2,120 research outputs found
Qualitative study in Loop Quantum Cosmology
This work contains a detailed qualitative analysis, in General Relativity and
in Loop Quantum Cosmology, of the dynamics in the associated phase space of a
scalar field minimally coupled with gravity, whose potential mimics the
dynamics of a perfect fluid with a linear Equation of State (EoS). Dealing with
the orbits (solutions) of the system, we will see that there are analytic ones,
which lead to the same dynamics as the perfect fluid, and our goal is to check
their stability, depending on the value of the EoS parameter, i.e., to show
whether the other orbits converge or diverge to these analytic solutions at
early and late times.Comment: 12 pages, 7 figures. Version accepted for publication in CQ
Nagel scaling and relaxation in the kinetic Ising model on a n-isotopic chain
The kinetic Ising model on a n-isotopic chain is considered in the framework
of Glauber dynamics. The chain is composed of N segments with n sites, each one
occupied by a different isotope. Due to the isotopic mass difference, the n
spins in each segment have different relaxation times in the absence of the
interactions, and consequently the dynamics of the system is governed by
multiple relaxation mechanisms. The solution is obtained in closed form for
arbitrary n, by reducing the problem to a set of n coupled equations, and it is
shown rigorously that the critical exponent z is equal to 2. Explicit results
are obtained numerically for any temperature and it is also shown that the
dynamic susceptibility satisfies the new scaling (Nagel scaling) proposed for
glass-forming liquids. This is in agreement with our recent results (L. L.
Goncalves, M. Lopez de Haro, J. Taguena-Martinez and R. B. Stinchcombe, Phys.
Rev. Lett. 84, 1507 (2000)), which relate this new scaling function to multiple
relaxation processes.Comment: 4 pages, 2 figures, presented at Ising Centennial Colloquium, to be
published in the Proceedings (Brazilian Journal of Physics.
The off-shell M5-brane and non-perturbative gauge theory
M5-branes wrapping a holomorphic curve in a Calabi-Yau manifold can be used
to construct four-dimensional N=1 gauge theories. In this paper we will
consider M5-brane configurations corresponding to N=2 theories broken to N=1 by
a superpotential for the adjoint scalar field. These M5-brane configurations
can be obtained by lifting suitable intersecting brane configurations in type
IIA, or equivalently by T-dualizing IIB configurations with branes and/or
fluxes. We will show that turning on non-trivial expectation values for the
glueball superfields corresponds to non-holomorphic deformations of the
M5-brane. We compute the superpotential and show it agrees with that computed
by Dijkgraaf and Vafa. Several aspects of the gauge theory, such as the
appearance of non-holomorphic one-forms with integer periods on the
Seiberg-Witten curve, have a natural interpretation from the M5-brane point of
view. We also explain the interpretation of the superpotential in terms of the
twisted (2,0) theory living on the fivebrane
Contact values of the radial distribution functions of additive hard-sphere mixtures in d dimensions: A new proposal
The contact values of the radial distribution functions
of a -dimensional mixture of (additive) hard spheres are considered. A
`universality' assumption is put forward, according to which
, where is a common function for all
the mixtures of the same dimensionality, regardless of the number of
components, is the packing fraction of the mixture, and is a
dimensionless parameter that depends on the size distribution and the diameters
of spheres and . For , this universality assumption holds for the
contact values of the Percus--Yevick approximation, the Scaled Particle Theory,
and, consequently, the Boublik--Grundke--Henderson--Lee--Levesque
approximation. Known exact consistency conditions are used to express
, , and in terms of the radial distribution
at contact of the one-component system. Two specific proposals consistent with
the above conditions (a quadratic form and a rational form) are made for the
-dependence of . For one-dimensional systems, the proposals for
the contact values reduce to the exact result. Good agreement between the
predictions of the proposals and available numerical results is found for
, 3, 4, and 5.Comment: 10 pages, 11 figures; Figure 1 changed; Figure 5 is new; New
references added; accepted for publication in J. Chem. Phy
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
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