30,525 research outputs found
On soft capacities, quasi-stationary distributions and the pathwise approach to metastability
Motivated by the study of the metastable stochastic Ising model at
subcritical temperature and in the limit of a vanishing magnetic field, we
extend the notion of (, )-capacities between sets, as well as
the associated notion of soft-measures, to the case of overlapping sets. We
recover their essential properties, sometimes in a stronger form or in a
simpler way, relying on weaker hypotheses. These properties allow to write the
main quantities associated with reversible metastable dynamics, e.g. asymptotic
transition and relaxation times, in terms of objects that are associated with
two-sided variational principles. We also clarify the connection with the
classical "pathwise approach" by referring to temporal means on the appropriate
time scale.Comment: 29 pages, 1 figur
Thermodynamic Limit for Mean-Field Spin Models
If the Boltzmann-Gibbs state of a mean-field -particle system
with Hamiltonian verifies the condition for every decomposition , then its free
energy density increases with . We prove such a condition for a wide class
of spin models which includes the Curie-Weiss model, its p-spin generalizations
(for both even and odd p), its random field version and also the finite pattern
Hopfield model. For all these cases the existence of the thermodynamic limit by
subadditivity and boundedness follows.Comment: 15 pages, few improvements. To appear in MPE
Symmetrization in Geometry
The concept of an -symmetrization is introduced, which provides a
convenient framework for most of the familiar symmetrization processes on
convex sets. Various properties of -symmetrizations are introduced and the
relations between them investigated. New expressions are provided for the
Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual
relationship between them. Characterizations of Steiner, Minkowski and central
symmetrization, in terms of natural properties that they enjoy, are given and
examples are provided to show that none of the assumptions made can be dropped
or significantly weakened. Other familiar symmetrizations, such as Schwarz
symmetrization, are discussed and several new ones introduced.Comment: A chacterization of central symmetrization has been added and several
typos have been corrected. This version has been accepted for publication on
Advances in Mathematic
Monte Carlo Predictions of Far-Infrared Emission from Spiral Galaxies
We present simulations of Far Infrared (FIR) emission by dust in spiral
galaxies, based on the Monte Carlo radiative transfer code of Bianchi, Ferrara
& Giovanardi (1996). The radiative transfer is carried out at several
wavelength in the Ultraviolet, optical and Near Infrared, to cover the range of
the stellar Spectral Energy Distribution (SED). Together with the images of the
galactic model, a map of the energy absorbed by dust is produced. Using
Galactic dust properties, the spatial distribution of dust temperature is
derived under the assumption of thermal equilibrium. A correction is applied
for non-equilibrium emission in the Mid Infrared. Images of dust emission can
then be produced at any wavelength in the FIR.
We show the application of the model to the spiral galaxy NGC 6946. The
observed stellar SED is used as input and models are produced for different
star-dust geometries. It is found that only optically thick dust disks can
reproduce the observed amount of FIR radiation. However, it is not possible to
reproduce the large FIR scalelength suggested by recent observation of spirals
at 200 um, even when the scalelength of the dust disk is larger than that for
stars. Optically thin models have ratios of optical/FIR scalelengths closer to
the 200um observations, but with smaller absolute scalelengths than optically
thick cases. The modelled temperature distributions are compatible with
observations of the Galaxy and other spirals. We finally discuss the
approximations of the model and the impact of a clumpy stellar and dust
structure on the FIR simulations.Comment: 19 pages, 6 figures, accepted by A&
Four dimensional Lie symmetry algebras and fourth order ordinary differential equations
Realizations of four dimensional Lie algebras as vector fields in the plane
are explicitly constructed. Fourth order ordinary differential equations which
admit such Lie symmetry algebras are derived. The route to their integration is
described.Comment: 12 page
The broad-band X-ray spectrum of the Seyfert 1 galaxy, MCG+8-11-11
We present a long (100 ks) Suzaku observation of one of the X-ray brightest
AGN, MCG+8-11-11. These data were complemented with the 54-month Swift BAT
spectrum, allowing us to perform a broad-band fit in the 0.6-150 keV range. The
fits performed in the 0.6-10 keV band give consistent results with respect to a
previous XMM-Newton observation, i.e. the lack of a soft excess, warm
absorption along the line of sight, a large Compton reflection component (R~1)
and the absence of a relativistic component of the neutral iron K
emission line. However, when the PIN and Swift BAT data are included, the
reflection amount drops significantly (R~0.2-0.3), and a relativistic iron line
is required, the latter confirmed by a phenomenological analysis in a
restricted energy band (3-10 keV). When a self-consistent model is applied to
the whole broadband data, the observed reflection component appears to be all
associated to the relativistic component of the iron K line. The
resulting scenario, though strongly model-dependent, requires that all the
reprocessing spectral components from Compton-thick material must be associated
to the accretion disc, and no evidence for the classical pc-scale torus is
found. The narrow core of the neutral iron K line is therefore produced
in a Compton-thin material, like the BLR, similarly to what found in another
Seyfert galaxy, NGC7213, but with the notable difference that MCG+8-11-11
presents spectral signatures from an accretion disc. The very low accretion
rate of NGC7213 could explain the lack of relativistic signatures in its
spectrum, but the absence of the torus in both sources is more difficult to
explain, since their luminosities are comparable, and their accretion rates are
completely different.Comment: 8 pages, 6 figure, accepted for publication in Astronomy and
Astrophysic
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