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 $l,m,\sigma$ 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 $h+k+l=$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 $G$, 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 $\dot x(t)=f(x(t))$, where the component $i$ of $f$ depends only on the cells $x_j(t)$ for which the arrow $j\rightarrow i$ exists in $G$. 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 $f$

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