4,644 research outputs found
The implications of resonant x-ray scattering data on the physics of the insulating phase of V_2O_3
We have performed a quantitative analysis of recent resonant x-ray scattering
experiments carried out in the antiferromagnetic phase of V_2O_3 by means of
numerical ab-initio simulations. In order to treat magnetic effects, we have
developed a method based on multiple scattering theory (MST) and a relativistic
extension of the Schr\"{o}dinger Equation, thereby working with the usual non
relativistic set of quantum numbers for angular and spin momenta.
Electric dipole-dipole (E1-E1), dipole-quadrupole (E1-E2) and
quadrupole-quadrupole (E2-E2) transition were considered altogether. We obtain
satisfactory agreement with experiments, both in energy and azimuthal scans.
All the main features of the V K edge Bragg-forbidden reflections with
odd can be interpreted in terms of the antiferromagnetic ordering only,
{\it ie}, they are of magnetic origin. In particular the ab-initio simulation
of the energy scan around the (1,1,1)-monoclinic reflection excludes the
possibility of any symmetry reduction due to a time-reversal breaking induced
by orbital ordering.Comment: 11 pages, 6 figure
Observation and inverse problems in coupled cell networks
A coupled cell network is a model for many situations such as food webs in
ecosystems, cellular metabolism, economical networks... It consists in a
directed graph , each node (or cell) representing an agent of the network
and each directed arrow representing which agent acts on which one. It yields a
system of differential equations , where the component
of depends only on the cells for which the arrow
exists in . In this paper, we investigate the observation problems in
coupled cell networks: can one deduce the behaviour of the whole network
(oscillations, stabilisation etc.) by observing only one of the cells? We show
that the natural observation properties holds for almost all the interactions
Spectroscopy of Close Companions to QSOs and the Ages of Interaction-Induced Starbursts
We present low-resolution absorption-line spectra of three candidate close (
< 3 arcsec) companions to the low redshift QSOs 3CR 323.1, PG 1700+518, and PKS
2135-147. The spectra were obtained with LRIS on the Keck telescopes and with
the Faint Object Spectrograph on the University of Hawaii 2.2 m telescope. For
3CR 323.1 and PG 1700+518, we measure relative velocities that are consistent
with an association between the QSOs and their companion galaxies. The spectral
features of the companion galaxy to 3CR 323.1 indicate a stellar population of
intermediate age (approx. 2.3 Gyr). In contrast, the spectrum of the companion
object to PG 1700+518 shows strong Balmer absorption lines from a relatively
young stellar population, along with the Mg Ib absorption feature and the 4000
A break from an older population. By modeling the two stellar components of
this spectrum, it is possible to estimate the time that has elapsed since the
end of the most recent major starburst event: we obtain approx. 0.1 Gyr. This
event may have coincided with an interaction that triggered the QSO activity.
Finally, our spectroscopy shows conclusively that the supposed companion to PKS
2135-147 is actually a projected Galactic G star.Comment: 10 pages, 5 Postscript figures. Latex (AASTEX). To appear in ApJ.
Letters, Volume 480 (1997
Numerical aspects of nonlinear Schrodinger equations in the presence of caustics
The aim of this text is to develop on the asymptotics of some 1-D nonlinear
Schrodinger equations from both the theoretical and the numerical perspectives,
when a caustic is formed. We review rigorous results in the field and give some
heuristics in cases where justification is still needed. The scattering
operator theory is recalled. Numerical experiments are carried out on the focus
point singularity for which several results have been proven rigorously.
Furthermore, the scattering operator is numerically studied. Finally,
experiments on the cusp caustic are displayed, and similarities with the focus
point are discussed.Comment: 20 pages. To appear in Math. Mod. Meth. Appl. Sc
Exponential decay for the damped wave equation in unbounded domains
We study the decay of the semigroup generated by the damped wave equation in
an unbounded domain. We first prove under the natural geometric control
condition the exponential decay of the semigroup. Then we prove under a weaker
condition the logarithmic decay of the solutions (assuming that the initial
data are smoother). As corollaries, we obtain several extensions of previous
results of stabilisation and control
On Quasar Masses and Quasar Host Galaxies
The mass of massive black holes in quasar cores can be deduced using the
typical velocities of Hb-emitting clouds in the Broad Line Region (BLR) and the
size of this region. However, this estimate depends on various assumptions and
is susceptible to large systematic errors. The Hb-deduced black hole mass in a
sample of 14 bright quasars is found here to correlate with the quasar host
galaxy luminosity, as determined with the Hubble Space Telescope (HST). This
correlation is similar to the black hole mass vs. bulge luminosity correlation
found by Magorrian et al. in a sample of 32 nearby normal galaxies. The
similarity of the two correlations is remarkable since the two samples involve
apparently different types of objects and since the black hole mass estimates
in quasars and in nearby galaxies are based on very different methods.
This similarity provides a ``calibration'' of the Hb-deduced black hole mass
estimate, suggesting it is accurate to +-0.5 on log scale. The similarity of
the two correlations also suggests that quasars reside in otherwise normal
galaxies, and that the luminosity of quasar hosts can be estimated to +-0.5 mag
based on the quasar continuum luminosity and the Hb line width. Future imaging
observations of additional broad-line active galaxies with the HST are required
in order to explore the extent, slope, and scatter of the black hole mass vs.
host bulge luminosity correlation in active galaxies.Comment: Accepted for publication in ApJ Letters, 7 pages, aas2pp4.st
Geometric optics and instability for semi-classical Schrodinger equations
We prove some instability phenomena for semi-classical (linear or) nonlinear
Schrodinger equations. For some perturbations of the data, we show that for
very small times, we can neglect the Laplacian, and the mechanism is the same
as for the corresponding ordinary differential equation. Our approach allows
smaller perturbations of the data, where the instability occurs for times such
that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde
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