Knots and links in lens spaces

The aim of this dissertation is to improve the knowledge of knots and links in lens spaces. If the lens space L(p,q) is defined as a 3-ball with suitable boundary identifications, then a link in L(p,q) can be represented by a disk diagram, i.e. a regular projection of the link on a disk. In this contest, we obtain a complete finite set of Reidemeister-type moves establishing equivalence, up to ambient isotopy. Moreover, the connections of this new diagram with both grid and band diagrams for links in lens spaces are shown. A Wirtinger-type presentation for the group of the link and a diagrammatic method giving the first homology group are described. A class of twisted Alexander polynomials for links in lens spaces is computed, showing its correlation with Reidemeister torsion. One of the most important geometric invariants of links in lens spaces is the lift in 3-sphere of a link L in L(p,q), that is the counterimage of L under the universal covering of L(p,q). Starting from the disk diagram of the link, we obtain a diagram of the lift in the 3-sphere. Using this construction it is possible to find different knots and links in L(p,q) having equivalent lifts, hence we cannot distinguish different links in lens spaces only from their lift. The two final chapters investigate whether several existing invariants for links in lens spaces are essential, i.e. whether they may assume different values on links with equivalent lift. Namely, we consider the fundamental quandle, the group of the link, the twisted Alexander polynomials, the Kauffman Bracket Skein Module and an HOMFLY-PT-type invariant.

A spectroscopic and photometric study of stellar populations in a sample of clusters in the Magellanic Clouds

This Ph.D. Thesis has been carried out in the framework of a long-term and large project devoted to describe the main photometric, chemical, evolutionary and integrated properties of a representative sample of Large and Small Magellanic Cloud (LMC and SMC respectively) clusters. The globular clusters system of these two Irregular galaxies provides a rich resource for investigating stellar and chemical evolution and to obtain a detailed view of the star formation history and chemical enrichment of the Clouds. The results discussed here are based on the analysis of high-resolution photometric and spectroscopic datasets obtained by using the last generation of imagers and spectrographs. The principal aims of this project are summarized as follows: • The study of the AGB and RGB sequences in a sample of MC clusters, through the analysis of a wide near-infrared photometric database, including 33 Magellanic globulars obtained in three observing runs with the near-infrared camera SOFI@NTT (ESO, La Silla). • The study of the chemical properties of a sample of MCs clusters, by using optical and near-infrared high-resolution spectra. 3 observing runs have been secured to our group to observe 9 LMC clusters (with ages between 100 Myr and 13 Gyr) with the optical high-resolution spectrograph FLAMES@VLT (ESO, Paranal) and 4 very young (<30 Myr) clusters (3 in the LMC and 1 in the SMC) with the near-infrared high-resolution spectrograph CRIRES@VLT. • The study of the photometric properties of the main evolutive sequences in optical Color- Magnitude Diagrams (CMD) obtained by using HST archive data, with the final aim of dating several clusters via the comparison between the observed CMDs and theoretical isochrones. The determination of the age of a stellar population requires an accurate measure of the Main Sequence (MS) Turn-Off (TO) luminosity and the knowledge of the distance modulus, reddening and overall metallicity. For this purpose, we limited the study of the age just to the clusters already observed with high-resolution spectroscopy, in order to date only clusters with accurate estimates of the overall metallicity.

Mg for hydrogen storage: synthesis, nanostructure and thermodynamics properties

Nowadays alternative energies are an extremely important topic and the possibility of using hydrogen as an energy carrier must be explored. Many problems infer the technological application of this abundant and powerful resource, one of them the possibility of storage. In the framework of suitable materials for hydrogen storage, magnesium has been the center of this study because it is cheap and the amount of stored hydrogen that it achieves (7.6 wt%) is extremely appealing. Nanostructure helps to overcome the slow hydrogen diffusion and the functionalization of surfaces with transition metals or oxides favors the hydrogen molecule dissociation/recombination. The aim of this research is the investigation of the metal-hydride transformation in magnesium nanoparticles synthesized by inert-gas condensation, exploiting the fact that they are a simple model system. The so produced nanostructured powder has been analyzed in response to nanoparticles surface functionalization by transition metal clusters, specifically palladium, nickel and titanium, chosen on the basis of their completely different Mg-related phase diagrams. The role of the intermetallic phases formed upon heating and hydrogenation treatments will be presented to provide a comprehensive picture of hydrogen sorption in this class of nanostructured storage materials.

Peak-to-Peak Output Current Ripple Analysis in Multiphase and Multilevel Inverters

Analysis of the peak-to-peak output current ripple amplitude for multiphase and multilevel inverters is presented in this PhD thesis. The current ripple is calculated on the basis of the alternating voltage component, and peak-to-peak value is defined by the current slopes and application times of the voltage levels in a switching period. Detailed analytical expressions of peak-to-peak current ripple distribution over a fundamental period are given as function of the modulation index. For all the cases, reference is made to centered and symmetrical switching patterns, generated either by carrier-based or space vector PWM. Starting from the definition and the analysis of the output current ripple in three-phase two-level inverters, the theoretical developments have been extended to the case of multiphase inverters, with emphasis on the five- and seven-phase inverters. The instantaneous current ripple is introduced for a generic balanced multiphase loads consisting of series RL impedance and ac back emf (RLE). Simplified and effective expressions to account for the maximum of the output current ripple have been defined. The peak-to-peak current ripple diagrams are presented and discussed. The analysis of the output current ripple has been extended also to multilevel inverters, specifically three-phase three-level inverters. Also in this case, the current ripple analysis is carried out for a balanced three-phase system consisting of series RL impedance and ac back emf (RLE), representing both motor loads and grid-connected applications. The peak-to-peak current ripple diagrams are presented and discussed. In addition, simulation and experimental results are carried out to prove the validity of the analytical developments in all the cases. The cases with different phase numbers and with different number of levels are compared among them, and some useful conclusions have been pointed out. Furthermore, some application examples are given.