2,894 research outputs found
Fundamental-measure density functional for the fluid of aligned hard hexagons: New insights in fundamental measure theory
In this article we obtain a fundamental measure functional for the model of
aligned hard hexagons in the plane. Our aim is not just to provide a functional
for a new, admittedly academic, model, but to investigate the structure of
fundamental measure theory. A model of aligned hard hexagons has similarities
with the hard disk model. Both share "lost cases", i.e. admit configurations of
three particles in which there is pairwise overlap but not triple overlap.
These configurations are known to be problematic for fundamental measure
functionals, which are not able to capture their contribution correctly. This
failure lies in the inability of these functionals to yield a correct low
density limit of the third order direct correlation function. Here we derive
the functional by projecting aligned hard cubes on the plane x+y+z=0. The
correct dimensional crossover behavior of these functionals permits us to
follow this strategy. The functional of aligned hard cubes, however, does not
have lost cases, so neither had the resulting functional for aligned hard
hexagons. The latter exhibits, in fact, a peculiar structure as compared to the
one for hard disks. It depends on a uniparametric family of weighted densities
through a new term not appearing in the functional for hard disks. Apart from
studying the freezing of this system, we discuss the implications of the
functional structure for new developments of fundamental measure theory.Comment: 10 pages, 9 figures, uses RevTeX
Reaching the millennium development goal for child mortality : improving equity and efficiency in Ecuador's health budget
health care; infant mortality; health policy;
What do emulsification failure and Bose-Einstein condensation have in common?
Ideal bosons and classical ring polymers formed via self-assembly, are known
to have the same partition function, and so analogous phase transitions. In
ring polymers, the analogue of Bose-Einstein condensation occurs when a ring
polymer of macroscopic size appears. We show that a transition of the same
general form occurs within a whole class of systems with self-assembly, and
illustrate it with the emulsification failure of a microemulsion phase of
water, oil and surfactant. As with Bose-Einstein condensation, the transition
occurs even in the absence of interactions.Comment: 7 pages, 1 figure, typeset with EUROTeX, uses epsfi
Cluster density functional theory for lattice models based on the theory of Mobius functions
Rosenfeld's fundamental measure theory for lattice models is given a rigorous
formulation in terms of the theory of Mobius functions of partially ordered
sets. The free-energy density functional is expressed as an expansion in a
finite set of lattice clusters. This set is endowed a partial order, so that
the coefficients of the cluster expansion are connected to its Mobius function.
Because of this, it is rigorously proven that a unique such expansion exists
for any lattice model. The low-density analysis of the free-energy functional
motivates a redefinition of the basic clusters (zero-dimensional cavities)
which guarantees a correct zero-density limit of the pair and triplet direct
correlation functions. This new definition extends Rosenfeld's theory to
lattice model with any kind of short-range interaction (repulsive or
attractive, hard or soft, one- or multi-component...). Finally, a proof is
given that these functionals have a consistent dimensional reduction, i.e. the
functional for dimension d' can be obtained from that for dimension d (d'<d) if
the latter is evaluated at a density profile confined to a d'-dimensional
subset.Comment: 21 pages, 2 figures, uses iopart.cls, as well as diagrams.sty
(included
A white dwarf-neutron star relativistic binary model for soft gamma-ray repeaters
A scenario for SGRs is introduced in which gravitational radiation reaction
effects drive the dynamics of an ultrashort orbital period X-ray binary
embracing a high-mass donor white dwarf (WD) to a rapidly rotating low
magnetised massive neutron star (NS) surrounded by a thick, dense and massive
accretion torus. Driven by GR reaction, sparsely, the binary separation
reduces, the WD overflows its Roche lobe and the mass transfer drives unstable
the accretion disk around the NS. As the binary circular orbital period is a
multiple integer number () of the period of the WD fundamental mode (Pons et
al. 2002), the WD is since long pulsating at its fundamental mode; and most of
its harmonics, due to the tidal interaction with its NS orbital companion.
Hence, when the powerful irradiation glows onto the WD; from the fireball
ejected as part of the disk matter slumps onto the NS, it is partially
absorbed. This huge energy excites other WD radial (-mode) pulsations
(Podsiadlowski 1991,1995). After each mass-transfer episode the binary
separation (and orbital period) is augmented significantly (Deloye & Bildsten
2003; Al\'ecyan & Morsink 2004) due to the binary's angular momentum
redistribution. Thus a new adiabatic inspiral phase driven by GR reaction
starts which brings the binary close again, and the process repeats. This model
allows to explain most of SGRs observational features: their recurrent
activity, energetics of giant superoutbursts and quiescent stages, and
particularly the intriguing subpulses discovered by BeppoSAX (Feroci et al.
1999), which are suggested here to be {\it overtones} of the WD radial
fundamental mode (see the accompanying paper: Mosquera Cuesta 2004b).Comment: This paper was submitted as a "Letter to the Editor" of MNRAS in July
17/2004. Since that time no answer or referee report was provided to the
Author [MNRAS publication policy limits reviewal process no longer than one
month (+/- half more) for the reviewal of this kind of submission). I hope
this contribution is not receiving a similar "peer-reviewing" as given to the
A. Dar and A. De Rujula's "Cannonball model for gamma-ray bursts", or to the
R.K. Williams' "Penrose process for energy extraction from rotating black
holes". The author welcomes criticisms and suggestions on this pape
Phase diagram of a two-dimensional lattice gas model of a ramp system
Using Monte Carlo Simulation and fundamental measure theory we study the
phase diagram of a two-dimensional lattice gas model with a nearest neighbor
hard core exclusion and a next-to-nearest neighbors finite repulsive
interaction. The model presents two competing ranges of interaction and, in
common with many experimental systems, exhibits a low density solid phase,
which melts back to the fluid phase upon compression. The theoretical approach
is found to provide a qualitatively correct picture of the phase diagram of our
model system.Comment: 14 pages, 8 figures, uses RevTex
Lattice density-functional theory of surface melting: the effect of a square-gradient correction
I use the method of classical density-functional theory in the
weighted-density approximation of Tarazona to investigate the phase diagram and
the interface structure of a two-dimensional lattice-gas model with three
phases -- vapour, liquid, and triangular solid. While a straightforward
mean-field treatment of the interparticle attraction is unable to give a stable
liquid phase, the correct phase diagram is obtained when including a suitably
chosen square-gradient term in the system grand potential. Taken this theory
for granted, I further examine the structure of the solid-vapour interface as
the triple point is approached from low temperature. Surprisingly, a novel
phase (rather than the liquid) is found to grow at the interface, exhibiting an
unusually long modulation along the interface normal. The conventional
surface-melting behaviour is recovered only by artificially restricting the
symmetries being available to the density field.Comment: 16 pages, 6 figure
Density functional theory for hard-sphere mixtures: the White-Bear version Mark II
In the spirit of the White-Bear version of fundamental measure theory we
derive a new density functional for hard-sphere mixtures which is based on a
recent mixture extension of the Carnahan-Starling equation of state. In
addition to the capability to predict inhomogeneous density distributions very
accurately, like the original White-Bear version, the new functional improves
upon consistency with an exact scaled-particle theory relation in the case of
the pure fluid. We examine consistency in detail within the context of
morphological thermodynamics. Interestingly, for the pure fluid the degree of
consistency of the new version is not only higher than for the original
White-Bear version but also higher than for Rosenfeld's original fundamental
measure theory.Comment: 16 pages, 3 figures; minor changes; J. Phys.: Condens. Matter,
accepte
A theorem on the absence of phase transitions in one-dimensional growth models with onsite periodic potentials
We rigorously prove that a wide class of one-dimensional growth models with
onsite periodic potential, such as the discrete sine-Gordon model, have no
phase transition at any temperature . The proof relies on the spectral
analysis of the transfer operator associated to the models. We show that this
operator is Hilbert-Schmidt and that its maximum eigenvalue is an analytic
function of temperature.Comment: 6 pages, no figures, submitted to J Phys A: Math Ge
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