Multiple stellar populations in globular clusters with photometry and low resolution spectroscopy

Our view of Globular Clusters has deeply changed in the last decade. Modern spectroscopic and photometric data have conclusively established that globulars are neither coeval nor monometallic, reopening the issue of the formation of such systems. Their formation is now schematized as a two-step process, during which the polluted matter from the more massive stars of a first generation gives birth, in the cluster innermost regions, to a second generation of stars with the characteristic signature of fully CNO-processed matter. To date, star-to-star variations in abundances of the light elements (C, N, O, Na) have been observed in stars of all evolutionary phases in all properly studied Galactic globular clusters. Multiple or broad evolutionary sequences have also been observed in nearly all the clusters that have been observed with good signal-to-noise in the appropriate photometric bands. The body of evidence suggests that spreads in light-element abundances can be fairly well traced by photometric indices including near ultraviolet passbands, as CNO abundance variations affect mainly wavelengths shorter than ~400 nm owing to the rise of some NH and CN molecular absorption bands. Here, we exploit this property of near ultraviolet photometry to trace internal chemical variations and combined it with low resolution spectroscopy aimed to derive carbon and nitrogen abundances in order to maximize the information on the multiple populations. This approach has been proven to be very effective in (i) detecting multiple population, (ii) characterizing their global properties (i.e., relative fraction of stars, location in the color-magnitude diagram, spatial distribution, and trends with cluster parameters) and (iii) precisely tagging their chemical properties (i.e., extension of the C-N anticorrelation, bimodalities in the N content).

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.

Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

Strength and ductility of corroded strands within the framework of safety assessment of existing bridges

Existing bridges built in the last 50 years face challenges due to states far different than those envisaged when they were designed, due to increased loads, ageing of materials, and poor maintenance. For post-tensioned bridges, the need emerged for reliable engineering tools for the evaluation of their capacity in case of steel corrosion due to lack of mortar injection. This can lead to sudden brittle collapses, highlighting the need for proper maintenance and monitoring. This thesis proposes a peak strength model for corroded strands, introducing a “group coefficient” that aims at considering corrosion variability in the wires constituting the strands. The application of the introduced model in a deterministic approach leads to the proposal of strength curves for corroded strands, which represent useful engineering tools for estimating their maximum strength considering both geometry of the corrosion and steel material parameters. Together with the proposed ultimate displacement curves, constitutive laws of the steel material reduced by the effects of corrosion can be obtained. The effects of corroded strands on post-tensioned beams can be evaluated through the reduced bending moment-curvature diagram accounting for these reduced stress-strain relationships. The application of the introduced model in a probabilistic approach allows to estimate peak strength probability functions and consecutive design-oriented safety factors to consider corrosion effects in safety assessment verifications. Both approaches consider two procedures that are based on the knowledge level of the corrosion in the strands. On the sidelines of this main research line, this thesis also presents a study of a seismic upgrading intervention of a case-study bridge through HDRB isolators providing a simplified procedure for the identification of the correct device. The study also investigates the effects due to the variability of the shear modulus of the rubber material of the HDRB isolators on the structural response of the isolated bridge.

Model selection and the vectorial misspecification-resistant information criterion in multivariate time series

The thesis deals with the problem of Model Selection (MS) motivated by information and prediction theory, focusing on parametric time series (TS) models. The main contribution of the thesis is the extension to the multivariate case of the Misspecification-Resistant Information Criterion (MRIC), a criterion introduced recently that solves Akaike’s original research problem posed 50 years ago, which led to the definition of the AIC. The importance of MS is witnessed by the huge amount of literature devoted to it and published in scientific journals of many different disciplines. Despite such a widespread treatment, the contributions that adopt a mathematically rigorous approach are not so numerous and one of the aims of this project is to review and assess them. Chapter 2 discusses methodological aspects of MS from information theory. Information criteria (IC) for the i.i.d. setting are surveyed along with their asymptotic properties; and the cases of small samples, misspecification, further estimators. Chapter 3 surveys criteria for TS. IC and prediction criteria are considered for: univariate models (AR, ARMA) in the time and frequency domain, parametric multivariate (VARMA, VAR); nonparametric nonlinear (NAR); and high-dimensional models. The MRIC answers Akaike’s original question on efficient criteria, for possibly-misspecified (PM) univariate TS models in multi-step prediction with high-dimensional data and nonlinear models. Chapter 4 extends the MRIC to PM multivariate TS models for multi-step prediction introducing the Vectorial MRIC (VMRIC). We show that the VMRIC is asymptotically efficient by proving the decomposition of the MSPE matrix and the consistency of its Method-of-Moments Estimator (MoME), for Least Squares multi-step prediction with univariate regressor. Chapter 5 extends the VMRIC to the general multiple regressor case, by showing that the MSPE matrix decomposition holds, obtaining consistency for its MoME, and proving its efficiency. The chapter concludes with a digression on the conditions for PM VARX models.