18,056 research outputs found
Qualitative Analysis of Polycycles in Filippov Systems
In this paper, we are concerned about the qualitative behaviour of planar
Filippov systems around some typical minimal sets, namely, polycycles. In the
smooth context, a polycycle is a simple closed curve composed by a collection
of singularities and regular orbits, inducing a first return map. Here, this
concept is extended to Filippov systems by allowing typical singularities lying
on the switching manifold. Our main goal consists in developing a method to
investigate the unfolding of polycycles in Filippov systems. In addition, we
applied this method to describe bifurcation diagrams of Filippov systems around
certain polycycles
Gravitation and Duality Symmetry
By generalizing the Hodge dual operator to the case of soldered bundles, and
working in the context of the teleparallel equivalent of general relativity, an
analysis of the duality symmetry in gravitation is performed. Although the
basic conclusion is that, at least in the general case, gravitation is not dual
symmetric, there is a particular theory in which this symmetry shows up. It is
a self dual (or anti-self dual) teleparallel gravity in which, due to the fact
that it does not contribute to the interaction of fermions with gravitation,
the purely tensor part of torsion is assumed to vanish. The ensuing fermionic
gravitational interaction is found to be chiral. Since duality is intimately
related to renormalizability, this theory may eventually be more amenable to
renormalization than teleparallel gravity or general relativity.Comment: 7 pages, no figures. Version 2: minor presentation changes,
references added. Accepted for publication in Int. J. Mod. Phys.
Non-nequilibrium model on Apollonian networks
We investigate the Majority-Vote Model with two states () and a noise
on Apollonian networks. The main result found here is the presence of the
phase transition as a function of the noise parameter . We also studies de
effect of redirecting a fraction of the links of the network. By means of
Monte Carlo simulations, we obtained the exponent ratio ,
, and for several values of rewiring probability . The
critical noise was determined and also was calculated. The
effective dimensionality of the system was observed to be independent on ,
and the value is observed for these networks. Previous
results on the Ising model in Apollonian Networks have reported no presence of
a phase transition. Therefore, the results present here demonstrate that the
Majority-Vote Model belongs to a different universality class as the
equilibrium Ising Model on Apollonian Network.Comment: 5 pages, 5 figure
Primordial magnetic fields constrained by CMB anisotropies and dynamo cosmology
Magneto-curvature stresses could deform magnetic field lines and this would
give rise to back reaction and restoring magnetic stresses [Tsagas, PRL
(2001)]. Barrow et al [PRD (2008)] have shown in Friedman universe the
expansion to be slow down in spatial section of negative Riemann curvatures.
From Chicone et al [CMP (1997)] paper, proved that fast dynamos in compact 2D
manifold implies negatively constant Riemannian curvature, here one applies the
Barrow-Tsagas ideas to cosmic dynamos. Fast dynamo covariant stretching of
Riemann slices of cosmic Lobachevsky plane is given. Inclusion of advection
term on dynamo equations [Clarkson et al, MNRAS (2005)] is considered. In
absence of advection a fast dynamo is also obtained. Viscous and restoring
forces on stretching particles decrease, as magnetic rates increase. From COBE
data (), one computes stretching
.
Zeldovich et al has computed the maximum magnetic growth rate as
. From COBE data one computes
a lower growth rate for the magnetic field as
, well-within Zeldovich et al
estimate. Instead of the Harrison value one obtains the
lower primordial field which yields the
at the Big Bang time.Comment: Dept of theoretical physics-UERJ-Brasi
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