How many geodesics join two points on a contact sub-Riemannian manifold?

We investigate the structure and the topology of the set of geodesics (critical points for the energy functional) between two points on a contact Carnot group G (or, more generally, corank-one Carnot groups). Denoting by (x, z) 08 R2n 7 R exponential coordinates on G, we find constants C1, C2 > 0 and R1,R2 such that the number (Formula Presented) of geodesics joining the origin with a generic point p = (x, z) satisfies: (Formula Presented) We give conditions for p to be joined by a unique geodesic and we specialize our computations to standard Heisenberg groups, where (Formula Presented) The set of geodesics joining the origin with p 60 p0, parametrized with their initial covector, is a topological space \u393(p), that naturally splits as the disjoint union (Formula Presented) where \u3930(p) is a finite set of isolated geodesics, while \u393 1e(p) contains continuous families of non-isolated geodesics (critical manifolds for the energy). We prove an estimate similar to (1) for the \u201ctopology\u201d (i.e. the total Betti number) of \u393(p), with no restriction on p. When G is the Heisenberg group, families appear if and only if p is a vertical nonzero point and each family is generated by the action of isometries on a given geodesic. Surprisingly, in more general cases, families of non-isometrically equivalent geodesics do appear. If the Carnot group G is the nilpotent approximation of a contact sub-Riemannian manifold M at a point p0, we prove that the number \u3bd(p) of geodesics in M joining p0 with p can be estimated from below with (Formula Presented) (p). The number \u3bd(p) estimates indeed geodesics whose image is contained in a coordinate chart around p0 (we call these \u201clocal\u201d geodesics). As a corollary we prove the existence of a sequence (Formula Presented) such that: (Formula Presented)i.e. the number of \u201clocal\u201d geodesics between two points can be arbitrarily large, in sharp contrast with the Riemannian case

Receiver-Based Auralization of Broadband Aircraft Flyover Noise Using the NASA Auralization Framework

The NASA Auralization Framework (NAF) consists of a set of dynamic link libraries (DLLs) to facilitate auralization of aircraft noise. Advanced capabilities for synthesis, propagation, and external interfaces are provided by the NAF Advanced Plugin Libraries (APL); a separate set of DLLs that are made accessible through the NAFs plugin architecture. In the typical time domain use case, the sound is first synthesized at the source location based on a source noise definition, and is then propagated in the time domain to a receiver on or near the ground. Alternatively, it may be desirable to synthesize the sound at the receiver, after it has been propagated in the frequency domain, e.g., when the source definition is inaccessible or when alternative propagation methods are needed. Receiver-based auralization requires three new developments in the NAF APL: a component plugin to interpolate the propagated noise spectra as a function of time for input to sound synthesis, and a path finder and path traversal plugin to calculate the effects of the differential propagation path length between the direct and ground reflected rays. This paper describes those developments and demonstrates their use in the auralization of broadband flyover noise

Evaluation of the perceived colour difference under different lighting for museum applications

The role of lighting in museums has a fundamental importance. Light influences the perception of colours and space in the collections on display, therefore, any type of lighting must be adequately analysed to confirm the suitability and undistorted colour rendering of the illuminated objects. A two-stage perceptual test was carried out for this purpose. Initially, the participants were asked to evaluate the illuminants according to criteria such as: the brilliance of the colours, the degree of pleasantness of the lighting and the degree of overall satisfaction of the setting. Subsequently, the efficiency of different illuminants for the identification of colour differences between two objects was tested. The results obtained were then compared with the most commonly used colour rendering and colour difference indicators in order to determine their potential and limits

Wilson Fermions and Axion Electrodynamics in Optical Lattices

The formulation of massless relativistic fermions in lattice gauge theories is hampered by the fundamental problem of species doubling, namely, the rise of spurious fermions modifying the underlying physics. A suitable tailoring of the fermion masses prevents such abundance of species, and leads to the so-called Wilson fermions. Here we show that ultracold atoms provide us with the first controllable realization of these paradigmatic fermions, thus generating a quantum simulator of fermionic lattice gauge theories. We describe a novel scheme that exploits laser-assisted tunneling in a cubic optical superlattice to design the Wilson fermion masses. The high versatility of this proposal allows us to explore a variety of interesting phases in three-dimensional topological insulators, and to test the remarkable predictions of axion electrodynamics.Comment: RevTex4 file, color figures, slightly longer than the published versio

Residues of Aflatoxins B1 and M1 in different biological matrices of swine orally administered aflatoxin B1 and Saccharomyces cerevisiae

Residui di aflatossine B1 e M1 in differenti matrici biologiche di suino alimentato con diete contenenti aflatossina B1 e Saccharomyces cerevisiae. \u2013 Le micotossine, e la aflatossina B1 (AFB1) in particolare, rappresentano da sempre un problema di sanit\ue0 pubblica a livello mondiale di difficile risoluzione. Scopo del presente lavoro \ue8 stato quello di valutare le quantit\ue0 di aflatossine B1 e M1, in fegato, rene, muscolo e grasso di suini che hanno assunto per 5 settimane diete sperimentalmente contaminate con 280 \ub5g/kg di AFB1. E\u2019 stata valutata anche la capacit\ue0 adsorbente del Saccharomyces cerevisiae nei confronti di AFB1, somministrando la micotossina (280 ppb) insieme ad una dieta contenente lo 0.2% del lievito. Le quote residuali delle due aflatossine sono state determinate con metodo HPLC in fluorescenza, previa purificazione con estrazione solida (SPE). Muscolo e grasso sono risultati costantemente negativi per entrambe le micotossine, mentre i livelli rilevati in fegato e rene appaiono molto bassi per la AFB1 (valori compresi tra 0.03-0.12 ppb) e leggermente superiori per la AFM1 (valori compresi tra 0.39-0.72 ppb)

X-ray sources and their optical counterparts in the globular cluster M 22

Using XMM-Newton EPIC imaging data, we have detected 50 low-luminosity X-ray sources in the field of view of M 22, where 5 +/- 3 of these sources are likely to be related to the cluster. Using differential optical photometry, we have identified probable counterparts to those sources belonging to the cluster. Using X-ray spectroscopic and timing studies, supported by the optical colours, we propose that the most central X-ray sources in the cluster are cataclysmic variables, millisecond pulsars, active binaries and a blue straggler. We also identify a cluster of galaxies behind this globular cluster.Comment: 11 pages, 7 figures, accepted for publication in A&

Reference frames and rigid motions in relativity: Applications

The concept of rigid reference frame and of constricted spatial metric, given in the previous work [\emph{Class. Quantum Grav.} {\bf 21}, 3067,(2004)] are here applied to some specific space-times: In particular, the rigid rotating disc with constant angular velocity in Minkowski space-time is analyzed, a new approach to the Ehrenfest paradox is given as well as a new explanation of the Sagnac effect. Finally the anisotropy of the speed of light and its measurable consequences in a reference frame co-moving with the Earth are discussed.Comment: 13 pages, 1 figur