Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

We find a Hermite-type basis for which the eigenvalue problem associated to the operator $H_{A,B}:=B(-\partial_x^2)+Ax^2$ acting on $L^2({\bf R};{\bf C}^2)$ becomes a three-terms recurrence. Here $A$ and $B$ are two constant positive definite matrices with no other restriction. Our main result provides an explicit characterization of the eigenvectors of $H_{A,B}$ that lie in the span of the first four elements of this basis when $AB\not= BA$.Comment: 11 pages, 1 figure. Some typos where corrected in this new versio

Markov Process of Muscle Motors

We study a Markov random process describing a muscle molecular motor behavior. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spend an exponential time depending on the state. The thin filament moves at its velocity proportional to average of all displacements of all motors. We assume that the time which a motor stays at the bound state does not depend on its displacement. Then one can find an exact solution of a non-linear equation appearing in the limit of infinite number of the motors.Comment: 10 page

Structured Optical Materials Controlled by Light

Materials of which the optical response is determined by their structure are of much interest both for their fundamental properties and applications. Examples range from simple gratings to photonic crystals. Obtaining control over the optical properties is of crucial importance in this context, and it is often attempted by electro-optical effect or by using magnetic fields. In this paper, we introduce the use of light to switch and tune the optical response of a structured material, exploiting a physical deformation induced by light itself. In this new strategy, light drives an elastic reshaping, which leads to different spectral properties and hence to a change in the optical response. This is made possible by the use of liquid crystalline networks structured by Direct Laser Writing. As a proof of concept, a grating structure with sub-millisecond time-response is demonstrated for optical beam steering exploiting an optically induced reversible shape-change. Experimental observations are combined with finite-element modeling to understand the actuation process dynamics and to obtain information on how to tune the time and the power response of this technology. This optical beam steerer serves as an example for achieving full optical control of light in broad range of structured optical materials

The extended structure of the remote cluster B514 in M31. Detection of extra-tidal stars

We present a study of the density profile of the remote M31 globular cluster B514, obtained from HST/ACS observations. Coupling the analysis of the distribution of the integrated light with star counts we can reliably follow the profile of the cluster out to r~35", corresponding to ~130pc. The profile is well fitted, out to ~15 core radii, by a King Model having C=1.65. With an estimated core radius r_c=0.38", this corresponds to a tidal radius of r_t~17" (~65pc). We find that both the light and the star counts profiles show a departure from the best fit King model for r>~8" - as a surface brightness excess at large radii, and the star counts profile shows a clear break in correspondence of the estimated tidal radius. Both features are interpreted as the signature of the presence of extratidal stars around the cluster. We also show that B514 has a half-light radius significantly larger than ordinary globular clusters of the same luminosity. In the M_V vs. log r_h plane, B514 lies in a region inhabited by peculiar clusters, like Omega Cen, G1, NGC2419 and others, as well as by the nuclei of dwarf elliptical galaxies.Comment: 9 pages, 6 figures. Accepted for publication in Astronomy & Astrophysic

Photonic artificial muscles: From micro robots to tissue engineering

Light responsive shape-changing polymers are able to mimic the function of biological muscles accomplishing mechanical work in response to selected stimuli. A variety of manufacturing techniques and chemical processes can be employed to shape these materials to different length scales, from centimeter fibers and films to 3D printed micrometric objects trying to replicate biological functions and operations. Controlled deformations shown to mimick basic animal operations such as walking, swimming or grabbing objects, while also controlling the refractive index and the geometry of devices, opens up the potential to implement tunable optical properties. Another possibility is that of combining artificial polymers with cells or biological tissue (such as intact cardiac trabeculae) with the aim to improve tissue formation in vitro or to support the mechanical function of damaged biological muscles. Such versatility is afforded by chemistry. New customized liquid crystalline monomers are presented here that modulate material properties for different applications. The role of synthetic material composition is highlighted as we demonstrate how using apparently similar molecular formulations, that liquid crystalline polymers can be adapted to different technological and medical challenges

Seeing deconvolution of globular clusters in M31

Seeing deconvolution of surface-brightness profiles using the regularized multi-Gaussian method is potentially a powerful method for extraction of morphological information from digital images. Here we illustrate this method by applying it to CCD images of six globular clusters in M31. We demonstrate that it is possible to make some judgments about the dynamical structure of M31 globulars, using good-seeing, deconvolved CCD images obtained from the ground; for example, whether they have post-core-collapse morphology or not. The effective resolution limit of the method is about 0.1-0.3 arcsec, for the CCD images obtained in FWHM ≃ 1 arcsec seeing, and sampling of 0.3 arcsec/pixel. We also demonstrate the robustness of the method, i.e., its insensivity to the exact choices of the functional representation of the point-spread function, details of the deconvolution technique, etc. The situation is equivalent in terms of angular resolution and sampling to observing globular clusters in the Virgo Cluster (e.g., around M87) with the Hubble Space Telescope, and the methods demonstrated here may be applied to HST data in the future. Dynamical structure of globular clusters, e.g., propensity for the post-core-collapse morphology as a function of position in the host galaxy, reflects the global dynamical evolution of a globular cluster system, as was already demonstrated for our galaxy. Similar studies of large samples of globulars in M31 and other Local Group galaxies from the ground, and out to Virgo with the HST, can provide valuable insights about the mass distribution in galaxies, and the formation and evolution of their globular cluster systems. This pilot study is a step in this direction

Correlations of Globular Cluster Properties: Their Interpretations and Uses

Correlations among the independently measured physical properties of globular clusters (GCs) can provide powerful tests for theoretical models and new insights into their dynamics, formation, and evolution. We review briefly some of the previous work, and present preliminary results from a comparative study of GC correlations in the Local Group galaxies. The results so far indicate that these diverse GC systems follow the same fundamental correlations, suggesting a commonality of formative and evolutionary processes which produce them.Comment: An invited review, to appear in "New Horizons in Globular Cluster Astronomy", eds. G. Piotto, G. Meylan, S.G. Djorgovski, and M. Riello, ASPCS, in press (2003). Latex file, 8 pages, 5 eps figures, style files include

L’ectopia tiroidea: problemi di diagnosi e terapia

Gli Autori analizzando la casistica di tireopatie operate in circa un ventennio (2.670) riportano i casi di ectopia tiroidea (22) giunti alla loro osservazione, discutendone le caratteristiche cliniche nonché l’approccio diagnostico e terapeutico. Talora asintomatica, talora emersa clinicamente solo a seguito di tiroidectomia, l’ectopia tiroidea può creare problemi sia di funzione sia, più frequentemente, locali da compressione che richiedono il trattamento chirurgico, sempre indicato a loro parere anche in forme asintomatiche. Seppur rara, infatti, non può essere trascurata l’ipotesi della degenerazione neoplastica, intercorsa in due casi nella loro esperienza