4,302 research outputs found
Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations
Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution
to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is
explicitly found. This allows the derivation of the equation of state for the
fluid taking both the virial and the compressibility routes. An analysis of the
virial coefficients and the determination of the radius of convergence of the
virial series are carried out. Molecular dynamics simulations of the same
system are also performed and a comparison between the simulation results for
the compressibility factor and theoretical expressions for the same quantity is
presented.Comment: 12 pages, 4 figures; v3: Equation (A.19) corrected (see
http://dx.doi.org/10.1063/1.2390712
Rescaled density expansions and demixing in hard-sphere binary mixtures
The demixing transition of a binary fluid mixture of additive hard spheres is
analyzed for different size asymmetries by starting from the exact low-density
expansion of the pressure. Already within the second virial approximation the
fluid separates into two phases of different composition with a lower consolute
critical point. By successively incorporating the third, fourth, and fifth
virial coefficients, the critical consolute point moves to higher values of the
pressure and to lower values of the partial number fraction of the large
spheres. When the exact low-density expansion of the pressure is rescaled to
higher densities as in the Percus-Yevick theory, by adding more exact virial
coefficients a different qualitative movement of the critical consolute point
in the phase diagram is found. It is argued that the Percus-Yevick factor
appearing in many empirical equations of state for the mixture has a deep
influence on the location of the critical consolute point, so that the
resulting phase diagram for a prescribed equation has to be taken with caution.Comment: 5 pages, 1 figure; to be published in The Journal of Chemical Physic
Black hole collapse simulated by vacuum fluctuations with a moving semi-transparent mirror
Creation of scalar massless particles in two-dimensional Minkowski
space-time--as predicted by the dynamical Casimir effect--is studied for the
case of a semitransparent mirror initially at rest, then accelerating for some
finite time, along a trajectory that simulates a black hole collapse (defined
by Walker, and Carlitz and Willey), and finally moving with constant velocity.
When the reflection and transmission coefficients are those in the model
proposed by Barton, Calogeracos, and Nicolaevici [r(w)=-i\alpha/(\w+i\alpha)
and s(w)=\w/(\w+i\alpha), with ], the Bogoliubov coefficients
on the back side of the mirror can be computed exactly. This allows us to prove
that, when is very large (case of an ideal, perfectly reflecting
mirror) a thermal emission of scalar massless particles obeying Bose-Einstein
statistics is radiated from the mirror (a black body radiation), in accordance
with results previously obtained in the literature. However, when is
finite (semitransparent mirror, a physically realistic situation) the striking
result is obtained that the thermal emission of scalar massless particles obeys
Fermi-Dirac statistics. We also show here that the reverse change of statistics
takes place in a bidimensional fermionic model for massless particles, namely
that the Fermi-Dirac statistics for the completely reflecting situation will
turn into the Bose-Einstein statistics for a partially reflecting, physical
mirror.Comment: 13 pages, no figures, version to appear in Physical Review
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
On the radial distribution function of a hard-sphere fluid
Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem.
Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B.
Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of
analytical forms of the radial distribution function of a fluid of hard spheres
are compared. While they share similar starting philosophy, the first one
involves the determination of eleven parameters while the second is a simple
extension of the solution of the Percus-Yevick equation. It is found that the
{second} approach has a better global accuracy and the further asset of
counting already with a successful generalization to mixtures of hard spheres
and other related systems.Comment: 3 pages, 1 figure; v2: slightly shortened, figure changed, to be
published in JC
- …