Modeling of the Terminal Velocities of the Dust Ejected Material by the Impact

We compute the distribution of velocities of the particles ejected by the impact of the projectile released from NASA Deep Impact spacecraft on the nucleus of comet 9P/Tempel 1 on the successive 20 hours following the collision. This is performed by the development and use of an ill-conditioned inverse problem approach, whose main ingredients are a set of observations taken by the Narrow Angle Camera (NAC) of OSIRIS onboard the Rosetta spacecraft, and a set of simple models of the expansion of the dust ejecta plume for different velocities. Terminal velocities are derived using a maximum likelihood estimator. We compare our results with published estimates of the expansion velocity of the dust cloud. Our approach and models reproduce well the velocity distribution of the ejected particles. We consider these successful comparisons of the velocities as an evidence for the appropriateness of the approach. This analysis provides a more thorough understanding of the properties of the Deep Impact dust cloud.Comment: Comments: 6 pages, 2 Postscript figures, To appear in the proceedings of "Deep Impact as a World Observatory Event - Synergies in Space, Time", ed. Hans Ulrich Kaeufl and Chris Sterken, Springer-Verla

On Cr−C^r-closing for flows on 2-manifolds

For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a $C^r$, $1\le r\le \infty$, vector field, with finitely many singularities, on a compact orientable surface M. Given a nontrivial recurrent point $p\in M$ of X, the holonomy map around p is semi-conjugate to an iet $E :[0,1) \to [0,1).$ If $E\in B$ then there exists a $C^r$ vector field Y, arbitrarily close to X, in the $C^r-$topology, such that Y has a closed trajectory passing through p.Comment: 7 pages, 1 figur

Nongauge bright soliton of the nonlinear Schrodinger (NLS) equation and a family of generalized NLS equations

We present an approach to the bright soliton solution of the NLS equation from the standpoint of introducing a constant potential term in the equation. We discuss a `nongauge' bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic sech^p solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg-de Vries and Benjamin-Bona-Mahony equations when p=2Comment: ~4 pages, 3 figures, 16 references, published versio

Experimental Study of the Role of Atomic Interactions on Quantum Transport

We report an experimental study of quantum transport for atoms confined in a periodic potential and compare between thermal and BEC initial conditions. We observe ballistic transport for all values of well depth and initial conditions, and the measured expansion velocity for thermal atoms is in excellent agreement with a single-particle model. For weak wells, the expansion of the BEC is also in excellent agreement with single-particle theory, using an effective temperature. We observe a crossover to a new regime for the BEC case as the well depth is increased, indicating the importance of interactions on quantum transport.Comment: 4 pages, 3 figure

Cross-Border Investment, Conflict of Laws, and the Privatization of Securities Law

The rapid acceleration of transnational investing is occurring in an environment in which emerging markets, and foreign interest in these markets, are exploding. The issues involved with cross-border investment, conflict of laws and the privatization of securities law are examined

Ion dynamics in a linear radio-frequency trap with a single cooling laser

We analyse the possibility of cooling ions with a single laser beam, due to the coupling between the three components of their motion induced by the Coulomb interaction. For this purpose, we numerically study the dynamics of ion clouds of up to 140 particles, trapped in a linear quadrupole potential and cooled with a laser beam propagating in the radial plane. We use Molecular Dynamics simulations and model the laser cooling by a stochastic process. For each component of the motion, we systematically study the dependence of the temperature with the anisotropy of the trapping potential. Results obtained using the full radio-frequency (rf) potential are compared to those of the corresponding pseudo-potential. In the rf case, the rotation symmetry of the potential has to be broken to keep ions inside the trap. Then, as for the pseudo-potential case, we show that the efficiency of the Coulomb coupling to thermalize the components of motion depends on the geometrical configuration of the cloud. Coulomb coupling appears to be not efficient when the ions organise as a line or a pancake and the three components of motion reach the same temperature only if the cloud extends in three dimensions

Type II supernovae as probes of environment metallicity: observations of host HII regions

Spectral modelling of SNII atmospheres indicates a clear dependence of metal line strengths on progenitor metallicity. This motivates further work to evaluate the accuracy with which these SNe can be used as metallicity indicators. To assess this accuracy we present a sample of SNII HII-region spectroscopy, from which environment abundances are derived. These environment abundances are compared to the observed strength of metal lines in SN spectra. Combining our sample with measurements from the literature, we present oxygen abundances of 119 host HII regions, by extracting emission line fluxes and using abundance diagnostics. Then, following Dessart et al., these abundances are compared to equivalent widths of Fe 5018 A at various time and colour epochs. Our distribution of inferred SNII host HII-region abundances has a range of ~0.6 dex. We confirm the dearth of SNeII exploding at metallicities lower than those found (on average) in the Large Magellanic Cloud. The equivalent width of Fe 5018 A at 50 days post explosion shows a statistically significant correlation with host HII-region oxygen abundance. The strength of this correlation increases if one excludes abundance measurements derived far from SN explosion sites. The correlation significance also increases if we only analyse a 'gold' IIP sample, and if a colour epoch is used in place of time. In addition, no evidence is found of correlation between progenitor metallicity and SN light-curve or spectral properties - except for that stated above with respect to Fe 5018 A equivalent width - suggesting progenitor metallicity is not a driving factor in producing the diversity observed in our sample. This study provides observational evidence of the usefulness of SNII as metallicity indicators. We finish with a discussion of the methodology needed to use SN spectra as independent metallicity diagnostics throughout the Universe.Comment: Accepted for publication in Astronomy and Astrophyci