4,575 research outputs found
Degenerations of LeBrun twistor spaces
We investigate various limits of the twistor spaces associated to the
self-dual metrics on n CP ^2, the connected sum of the complex projective
planes, constructed by C. LeBrun. In particular, we explicitly present the
following 3 kinds of degenerations whose limits of the metrics are: (a) LeBrun
metrics on (n-1) CP ^2$, (b) (Another) LeBrun metrics on the total space of the
line bundle O(-n) over CP ^1 (c) The hyper-Kaehler metrics on the small
resolution of rational double points of type A_{n-1}, constructed by Gibbons
and Hawking.Comment: 21 pages, 7 figures. V2: A new section added at the end of the
article. V3: Reference slightly update
Toric anti-self-dual Einstein metrics via complex geometry
Using the twistor correspondence, we give a classification of toric
anti-self-dual Einstein metrics: each such metric is essentially determined by
an odd holomorphic function. This explains how the Einstein metrics fit into
the classification of general toric anti-self-dual metrics given in an earlier
paper (math.DG/0602423). The results complement the work of Calderbank-Pedersen
(math.DG/0105263), who describe where the Einstein metrics appear amongst the
Joyce spaces, leading to a different classification. Taking the twistor
transform of our result gives a new proof of their theorem.Comment: v2. Published version. Additional references. 14 page
Open TURNS: An industrial software for uncertainty quantification in simulation
The needs to assess robust performances for complex systems and to answer
tighter regulatory processes (security, safety, environmental control, and
health impacts, etc.) have led to the emergence of a new industrial simulation
challenge: to take uncertainties into account when dealing with complex
numerical simulation frameworks. Therefore, a generic methodology has emerged
from the joint effort of several industrial companies and academic
institutions. EDF R&D, Airbus Group and Phimeca Engineering started a
collaboration at the beginning of 2005, joined by IMACS in 2014, for the
development of an Open Source software platform dedicated to uncertainty
propagation by probabilistic methods, named OpenTURNS for Open source Treatment
of Uncertainty, Risk 'N Statistics. OpenTURNS addresses the specific industrial
challenges attached to uncertainties, which are transparency, genericity,
modularity and multi-accessibility. This paper focuses on OpenTURNS and
presents its main features: openTURNS is an open source software under the LGPL
license, that presents itself as a C++ library and a Python TUI, and which
works under Linux and Windows environment. All the methodological tools are
described in the different sections of this paper: uncertainty quantification,
uncertainty propagation, sensitivity analysis and metamodeling. A section also
explains the generic wrappers way to link openTURNS to any external code. The
paper illustrates as much as possible the methodological tools on an
educational example that simulates the height of a river and compares it to the
height of a dyke that protects industrial facilities. At last, it gives an
overview of the main developments planned for the next few years
Deformation of LeBrun's ALE metrics with negative mass
In this article we investigate deformations of a scalar-flat K\"ahler metric
on the total space of complex line bundles over CP^1 constructed by C. LeBrun.
In particular, we find that the metric is included in a one-dimensional family
of such metrics on the four-manifold, where the complex structure in the
deformation is not the standard one.Comment: 20 pages, no figure. V2: added two references, filled a gap in the
proof of Theorem 1.2. V3: corrected a wrong statement about Kuranishi family
of a Hirzebruch surface stated in the last paragraph in the proof of Theorem
1.2, and fixed a relevant error in the proof. Also added a reference [24]
about Kuranishi family of Hirzebruch surface
EGRET Observations of the Diffuse Gamma-Ray Emission in Orion: Analysis Through Cycle 6
We present a study of the high-energy diffuse emission observed toward Orion
by the Energetic Gamma-Ray Experiment Telescope (EGRET) on the Compton
Gamma-Ray Observatory. The total exposure by EGRET in this region has increased
by more than a factor of two since a previous study. A simple model for the
diffuse emission adequately fits the data; no significant point sources are
detected in the region studied ( to and ) in either the composite dataset or in two separate
groups of EGRET viewing periods considered. The gamma-ray emissivity in Orion
is found to be for E > 100 MeV,
and the differential emissivity is well-described as a combination of
contributions from cosmic-ray electrons and protons with approximately the
local density. The molecular mass calibrating ratio is .Comment: 16 pages, including 5 figures. 3 Tables as three separate files.
Latex document, needs AASTEX style files. Accepted for publication in Ap
Registration of the First Thermonuclear X-ray Burst from AX J1754.2-2754
During the analysis of the INTEGRAL observatory archival data we found a
powerful X-ray burst, registered by JEM-X and IBIS/ISGRI telescopes on April
16, 2005 from a weak and poorly known source AX J1754.2-2754. Analysis of the
burst profiles and spectrum shows, that it was a type I burst, which result
from thermonuclear explosion on the surface of nutron star. It means that we
can consider AX J1754.2-2754 as an X-ray burster. Certain features of burst
profile at its initial stage witness of a radiation presure driven strong
expansion and a corresponding cooling of the nutron star photosphere. Assuming,
that the luminosity of the source at this phase was close to the Eddington
limit, we estimated the distance to the burst source d=6.6+/-0.3 kpc (for
hidrogen atmosphere of the neutron star) and d=9.2+/-0.4 kpc (for helium
atmosphere).Comment: 12 pages, 6 figure
The signature of 44Ti in Cassiopeia A revealed by IBIS/ISGRI on INTEGRAL
We report the detection of both the 67.9 and 78.4 keV 44Sc gamma-ray lines in
Cassiopeia A with the INTEGRAL IBIS/ISGRI instrument. Besides the robustness
provided by spectro-imaging observations, the main improvements compared to
previous measurements are a clear separation of the two 44Sc lines together
with an improved significance of the detection of the hard X-ray continuum up
to 100 keV. These allow us to refine the determination of the 44Ti yield and to
constrain the nature of the nonthermal continuum emission. By combining
COMPTEL, BeppoSAX/PDS and ISGRI measurements, we find a line flux of (2.5 +/-
0.3)*10(-5) cm(-2) s(-1) leading to a synthesized 44Ti mass of 1.6
(+0.6-0.3)*10(-4) solar mass. This high value suggests that Cas A is peculiar
in comparison to other young supernova remnants, from which so far no line
emission from 44Ti decay has been unambiguously detected.Comment: 5 pages, 4 figures, Accepted for publication in ApJ
Properties of equations of the continuous Toda type
We study a modified version of an equation of the continuous Toda type in 1+1
dimensions. This equation contains a friction-like term which can be switched
off by annihilating a free parameter \ep. We apply the prolongation method,
the symmetry and the approximate symmetry approach. This strategy allows us to
get insight into both the equations for \ep =0 and \ep \ne 0, whose
properties arising in the above frameworks are mutually compared. For \ep =0,
the related prolongation equations are solved by means of certain series
expansions which lead to an infinite- dimensional Lie algebra. Furthermore,
using a realization of the Lie algebra of the Euclidean group , a
connection is shown between the continuous Toda equation and a linear wave
equation which resembles a special case of a three-dimensional wave equation
that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial
solutions to the wave equation expressed in terms of Bessel functions are
determined.
For \ep\,\ne\,0, we obtain a finite-dimensional Lie algebra with four
elements. A matrix representation of this algebra yields solutions of the
modified continuous Toda equation associated with a reduced form of a
perturbative Liouville equation. This result coincides with that achieved in
the context of the approximate symmetry approach. Example of exact solutions
are also provided. In particular, the inverse of the exponential-integral
function turns out to be defined by the reduced differential equation coming
from a linear combination of the time and space translations. Finally, a Lie
algebra characterizing the approximate symmetries is discussed.Comment: LaTex file, 27 page
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