Method to measure off-axis displacements based on the analysis of the intensity distribution of a vortex beam

We study the properties of the Fraunhofer diffraction patterns produced by Gaussian beams crossing spiral phase plates. We show, both analytically and numerically, that off-axis displacements of the input beam produce asymmetric diffraction patterns. The intensity profile along the direction of maximum asymmetry shows two different peaks. We find that the intensity ratio between these two peaks decreases exponentially with the off-axis displacement of the incident beam, the decay being steeper for higher strengths of the optical singularity of the spiral phase plate. We analyze how this intensity ratio can be used to measure small misalignments of the input beam with a very high precision.Comment: 8 pages, 4 figures. Accepted for publication in PR

Rotating Globular Clusters

Internal rotation is considered to play a major role in the dynamics of some globular clusters. However, in only few cases it has been studied by quantitative application of realistic and physically justified global models. Here we present a dynamical analysis of the photometry and three-dimensional kinematics of omega Cen, 47 Tuc, and M15, by means of a recently introduced family of self-consistent axisymmetric rotating models. The three clusters, characterized by different relaxation conditions, show evidence of differential rotation and deviations from sphericity. The combination of line-of-sight velocities and proper motions allows us to determine their internal dynamics, predict their morphology, and estimate their dynamical distance. The well-relaxed cluster 47 Tuc is very well interpreted by our model; internal rotation is found to explain the observed morphology. For M15, we provide a global model in good agreement with the data, including the central behavior of the rotation profile and the shape of the ellipticity profile. For the partially relaxed cluster omega Cen, the selected model reproduces the complex three-dimensional kinematics; in particular the observed anisotropy profile, characterized by a transition from isotropy, to weakly-radial anisotropy, and then to tangential anisotropy in the outer parts. The discrepancy found for the steep central gradient in the observed line-of-sight velocity dispersion profile and for the ellipticity profile is ascribed to the condition of only partial relaxation of this cluster and the interplay between rotation and radial anisotropy.Comment: 19 pages, 14 figures, accepted for publication in the Astrophysical Journa

Tradizione manoscritta e citazioni epigrafiche di Ovidio. Una nota su Trist. 1, 3, 25 e Pont. 1, 2, 111 alla luce di alcuni confronti epigrafici

This paper discusses two verses of Ovid’s Tristia (1, 3, 25) and Epistulae ex Ponto (1, 2, 111), for which the manuscript tradition is discordant. These lines are quoted in three epigraphic documents: CLE 1339 = ICVR, I 3903, CLE 1979 = ICVR, VIII 23529 and CLE 1988 = CIL, VI 37965. How reliable are the quotations in the Latin inscriptions? Do they help to reassess the Ovidian text? The main purpose of this study is to answer such questions, with respect to these particular cases

Technical Note: REFIR-PAD level 1 data analysis and performance characterization

The outgoing long-wave radiation from the Earth's atmosphere in the far infrared spectral region is mostly unexplored, while is well recognized that the water vapour contribution to greenhouse trapping is dominant in this region. The Radiation Explorer in the Far InfraRed (REFIR) study has proven the feasibility of a space-borne Fourier transform spectrometer able to perform the measurement in the 100–1100 cm<sup>−1</sup> range with a resolution of 0.5 cm<sup>−1</sup>. Following this work a prototype of the spectrometer named REFIR-PAD (Prototype for Applications and Development) has been developed to observe the atmospheric radiance from both ground-based sites and from stratospheric balloon platforms. In this work we describe the REFIR-PAD level 1 data analysis procedure, that, starting from raw instrumental data produces the calibrated atmospheric spectral radiance. Performances of the procedure are also described

A uniqueness result for the continuity equation in two dimensions

We consider certain properties of maps of class C 2 from Rd to Rd 121 that are strictly related to Sard\u2019s theorem, and show that some of them can be extended to Lipschitz maps, while others still require some additional regularity. We also give counterexamples showing that, in term of regularity, our results are optimal

LISA: Mars and the limits of life

We describe the results of the first tests made on LISA, a simulator of planetary environments designed and built in Padua, dedicated to the study of the limit of bacterial life on the planet Mars. Tests on the cryogenic circuit, on the UV illumination and on bacterial coltures at room temperature that shall be used as references are described.Comment: 4 pages, 3 figures. Mem. SAIt, in pres

On the Lp-differentiability of certain classes of functions

We prove the Lp-differentiability at almost every point for convolution products on \u211dd of the form K*\u3bc, where \u3bc is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation

Reduction on characteristics for continuous solutions of a scalar balance law

We consider continuous solutions u to the balance equation ∂t u(t, x) + ∂x [f (u(t, x))] = g(t, x) f ∈ C 2 (R), g ∈ L∞ (R) for a bounded source term g. Continuity improves to H ̈lder continuity o when f is uniformly convex, but it is not more regular in general. We discuss the reduction to ODEs on characteristics, mainly based on the joint works [5, 1]. We provide here local regularity results holding in the region where f (u)f (u) = 0 and only in the simpler case of autonomous sources g = g(x), but for solutions u(t, x) which may depend on time. This corresponds to a local regularity result, in that region, for the system of ODEs γ(t) = f (u(t, γ(t))) ̇ d u(t, γ(t)) = g(t, γ(t)). d