Existence and Stability of standing waves for supercritical NLS with a Partial Confinement

We prove the existence of orbitally stable ground states to NLS with a partial confinement together with qualitative and symmetry properties. This result is obtained for nonlinearities which are $L^2$-supercritical, in particular we cover the physically relevant cubic case. The equation that we consider is the limit case of the cigar-shaped model in BEC.Comment: Revised version, accepted on Comm. Math. Physic

Junctions of anyonic Luttinger wires

We present an extended study of anyonic Luttinger liquids wires jointing at a single point. The model on the full line is solved with bosonization and the junction of an arbitrary number of wires is treated imposing boundary conditions that preserve exact solvability in the bosonic language. This allows to reach, in the low momentum regime, some of the critical fixed points found with the electronic boundary conditions. The stability of all the fixed points is discussed.Comment: 16 pages, 2 figures, typos corrected, Refs adde

Detection of a population gradient in the Sagittarius Stream

We present a quantitative comparison between the Horizontal Branch morphology in the core of the Sagittarius dwarf spheroidal galaxy (Sgr) and in a wide field sampling a portion of its tidal stream (Sgr Stream), located tens of kpc away from the center of the parent galaxy. We find that the Blue Horizontal Branch (BHB) stars in that part of the Stream are five times more abundant than in the Sgr core, relative to Red Clump stars. The difference in the ratio of BHB to RC stars between the two fields is significant at the 4.8 sigma level. This indicates that the old and metal-poor population of Sgr was preferentially stripped from the galaxy in past peri-Galactic passages with respect to the intermediate-age metal rich population that presently dominates the bound core of Sgr, probably due to a strong radial gradient that was settled within the galaxy before its disruption. The technique adopted in the present study allows to trace population gradients along the whole extension of the Stream.Comment: 4 pages, 3 .ps figures (fig. 1 at low resolution); Accepted for publication by A&A Letter

A dwarf galaxy remnant in Canis Major: the fossil of an in-plane accretion onto the Milky Way

We present an analysis of the asymmetries in the population of Galactic M-giant stars present in the 2MASS All Sky catalogue. Several large-scale asymmetries are detected, the most significant of which is a strong elliptical-shaped stellar over-density, close to the Galactic plane at (l=240, b=-8), in the constellation of Canis Major. A small grouping of globular clusters (NGC 1851, NGC 1904, NGC 2298, and NGC 2808), coincident in position and radial velocity, surround this structure, as do a number of open clusters. The population of M-giant stars in this over-density is similar in number to that in the core of the Sagittarius dwarf galaxy. We argue that this object is the likely dwarf galaxy progenitor of the ring-like structure that has recently been found at the edge of the Galactic disk. A numerical study of the tidal disruption of an accreted dwarf galaxy is presented. The simulated debris fits well the extant position, distance and velocity information on the ``Galactic Ring'', as well as that of the M-giant over-densities, suggesting that all these structures are the consequence of a single accretion event. The disrupted dwarf galaxy stream orbits close to the Galactic Plane, with a pericentre at approximately the Solar circle, an orbital eccentricity similar to that of stars in the Galactic thick disk, as well as a vertical scale height similar to that of the thick disk. This finding strongly suggests that the Canis Major dwarf galaxy is a building block of the Galactic thick disk, that the thick disk is continually growing, even up to the present time, and that thick disk globular clusters were accreted onto the Milky Way from dwarf galaxies in co-planar orbits.Comment: 13 pages, 18 figures (2 in colour), accepted for publication in MNRA

On the orbital stability for a class of nonautonomous NLS

Following the original approach introduced by T. Cazenave and P.L. Lions in \cite{CaLi} we prove the existence and the orbital stability of standing waves for the following class of NLS: \label{intr1} i\partial_t u+ \Delta u - V(x) u + Q(x) u|u|^{p-2}=0, \hbox{} (t,x) \in \R\times \R^n, \hbox{} 2<p<2+\frac 4n and \label{intr2} i\partial_t u - \Delta^2 u - V(x) u + Q(x) u|u|^{p-2}=0, \hbox{} (t,x) \in \R\times \R^n, \hbox{} 2<p<2+\frac 8n under suitable assumptions on the potentials $V(x)$ and $Q(x)$. More precisely we assume $V(x), Q(x) \in L^\infty(\R^n)$ and $meas\{Q(x)>\lambda_0\}\in (0,\infty)$ for a suitable $\lambda_0>0$. The main point is the analysis of the compactness of minimiziang sequences to suitable constrained minimization problems related to \eqref{intr1} and \eqref{intr2}