On the dimensions of secant varieties of Segre-Veronese varieties

This paper explores the dimensions of higher secant varieties to Segre-Veronese varieties. The main goal of this paper is to introduce two different inductive techniques. These techniques enable one to reduce the computation of the dimension of the secant variety in a high dimensional case to the computation of the dimensions of secant varieties in low dimensional cases. As an application of these inductive approaches, we will prove non-defectivity of secant varieties of certain two-factor Segre-Veronese varieties. We also use these methods to give a complete classification of defective s-th Segre-Veronese varieties for small s. In the final section, we propose a conjecture about defective two-factor Segre-Veronese varieties.Comment: Revised version. To appear in Annali di Matematica Pura e Applicat

Response of an atomic Bose-Einstein condensate to a rotating elliptical trap

We investigate numerically the response of an atomic Bose-Einstein condensate to a weakly-elliptical rotating trap over a large range of rotation frequencies. We analyse the quadrupolar shape oscillation excited by rotation, and discriminate between its stable and unstable regimes. In the latter case, where a vortex lattice forms, we compare with experimental observations and find good agreement. By examining the role of thermal atoms in the process, we infer that the process is temperature-independent, and show how terminating the rotation gives control over the number of vortices in the lattice. We also study the case of critical rotation at the trap frequency, and observe large centre-of-mass oscillations of the condensate.Comment: 14 pages, 8 figure

Effet antihypertensif de BpF2, une fraction d\'extrait aqueux de feuilles de Bidens pilosa L. (Asteraceae) chez le lapin

Les feuilles de Bidens pilosa L. sont largement utilisées dans la pharmacopée traditionnelle. Nous avons cherché à mettre en évidence les effets antihypertensifs de ces feuilles. L'analyse phytochimique révèle que la fraction 2, dénommée BpF2, de l\'extrait aqueux des feuilles de Bidens pilosa L. (Asteraceae), contient des flavonoïdes, des polyphénols et des tanins catéchiques. Pour des doses comprises entre 1 et 25 mg/kg de poids corporel, cette fraction chromatographique induit une hypotension dose-dépendante chez le lapin. Cet effet explique le potentiel antihypertenseur de cette fraction. Ces effets ressemblent à ceux bien connus de l\'acétylcholine (ACh). Toutefois, alors que l\'atropine inhibe totalement l\'hypotension induite par l\'ACh, elle ne reverse que partiellement l\'hypotension provoquée par BpF2. Ces résultats suggèrent fortement la présence de deux types de principes actifs dans cette fraction active BpF2: - les principes actifs cholinomimétiques de type muscarinique, - les principes actifs non cholinomimétiques dont la nature reste à déterminer. La présence de ces substances dans la fraction active pourrait justifier, au moins en partie, l\'utilisation traditionnelle de Bidens pilosa L. contre l\'hypertension artérielle.The fraction 2, called BpF2, of the aqueous extract from Bidens pilosa L. (Asteraceae) leaves, contained flavonoids, polyphenols and catechic tannins. For doses ranging from 1 to 25 mg/kg of body weight, this chromatographic fraction induced a dose-dependent hypotension in the rabbit. This effect explained the antihypertensive potential of the fraction. These effects resembled those well-known of acetylcholine (ACh). However, whereas atropine completely inhibited the effect induced by ACh, its action remained partial on that caused by BpF2. These results suggested the presence of two types of active components in BpF2 fraction. - muscarinic and cholinomimetic activity, - non cholinomimetic activity to be clarified. The study showed at least two hypotensive activities in BpF2 fraction, justifying the traditional use of Bidens pilosa L. against hypertension. Keywords: Bidens pilosa L., acetylcholine, muscarinic cholinomimetic activity, non cholinomimetic activity.Sciences & Nature Vol. 5 (1) 2008: pp. 29-3

Fifty-fold improvement in the number of quantum degenerate fermionic atoms

We have produced a quantum degenerate Li-6 Fermi gas with up to 7 x 10^7 atoms, an improvement by a factor of fifty over all previous experiments with degenerate Fermi gases. This was achieved by sympathetic cooling with bosonic Na-23 in the F=2, upper hyperfine ground state. We have also achieved Bose-Einstein condensation of F=2 sodium atoms by direct evaporation

Beyond the Landau Criterion for Superfluidity

According to the Landau criterion for superfluidity, a Bose-Einstein condensate flowing with a group velocity smaller than the sound velocity is energetically stable to the presence of perturbing potentials. We found that this is strictly correct only for vanishingly small perturbations. The superfluid critical velocity strongly depends on the strength and shape of the defect. We quantitatively study, both numerically and with an approximate analytical model, the dynamical response of a one-dimensional condensate flowing against an istantaneously raised spatially periodic defect. We found that the critical velocity $v_c$ decreases by incresing the strength of the defect $V_0$, up to to a critical value of the defect intensity where the critical velocity vanishes

Tkachenko modes of vortex lattices in rapidly rotating Bose-Einstein condensates

We calculate the in-plane modes of the vortex lattice in a rotating Bose condensate from the Thomas-Fermi to the mean-field quantum Hall regimes. The Tkachenko mode frequency goes from linear in the wavevector, $k$, for lattice rotational velocities, $\Omega$, much smaller than the lowest sound wave frequency in a finite system, to quadratic in $k$ in the opposite limit. The system also supports an inertial mode of frequency $\ge 2\Omega$. The calculated frequencies are in good agreement with recent observations of Tkachenko modes at JILA, and provide evidence for the decrease in the shear modulus of the vortex lattice at rapid rotation.Comment: 4 pages, 2 figure

Two-component Bose-Einstein Condensates with Large Number of Vortices

We consider the condensate wavefunction of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of $^{87}$Rb or $^{23}$Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of $\sqrt{3}$, and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.Comment: 4 pages, 2 figures, RevTe

Theory of vortex-lattice melting in a one-dimensional optical lattice

We investigate quantum and temperature fluctuations of a vortex lattice in a one-dimensional optical lattice. We discuss in particular the Bloch bands of the Tkachenko modes and calculate the correlation function of the vortex positions along the direction of the optical lattice. Because of the small number of particles in the pancake Bose-Einstein condensates at every site of the optical lattice, finite-size effects become very important. Moreover, the fluctuations in the vortex positions are inhomogeneous due to the inhomogeneous density. As a result, the melting of the lattice occurs from the outside inwards. However, tunneling between neighboring pancakes substantially reduces the inhomogeneity as well as the size of the fluctuations. On the other hand, nonzero temperatures increase the size of the fluctuations dramatically. We calculate the crossover temperature from quantum melting to classical melting. We also investigate melting in the presence of a quartic radial potential, where a liquid can form in the center instead of at the outer edge of the pancake Bose-Einstein condensates.Comment: 17 pages, 17 figures, submitted to Phys. Rev. A, references update

Effet antihypertensif d\'un extrait aqueux d\'écorce de tronc de Parkia biglobosa (mimosaceae) sur la pression artérielle de lapin.

Un extrait aqueux des écorces de tronc de Parkia biglobosa (EAPB), à des concentrations comprises entre 1,18 et 18, 93 mg/kg de poids corporel, induit une hypotension dose dépendante sur la pression artérielle de lapin. L'interaction Adrénaline - EAPB a révélé une réduction significative (

Vortex Nucleation in a Stirred Bose-Einstein Condensate

We studied the nucleation of vortices in a Bose-Einstein condensate stirred by a laser beam. We observed the vortex cores using time-of-flight absorption imaging. By varying the size of the stirrer, we observed either discrete resonances or a broad response as a function of the frequency of the stirrer's motion. Stirring beams small compared to the condensate size generated vortices below the critical rotation frequency for the nucleation of surface modes, suggesting a local mechanism of generation. In addition, we observed the centrifugal distortion of the condensate due to the rotating vortex lattice and found evidence for bent vortices