Detection of Gravitational Waves from Eccentric Compact Binaries

Coalescing compact binaries have been pointed out as the most promising source of gravitational waves for kilometer-size interferometers such as LIGO. Gravitational wave signals are extracted from the noise in the detectors by matched filtering. This technique performs really well if an a priori theoretical knowledge of the signal is available. The information known about the possible sources is used to construct a model of the expected waveforms (templates). A common assumption made when constructing templates for coalescing compact binaries is that the companions move in a quasi-circular orbit. Some scenarios, however, predict the existence of eccentric binaries. We investigate the loss in signal-to-noise ratio induced by non-optimal filtering of eccentric signals.Comment: 5 pages, 2 figures, to appear in the proceedings of the 8th Canadian Conference on General Relativity and Relativistic Astrophysic

Two soliton solutions to the three dimensional gravitational Hartree equation

We construct non dispersive two soliton solutions to the three dimensional gravitational Hartree equation whose trajectories asymptotically reproduce the nontrapped dynamics of the gravitational two body problem.Comment: Submitted for publicatio

Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations

We consider a family of dispersion generalized Benjamin-Ono equations (dgBO) which are critical with respect to the L2 norm and interpolate between the critical modified (BO) equation and the critical generalized Korteweg-de Vries equation (gKdV). First, we prove local well-posedness in the energy space for these equations, extending results by Kenig, Ponce and Vega concerning the (gKdV) equations. Second, we address the blow up problem in the spirit of works of Martel and Merle on the critical (gKdV) equation, by studying rigidity properties of the (dgBO) flow in a neighborhood of solitons. We prove that when the model is close to critical (gKdV), solutions of negative energy close to solitons blow up in finite or infinite time in the energy space. The blow up proof requires in particular extensions to (dgBO) of monotonicity results for localized versions of L2 norms by pseudo-differential operator tools.Comment: Submitte

More on the Impact of Bankruptcy Reform in Canada

The0501n objective of the new Bankruptcy Act (Bill C-22) is to promote the use of financial reorganization in order to increase the chances of survival of businesses that are experiencing financial difficulties and, as a consequence, to save jobs. Data from a sample of 417 commercial bankruptcies and 393 financial reorganizations are used to determine whether or not this represents an improvement over the previous system and whether or not the objective to increase the proportion of reorganizations will be met. Results from the statistical and logit analyses suggest that (i) the new voting requirement will increase the number of accepted proposals by 1.5 percentage points, (ii) the change in Crown priority will raise the success and acceptance rate by 2.32 and 0.79 percent respectively and (iii) the changes relating to stay of proceedings are expected to raise the use of holding proposals and thus reduce the likelihood of acceptance of a proposal by unsecured creditors. Finally, that there are several reasons to believe that encouraging firms that would otherwise have opted for bankruptcy to reorganize will not be an efficiency gain for the Canadian economy. L'objectif principal poursuivi par la réforme à la Loi sur la faillite (Bill C-22) est de promouvoir la réorganisation au détriment de la faillite pour les entreprises en difficultés financières afin d'accroître leurs chances de survie et ainsi de sauver des emplois. Les résultats des analyses statistique et économétrique d'une banque de données originales comprenant 417 dossiers de faillite commerciale et 393 dossiers de réorganisation commerciale concluent que (i) l'introduction d'un nouveau critère d'acceptation d'une proposition de réorganisation augmentera la probabilité d'acceptation de 1.5 points de pourcentage ; (ii) les changements apportés à la priorité des créances du gouvernement entraîneront une augmentation de la probabilité de succès et d'acceptation d'une proposition de l'ordre de 2.32 et 0.79 pour-cent respectivement ; et (iii) les changements quant au gel des procédures des créanciers pourraient se traduire dans une augmentation de proposition de type provisoire ce qui devrait diminuer la probabilité d'acceptation de la part des créanciers. Finalement, tout laisse croire que la promotion de la réorganisation financière entraînera une augmentation des coûts de faillite au Canada.Bankruptcy; Reorganization; Bankruptcy law, Faillite ; Réorganisation ; Loi sur la faillite

Light Propagation in Inhomogeneous Universes. V. Gravitational Lensing of Distant Supernovae

We use a series of ray-tracing experiments to determine the magnification distribution of high-redshift sources by gravitational lensing. We determine empirically the relation between magnification and redshift, for various cosmological models. We then use this relation to estimate the effect of lensing on the determination of the cosmological parameters from observations of high-z supernovae. We found that, for supernovae at redshifts z<1.8 the effect of lensing is negligible compared to the intrinsic uncertainty in the measurements. Using mock data in the range 1.8<z<8, we show that the effect of lensing can become significant. Hence, if a population of very-high-z supernovae was ever discovered, it would be crucial to fully understand the effect of lensing, before these SNe could be used to constrain cosmological models. We show that the distance moduli m-M for an open CDM universe and a LCDM universe are comparable at z>2. Therefore if supernovae up to these redshifts were ever discovered, it is still the ones in the range 0.3<z<1 that would distinguish these two models.Comment: 15 pages. Accepted for publication in The Astrophysical Journal. References adde

Description of the inelastic collision of two solitary waves for the BBM equation

We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves).Comment: submitted for publication. Corrected typo in Theorem 1.