346 research outputs found
Simple equation of state for hard disks on the hyperbolic plane
A simple equation of state for hard disks on the hyperbolic plane is
proposed. It yields the exact second virial coefficient and contains a pole at
the highest possible packing. A comparison with another very recent theoretical
proposal and simulation data is presented.Comment: 3 pages, 1 figur
Demixing can occur in binary hard-sphere mixtures with negative non-additivity
A binary fluid mixture of non-additive hard spheres characterized by a size
ratio and a non-additivity parameter
is considered in infinitely many
dimensions. From the equation of state in the second virial approximation
(which is exact in the limit ) a demixing transition with a
critical consolute point at a packing fraction scaling as
is found, even for slightly negative non-additivity, if
. Arguments concerning the stability of the
demixing with respect to freezing are provided.Comment: 4 pages, 2 figures; title changed; final paragraph added; to be
published in PRE as a Rapid Communicatio
On the liquid-glass transition line in monatomic Lennard-Jones fluids
A thermodynamic approach to derive the liquid-glass transition line in the
reduced temperature vs reduced density plane for a monatomic Lennard-Jones
fluid is presented. The approach makes use of a recent reformulation of the
classical perturbation theory of liquids [M. Robles and M. L\'opez de Haro,
Phys. Chem. Chem. Phys. {\bf 3}, 5528 (2001)] which is at grips with a rational
function approximation for the Laplace transform of the radial distribution
function of the hard-sphere fluid. The only input required is an equation of
state for the hard-sphere system. Within the Mansoori-Canfield/Rasaiah-Stell
variational perturbation theory, two choices for such an equation of state,
leading to a glass transition for the hard-sphere fluid, are considered. Good
agreement with the liquid-glass transition line derived from recent molecular
dynamic simulations [Di Leonardo et al., Phys. Rev. Lett. {\bf 84}, 6054(2000)]
is obtained.Comment: 4 pages, 2 figure
Multicomponent fluids of hard hyperspheres in odd dimensions
Mixtures of hard hyperspheres in odd space dimensionalities are studied with
an analytical approximation method. This technique is based on the so-called
Rational Function Approximation and provides a procedure for evaluating
equations of state, structure factors, radial distribution functions, and
direct correlations functions of additive mixtures of hard hyperspheres with
any number of components and in arbitrary odd-dimension space. The method gives
the exact solution of the Ornstein--Zernike equation coupled with the
Percus--Yevick closure, thus extending to arbitrary odd dimension the solution
for hard-sphere mixtures [J. L. Lebowitz, Phys.\ Rev.\ \textbf{133}, 895
(1964)]. Explicit evaluations for binary mixtures in five dimensions are
performed. The results are compared with computer simulations and a good
agreement is found.Comment: 16 pages, 8 figures; v2: slight change of notatio
Structural properties of fluids interacting via piece-wise constant potentials with a hard core
The structural properties of fluids whose molecules interact via potentials
with a hard core plus two piece-wise constant sections of different widths and
heights are presented. These follow from the more general development
previously introduced for potentials with a hard core plus piece-wise
constant sections [Condens. Matter Phys. {\bf 15}, 23602 (2012)] in which use
was made of a semi-analytic rational-function approximation method. The results
of illustrative cases comprising eight different combinations of wells and
shoulders are compared both with simulation data and with those that follow
from the numerical solution of the Percus-Yevick and hypernetted-chain integral
equations. It is found that the rational-function approximation generally
predicts a more accurate radial distribution function than the Percus-Yevick
theory and is comparable or even superior to the hypernetted-chain theory. This
superiority over both integral equation theories is lost, however, at high
densities, especially as the widths of the wells and/or the barriers increase.Comment: 10 pages, 11 figures; v2: Old Fig. 1 removed, new text on the
correlation length, 7 new references added, plus other minor change
Rational-function approximation for fluids interacting via piece-wise constant potentials
The structural properties of fluids whose molecules interact via potentials
with a hard-core plus n piece-wise constant sections of different widths and
heights are derived using a (semi-analytical) rational-function approximation
method. The results are illustrated for the cases of a square-shoulder plus
square-well potential and a shifted square-well potential and compared both
with simulation data and with those that follow from the (numerical) solutions
of the Percus-Yevick integral equation.Comment: 12 pages, 2 figures; submitted to a special issue of Condensed Matter
Physics in occasion of the 60th birthday of Prof. Orest Pizi
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