according to the statistics used,
suitably generalized outside equilibrium. Therefore this gives a simple proof
that they are causal in a neighborhood of equilibrium. We also find a bigger
set of dissipative divergence type theories which are only pseudo-statistical,
in the sense that the third rank tensor of the fluid theory has the symmetry
and trace properties of a third momentum of an statistical distribution, but
the energy-momentum tensor, while having the form of a second momentum
distribution, it is so for a different distribution function. This set also
contains a subclass (including the one already mentioned) of manifestly causal
theories.Comment: LaTex, documentstyle{article
A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory
We describe an asymptotic procedure for deriving continuum equations from the
kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of
Enskog, we expand in the mean flight time of the constituent particles of the
gas, but we do not adopt the Chapman-Enskog device of simplifying the formulae
at each order by using results from previous orders. In this way, we are able
to derive a new set of fluid dynamical equations from kinetic theory, as we
illustrate here for the relaxation model for monatomic gases. We obtain a
stress tensor that contains a dynamical pressure term (or bulk viscosity) that
is process-dependent and our heat current depends on the gradients of both
temperature and density. On account of these features, the equations apply to a
greater range of Knudsen number (the ratio of mean free path to macroscopic
scale) than do the Navier-Stokes equations, as we see in the accompanying
paper. In the limit of vanishing Knudsen number, our equations reduce to the
usual Navier-Stokes equations with no bulk viscosity.Comment: 16 page
Numerical Investigation of a Mesoscopic Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process
In this paper a spatial homogeneous vehicular traffic flow model based on a
stochastic master equation of Boltzmann type in the acceleration variable is
solved numerically for a special driver interaction model. The solution is done
by a modified direct simulation Monte Carlo method (DSMC) well known in non
equilibrium gas kinetic. The velocity and acceleration distribution functions
in stochastic equilibrium, mean velocity, traffic density, ACN, velocity
scattering and correlations between some of these variables and their car
density dependences are discussed.Comment: 23 pages, 10 figure
Derivation of fluid dynamics from kinetic theory with the 14--moment approximation
We review the traditional derivation of the fluid-dynamical equations from
kinetic theory according to Israel and Stewart. We show that their procedure to
close the fluid-dynamical equations of motion is not unique. Their approach
contains two approximations, the first being the so-called 14-moment
approximation to truncate the single-particle distribution function. The second
consists in the choice of equations of motion for the dissipative currents.
Israel and Stewart used the second moment of the Boltzmann equation, but this
is not the only possible choice. In fact, there are infinitely many moments of
the Boltzmann equation which can serve as equations of motion for the
dissipative currents. All resulting equations of motion have the same form, but
the transport coefficients are different in each case.Comment: 15 pages, 3 figures, typos fixed and discussions added; EPJA: Topical
issue on "Relativistic Hydro- and Thermodynamics
Second Order Dissipative Fluid Dynamics for Ultra-Relativistic Nuclear Collisions
The M\"uller-Israel-Stewart second order theory of relativistic imperfect
fluids based on Grad's moment method is used to study the expansion of hot
matter produced in ultra-relativistic heavy ion collisions. The temperature
evolution is investigated in the framework of the Bjorken boost-invariant
scaling limit. The results of these second-order theories are compared to those
of first-order theories due to Eckart and to Landau and Lifshitz and those of
zeroth order (perfect fluid) due to Euler.Comment: 5 pages, 4 figures, size of y-axis tick marks for Figs. 3 and 4 fixe
Extended hydrodynamics from Enskog's equation for a two-dimensional system general formalism
Balance equations are derived from Enskog's kinetic equation for a
two-dimensional system of hard disks using Grad's moment expansion method. This
set of equations constitute an extended hydrodynamics for moderately dense
bi-dimensional fluids. The set of independent hydrodynamic fields in the
present formulations are: density, velocity, temperature {\em and
also}--following Grad's original idea--the symmetric and traceless pressure
tensor and the heat flux vector . An approximation
scheme similar in spirit to one made by Grad in his original work is made. Once
the hydrodynamics is derived it is used to discuss the nature of a simple
one-dimensional heat conduction problem. It is shown that, not too far from
equilibrium, the nonequilibrium pressure in this case only depends on the
density, temperature and heat flux vector.Comment: :9 pages, 1 figure, This will appear in J. Stat. Phys. with minor
corrections and corresponds to Ref[9] of cond-mat/050710
Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
It is shown that the hydrodynamic modes of a dilute granular gas of inelastic
hard spheres can be identified, and calculated in the long wavelength limit.
Assuming they dominate at long times, formal expressions for the Navier-Stokes
transport coefficients are derived. They can be expressed in a form that
generalizes the Green-Kubo relations for molecular systems, and it is shown
that they can also be evaluated by means of -particle simulation methods.
The form of the hydrodynamic modes to zeroth order in the gradients is used to
detect the presence of inherent velocity correlations in the homogeneous
cooling state, even in the low density limit. They manifest themselves in the
fluctuations of the total energy of the system. The theoretical predictions are
shown to be in agreement with molecular dynamics simulations. Relevant related
questions deserving further attention are pointed out
Comparison and optimization of sheep in vivo intervertebral disc injury model.
Background
The current standard of care for intervertebral disc (IVD) herniation, surgical discectomy, does not repair annulus fibrosus (AF) defects, which is partly due to the lack of effective methods to do so and is why new repair strategies are widely investigated and tested preclinically. There is a need to develop a standardized IVD injury model in large animals to enable comparison and interpretation across preclinical study results. The purpose of this study was to compare in vivo IVD injury models in sheep to determine which annulus fibrosus (AF) defect type combined with partial nucleus pulposus (NP) removal would better mimic degenerative human spinal pathologies.
Methods
Six skeletally mature sheep were randomly assigned to one of the two observation periods (1 and 3 months) and underwent creation of 3 different AF defect types (slit, cruciate, and box-cut AF defects) in conjunction with 0.1âg NP removal in three lumbar levels using a lateral retroperitoneal surgical approach. The spine was monitored by clinical CT scans pre- and postoperatively, at 2âweeks and euthanasia, and by magnetic resonance imaging (MRI) and histology after euthanasia to determine the severity of degeneration (disc height loss, Pfirrmann grading, semiquantitative histopathology grading).
Results
All AF defects led to significant degenerative changes detectable on CT and MR images, produced bulging of disc tissue without disc herniation and led to degenerative and inflammatory histopathological changes. However, AF defects were not equal in terms of disc height loss at 3âmonths postoperatively; the cruciate and box-cut AF defects showed significantly decreased disc height compared to their preoperative height, with the box-cut defect creating the greatest disc height loss, while the slit AF defect showed restoration of normal preoperative disc height.
Conclusions
The tested IVD injury models do not all generate comparable disc degeneration but can be considered suitable IVD injury models to investigate new treatments. Results of the current study clearly indicate that slit AF defect should be avoided if disc height is used as one of the main outcomes; additional confirmatory studies may be warranted to generalize this finding
Some thoughts about nonequilibrium temperature
The main objective of this paper is to show that, within the present
framework of the kinetic theoretical approach to irreversible thermodynamics,
there is no evidence that provides a basis to modify the ordinary Fourier
equation relating the heat flux in a non-equilibrium steady state to the
gradient of the local equilibrium temperature. This fact is supported, among
other arguments, through the kinetic foundations of generalized hydrodynamics.
Some attempts have been recently proposed asserting that, in the presence of
non-linearities of the state variables, such a temperature should be replaced
by the non-equilibrium temperature as defined in Extended Irreversible
Thermodynamics. In the approximations used for such a temperature there is so
far no evidence that sustains this proposal.Comment: 13 pages, TeX, no figures, to appear in Mol. Phy
Evaporation boundary conditions for the R13 equations of rarefied gas dynamics
The regularized 13 moment (R13) equations are a macroscopic model for the description of rarefied gas flows in the transition regime. The equations have been shown to give meaningful results for Knudsen numbers up to about 0.5. Here, their range of applicability is extended by deriving and testing boundary conditions for evaporating and condensing interfaces. The macroscopic interface conditions are derived from the microscopic interface conditions of kinetic theory. Tests include evaporation into a half-space and evaporation/condensation of a vapor between two liquid surfaces of different temperatures. Comparison indicates that overall the R13 equations agree better with microscopic solutions than classical hydrodynamics
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