2,840 research outputs found
Comment on "Theory and computer simulation for the equation of state of additive hard-disk fluid mixtures"
A flaw in the comparison between two different theoretical equations of state
for a binary mixture of additive hard disks and Monte Carlo results, as
recently reported in C. Barrio and J. R. Solana, Phys. Rev. E 63, 011201
(2001), is pointed out. It is found that both proposals, which require the
equation of state of the single component system as input, lead to comparable
accuracy but the one advocated by us [A. Santos, S. B. Yuste, and M. L\'{o}pez
de Haro, Mol. Phys. 96, 1 (1999)] is simpler and complies with the exact limit
in which the small disks are point particles.Comment: 4 pages, including 1 figur
The semiclassical--Sobolev orthogonal polynomials: a general approach
We say that the polynomial sequence is a semiclassical
Sobolev polynomial sequence when it is orthogonal with respect to the inner
product where is a semiclassical linear functional,
is the differential, the difference or the --difference
operator, and is a positive constant. In this paper we get algebraic
and differential/difference properties for such polynomials as well as
algebraic relations between them and the polynomial sequence orthogonal with
respect to the semiclassical functional . The main goal of this article
is to give a general approach to the study of the polynomials orthogonal with
respect to the above nonstandard inner product regardless of the type of
operator considered. Finally, we illustrate our results by
applying them to some known families of Sobolev orthogonal polynomials as well
as to some new ones introduced in this paper for the first time.Comment: 23 pages, special issue dedicated to Professor Guillermo Lopez
lagomasino on the occasion of his 60th birthday, accepted in Journal of
Approximation Theor
The second and third Sonine coefficients of a freely cooling granular gas revisited
In its simplest statistical-mechanical description, a granular fluid can be
modeled as composed of smooth inelastic hard spheres (with a constant
coefficient of normal restitution ) whose velocity distribution
function obeys the Enskog-Boltzmann equation. The basic state of a granular
fluid is the homogeneous cooling state, characterized by a homogeneous,
isotropic, and stationary distribution of scaled velocities, .
The behavior of in the domain of thermal velocities ()
can be characterized by the two first non-trivial coefficients ( and
) of an expansion in Sonine polynomials. The main goals of this paper are
to review some of the previous efforts made to estimate (and measure in
computer simulations) the -dependence of and , to report new
computer simulations results of and for two-dimensional systems,
and to investigate the possibility of proposing theoretical estimates of
and with an optimal compromise between simplicity and accuracy.Comment: 12 pages, 5 figures; v2: minor change
Navier-Stokes transport coefficients of -dimensional granular binary mixtures at low density
The Navier-Stokes transport coefficients for binary mixtures of smooth
inelastic hard disks or spheres under gravity are determined from the Boltzmann
kinetic theory by application of the Chapman-Enskog method for states near the
local homogeneous cooling state. It is shown that the Navier-Stokes transport
coefficients are not affected by the presence of gravity. As in the elastic
case, the transport coefficients of the mixture verify a set of coupled linear
integral equations that are approximately solved by using the leading terms in
a Sonine polynomial expansion. The results reported here extend previous
calculations [V. Garz\'o and J. W. Dufty, Phys. Fluids {\bf 14}, 1476 (2002)]
to an arbitrary number of dimensions. To check the accuracy of the
Chapman-Enskog results, the inelastic Boltzmann equation is also numerically
solved by means of the direct simulation Monte Carlo method to evaluate the
diffusion and shear viscosity coefficients for hard disks. The comparison shows
a good agreement over a wide range of values of the coefficients of restitution
and the parameters of the mixture (masses and sizes).Comment: 6 figures, to be published in J. Stat. Phy
Characterization and control of phase fluctuations in elongated Bose-Einstein condensates
Quasi one dimensional Bose-Einstein condensates (BECs) in elongated traps
exhibit significant phase fluctuations even at very low temperatures. We
present recent experimental results on the dynamic transformation of phase
fluctuations into density modulations during time-of-flight and show the
excellent quantitative agreement with the theoretical prediction. In addition
we confirm that under our experimental conditions, in the magnetic trap density
modulations are strongly suppressed even when the phase fluctuates. The paper
also discusses our theoretical results on control of the condensate phase by
employing a time-dependent perturbation. Our results set important limitations
on future applications of BEC in precision atom interferometry and atom optics,
but at the same time suggest pathways to overcome these limitations.Comment: 9 pages, 7 figure
Cocoa Butter Saturated with Supercritical Carbon Dioxide: Measurements and Modelling of Solubility, Volumetric Expansion, Density and Viscosity
International audienceThe use of supercritical carbon dioxide technology for lipid processing has recently developed at the expense of traditional processes. For designing new processes the knowledge of thermophysical properties is a prerequisite. This work is focused on the characterization of physical and thermodynamic properties of CO2-cocoa butter (CB) saturated mixture. Measurements of density, volumetric expansion, viscosity and CO2 solubility were carried out on CB-rich phase at 313 and 353 K and pressures up to 40 MPa. The experimental techniques have previously been compared and validated. Density measurements of CB and CB saturated with CO2, were performed using the vibrating tube technology at pressures ranging from 0.1 to 25 MPa. Experimental values correlated well with the modified Tait equation. CO2 solubility measurements were coupled to those of density in the same pressures ranges. At 25 MPa, the solubility of CO2 is 31.4 % and 28.7 % at 313 and 353 K. Phase behaviour was investigated using a view cell in order to follow the expansion of the CB-rich phase with the rise in pressure. Volumetric expansion up to 47 % was measured and correlated to the CO2 solubility. Phase inversion was observed at 313 K and 40 MPa. Lastly, we developed an innovative falling ball viscometer for high pressure measurements. Viscosity measurements were carried out up to 25 MPa showing a viscosity reduction up to 90 % upon CO2 dissolution. These results were correlated with two empirical models. A new model here presented, was favourably compared with the Grunberg and Nissan model. All the experimental results are consistent with the available literature data for the CB-CO2 mixture and other fat systems. This work is a new contribution to the characterization of physical and thermodynamic behaviour of fats in contact with CO2 which is necessary to design supercritical fluid processes for fats processing
Diffusion of impurities in a granular gas
Diffusion of impurities in a granular gas undergoing homogeneous cooling
state is studied. The results are obtained by solving the Boltzmann--Lorentz
equation by means of the Chapman--Enskog method. In the first order in the
density gradient of impurities, the diffusion coefficient is determined as
the solution of a linear integral equation which is approximately solved by
making an expansion in Sonine polynomials. In this paper, we evaluate up to
the second order in the Sonine expansion and get explicit expressions for
in terms of the restitution coefficients for the impurity--gas and gas--gas
collisions as well as the ratios of mass and particle sizes. To check the
reliability of the Sonine polynomial solution, analytical results are compared
with those obtained from numerical solutions of the Boltzmann equation by means
of the direct simulation Monte Carlo (DSMC) method. In the simulations, the
diffusion coefficient is measured via the mean square displacement of
impurities. The comparison between theory and simulation shows in general an
excellent agreement, except for the cases in which the gas particles are much
heavier and/or much larger than impurities. In theses cases, the second Sonine
approximation to improves significantly the qualitative predictions made
from the first Sonine approximation. A discussion on the convergence of the
Sonine polynomial expansion is also carried out.Comment: 9 figures. to appear in Phys. Rev.
An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux
In the steady Couette flow of a granular gas the sign of the heat flux
gradient is governed by the competition between viscous heating and inelastic
cooling. We show from the Boltzmann equation for inelastic Maxwell particles
that a special class of states exists where the viscous heating and the
inelastic cooling exactly compensate each other at every point, resulting in a
uniform heat flux. In this state the (reduced) shear rate is enslaved to the
coefficient of restitution , so that the only free parameter is the
(reduced) thermal gradient . It turns out that the reduced moments of
order are polynomials of degree in , with coefficients that
are nonlinear functions of . In particular, the rheological properties
() are independent of and coincide exactly with those of the
simple shear flow. The heat flux () is linear in the thermal gradient
(generalized Fourier's law), but with an effective thermal conductivity
differing from the Navier--Stokes one. In addition, a heat flux component
parallel to the flow velocity and normal to the thermal gradient exists. The
theoretical predictions are validated by comparison with direct Monte Carlo
simulations for the same model.Comment: 16 pages, 4 figures,1 table; v2: minor change
Estudia comparativo de los cariatipos de Acrotylus insubricus Scop. y A. fischeri Azam. (Orthoptera: Acrididae)
Mediante el estudio de1 cariotipo de Acrotylus insubricus y A. fischeri se confirma que se trata de dos especies distintas
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