185 research outputs found
Four-quark energies in SU(2) lattice Monte Carlo using a tetrahedral geometry
This contribution -- a continuation of earlier work -- reports on recent
developments in the calculation and understanding of 4-quark energies generated
using lattice Monte Carlo techniques.Comment: 3 pages, latex, no figures, contribution to Lattice 9
The extended gaussian ensemble and metastabilities in the Blume-Capel model
The Blume-Capel model with infinite-range interactions presents analytical
solutions in both canonical and microcanonical ensembles and therefore, its
phase diagram is known in both ensembles. This model exhibits nonequivalent
solutions and the microcanonical thermodynamical features present peculiar
behaviors like nonconcave entropy, negative specific heat, and a jump in the
thermodynamical temperature. Examples of nonequivalent ensembles are in general
related to systems with long-range interactions that undergo canonical
first-order phase transitions. Recently, the extended gaussian ensemble (EGE)
solution was obtained for this model. The gaussian ensemble and its extended
version can be considered as a regularization of the microcanonical ensemble.
They are known to play the role of an interpolating ensemble between the
microcanonical and the canonical ones. Here, we explicitly show how the
microcanonical energy equilibrium states related to the metastable and unstable
canonical solutions for the Blume-Capel model are recovered from EGE, which
presents a concave "extended" entropy as a function of energy.Comment: 6 pages, 5 eps figures. Presented at the XI Latin American Workshop
on Nonlinear Phenomena, October 05-09 (2009), B\'uzios (RJ), Brazil. To
appear in JPC
Ground state of a polydisperse electrorheological solid: Beyond the dipole approximation
The ground state of an electrorheological (ER) fluid has been studied based
on our recently proposed dipole-induced dipole (DID) model. We obtained an
analytic expression of the interaction between chains of particles which are of
the same or different dielectric constants. The effects of dielectric constants
on the structure formation in monodisperse and polydisperse electrorheological
fluids are studied in a wide range of dielectric contrasts between the
particles and the base fluid. Our results showed that the established
body-centered tetragonal ground state in monodisperse ER fluids may become
unstable due to a polydispersity in the particle dielectric constants. While
our results agree with that of the fully multipole theory, the DID model is
much simpler, which offers a basis for computer simulations in polydisperse ER
fluids.Comment: Accepted for publications by Phys. Rev.
Non-power law constant flux solutions for the Smoluchowski coagulation equation
It is well known that for a large class of coagulation kernels, Smoluchowski
coagulation equations have particular power law solutions which yield a
constant flux of mass along all scales of the system. In this paper, we prove
that for some choices of the coagulation kernels there are solutions with a
constant flux of mass along all scales which are not power laws. The result is
proved by means of a bifurcation argument.Comment: 35 page
Asymptotics of the solutions of the stochastic lattice wave equation
We consider the long time limit theorems for the solutions of a discrete wave
equation with a weak stochastic forcing. The multiplicative noise conserves the
energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck
equation for the limit wave function that holds both for square integrable and
statistically homogeneous initial data. The limit is understood in the
point-wise sense in the former case, and in the weak sense in the latter. On
the other hand, the weak limit for square integrable initial data is
deterministic
Monte Carlo Simulations of Some Dynamical Aspects of Drop Formation
In this work we present some results from computer simulations of dynamical
aspects of drop formation in a leaky faucet. Our results, which agree very well
with the experiments, suggest that only a few elements, at the microscopic
level, would be necessary to describe the most important features of the
system. We were able to set all parameters of the model in terms of real ones.
This is an additional advantage with respect to previous theoretical works.Comment: 7 pages (Latex), 6 figures (PS) Accepted to publication in Int. J.
Mod. Phys. C Source Codes at http://www.if.uff.br/~arlim
A Study of Degenerate Four-quark states in SU(2) Lattice Monte Carlo
The energies of four-quark states are calculated for geometries in which the
quarks are situated on the corners of a series of tetrahedra and also for
geometries that correspond to gradually distorting these tetrahedra into a
plane. The interest in tetrahedra arises because they are composed of {\bf
three } degenerate partitions of the four quarks into two two-quark colour
singlets. This is an extension of earlier work showing that geometries with
{\bf two} degenerate partitions (e.g.\ squares) experience a large binding
energy. It is now found that even larger binding energies do not result, but
that for the tetrahedra the ground and first excited states become degenerate
in energy. The calculation is carried out using SU(2) for static quarks in the
quenched approximation with on a lattice. The
results are analysed using the correlation matrix between different euclidean
times and the implications of these results are discussed for a model based on
two-quark potentials.Comment: Original Raw PS file replace by a tarred, compressed and uuencoded PS
fil
Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension
We consider the long time, large scale behavior of the Wigner transform
W_\eps(t,x,k) of the wave function corresponding to a discrete wave equation
on a 1-d integer lattice, with a weak multiplicative noise. This model has been
introduced in Basile, Bernardin, and Olla to describe a system of interacting
linear oscillators with a weak noise that conserves locally the kinetic energy
and the momentum. The kinetic limit for the Wigner transform has been shown in
Basile, Olla, and Spohn. In the present paper we prove that in the unpinned
case there exists such that for any the
weak limit of W_\eps(t/\eps^{3/2\gamma},x/\eps^{\gamma},k), as \eps\ll1,
satisfies a one dimensional fractional heat equation with . In the pinned case an analogous
result can be claimed for W_\eps(t/\eps^{2\gamma},x/\eps^{\gamma},k) but the
limit satisfies then the usual heat equation
Kinetic Limit for Wave Propagation in a Random Medium
We study crystal dynamics in the harmonic approximation. The atomic masses
are weakly disordered, in the sense that their deviation from uniformity is of
order epsilon^(1/2). The dispersion relation is assumed to be a Morse function
and to suppress crossed recollisions. We then prove that in the limit epsilon
to 0 the disorder averaged Wigner function on the kinetic scale, time and space
of order epsilon^(-1), is governed by a linear Boltzmann equation.Comment: 71 pages, 3 figure
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