35,717 research outputs found
Efficient Enumeration of Induced Subtrees in a K-Degenerate Graph
In this paper, we address the problem of enumerating all induced subtrees in
an input k-degenerate graph, where an induced subtree is an acyclic and
connected induced subgraph. A graph G = (V, E) is a k-degenerate graph if for
any its induced subgraph has a vertex whose degree is less than or equal to k,
and many real-world graphs have small degeneracies, or very close to small
degeneracies. Although, the studies are on subgraphs enumeration, such as
trees, paths, and matchings, but the problem addresses the subgraph
enumeration, such as enumeration of subgraphs that are trees. Their induced
subgraph versions have not been studied well. One of few example is for
chordless paths and cycles. Our motivation is to reduce the time complexity
close to O(1) for each solution. This type of optimal algorithms are proposed
many subgraph classes such as trees, and spanning trees. Induced subtrees are
fundamental object thus it should be studied deeply and there possibly exist
some efficient algorithms. Our algorithm utilizes nice properties of
k-degeneracy to state an effective amortized analysis. As a result, the time
complexity is reduced to O(k) time per induced subtree. The problem is solved
in constant time for each in planar graphs, as a corollary
Jet Collimation by Small-Scale Magnetic Fields
A popular model for jet collimation is associated with the presence of a
large-scale and predominantly toroidal magnetic field originating from the
central engine (a star, a black hole, or an accretion disk). Besides the
problem of how such a large-scale magnetic field is generated, in this model
the jet suffers from the fatal long-wave mode kink magnetohydrodynamic
instability. In this paper we explore an alternative model: jet collimation by
small-scale magnetic fields. These magnetic fields are assumed to be local,
chaotic, tangled, but are dominated by toroidal components. Just as in the case
of a large-scale toroidal magnetic field, we show that the ``hoop stress'' of
the tangled toroidal magnetic fields exerts an inward force which confines and
collimates the jet. The magnetic ``hoop stress'' is balanced either by the gas
pressure of the jet, or by the centrifugal force if the jet is spinning. Since
the length-scale of the magnetic field is small (< the cross-sectional radius
of the jet << the length of the jet), in this model the jet does not suffer
from the long-wave mode kink instability. Many other problems associated with
the large-scale magnetic field are also eliminated or alleviated for
small-scale magnetic fields. Though it remains an open question how to generate
and maintain the required small-scale magnetic fields in a jet, the scenario of
jet collimation by small-scale magnetic fields is favored by the current study
on disk dynamo which indicates that small-scale magnetic fields are much easier
to generate than large-scale magnetic fields.Comment: 14 pages, no figur
Are Magnetic Wind-Driving Disks Inherently Unstable?
There have been claims in the literature that accretion disks in which a
centrifugally driven wind is the dominant mode of angular momentum transport
are inherently unstable. This issue is considered here by applying an
equilibrium-curve analysis to the wind-driving, ambipolar diffusion-dominated,
magnetic disk model of Wardle & Konigl (1993). The equilibrium solution curves
for this class of models typically exhibit two distinct branches. It is argued
that only one of these branches represents unstable equilibria and that a real
disk/wind system likely corresponds to a stable solution.Comment: 5 pages, 2 figures, to be published in ApJ, vol. 617 (2004 Dec 20).
Uses emulateapj.cl
Broadening effects due to alloy scattering in Quantum Cascade Lasers
We report on calculations of broadening effects in QCL due to alloy
scattering. The output of numerical calculations of alloy broadened Landau
levels compare favorably with calculations performed at the self-consistent
Born approximation. Results for Landau level width and optical absorption are
presented. A disorder activated forbidden transition becomes significant in the
vicinity of crossings of Landau levels which belong to different subbands. A
study of the time dependent survival probability in the lowest Landau level of
the excited subband is performed. It is shown that at resonance the population
relaxation occurs in a subpicosecond scale.Comment: 7 pages, 8 figure
Building analytical three-field cosmological models
A difficult task to deal with is the analytical treatment of models composed
by three real scalar fields, once their equations of motion are in general
coupled and hard to be integrated. In order to overcome this problem we
introduce a methodology to construct three-field models based on the so-called
"extension method". The fundamental idea of the procedure is to combine three
one-field systems in a non-trivial way, to construct an effective three scalar
field model. An interesting scenario where the method can be implemented is
within inflationary models, where the Einstein-Hilbert Lagrangian is coupled
with the scalar field Lagrangian. We exemplify how a new model constructed from
our method can lead to non-trivial behaviors for cosmological parameters.Comment: 11 pages, and 3 figures, updated version published in EPJ
Spatially resolved physical and chemical properties of the planetary nebula NGC 3242
Optical integral-field spectroscopy was used to investigate the planetary
nebula NGC 3242. We analysed the main morphological components of this source,
including its knots, but not the halo. In addition to revealing the properties
ofthe physical and chemical nature of this nebula, we also provided reliable
spatially resolved constraints that can be used for future photoionisation
modelling of the nebula. The latter is ultimately necessary to obtain a fully
self-consistent 3D picture of the physical and chemical properties of the
object. The observations were obtained with the VIMOS instrument attached to
VLT-UT3. Maps and values for specific morphological zones for the detected
emission-lines were obtained and analysed with routines developed by the
authors to derive physical and chemical conditions of the ionised gas in a 2D
fashion. We obtained spatially resolved maps and mean values of the electron
densities, temperatures, and chemical abundances, for specific morphological
structures in NGC 3242. These results show the pixel-to-pixel variations of the
the small- and large-scale structures of the source. These diagnostic maps
provide information free from the biases introduced by traditional single
long-slit observations. In general, our results are consistent with a uniform
abundance distribution for the object, whether we look at abundance maps or
integrated fluxes from specified morphological structures. The results indicate
that special care should be taken with the calibration of the data and that
only data with extremely good signal-to-noise ratio and spectral coverage
should be used to ensure the detection of possible spatial variations.Comment: 11 pages, 8 figures accepted for publication in Astronomy &
Astrophysic
Nontopological self-dual Maxwell-Higgs vortices
We study the existence of self-dual nontopological vortices in generalized
Maxwell-Higgs models recently introduced in Ref. \cite{gv}. Our investigation
is explicitly illustrated by choosing a sixth-order self-interaction potential,
which is the simplest one allowing the existence of nontopological structures.
We specify some Maxwell-Higgs models yielding BPS nontopological vortices
having energy proportional to the magnetic flux, , and whose profiles
are numerically achieved. Particularly, we investigate the way the new
solutions approach the boundary values, from which we verify their
nontopological behavior. Finally, we depict the profiles numerically found,
highlighting the main features they present.Comment: 6 pages, 4 figure
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