Dynamics of the Heisenberg XXZ model across the ferromagnetic transition

In questa tesi viene presentata un'analisi numerica dell'evoluzione dinamica del modello di Heisenberg XXZ, la cui simulazione è stata effettuata utilizzando l'algoritmo che va sotto il nome di DMRG. La transizione di fase presa in esame è quella dalla fase paramagnetica alla ferromagnetica: essa viene simulata in una catena di 12 siti per vari tempi di quench. In questo modo si sono potuti esplorare diversi regimi di transizione, da quello istantaneo al quasi-adiabatico. Come osservabili sono stati scelti l'entropia di entanglement, la magnetizzazione di mezza catena e lo spettro dell'entanglement, particolarmente adatti per caratterizzare la fisica non all'equilibrio di questo tipo di sistemi. Lo scopo dell'analisi è tentare una descrizione della dinamica fuori dall'equilibrio del modello per mezzo del meccanismo di Kibble-Zurek, che mette in relazione la sviluppo di una fase ordinata nel sistema che effettua la transizione quantistica alla densità di difetti topologici, la cui legge di scala è predicibile e legata agli esponenti critici universali caratterizzanti la transizione.

Analysis of the Kohn Laplacian on the Heisenberg Group and on Cauchy-Riemann Manifolds

The purpose of this study is to analyse the regularity of a differential operator, the Kohn Laplacian, in two settings: the Heisenberg group and the strongly pseudoconvex CR manifolds. The Heisenberg group is defined as a space of dimension 2n+1 with a product. It can be seen in two different ways: as a Lie group and as the boundary of the Siegel UpperHalf Space. On the Heisenberg group there exists the tangential CR complex. From this we define its adjoint and the Kohn-Laplacian. Then we obtain estimates for the Kohn-Laplacian and find its solvability and hypoellipticity. For stating L^p and Holder estimates, we talk about homogeneous distributions. In the second part we start working with a manifold M of real dimension 2n+1. We say that M is a CR manifold if some properties are satisfied. More, we say that a CR manifold M is strongly pseudoconvex if the Levi form defined on M is positive defined. Since we will show that the Heisenberg group is a model for the strongly pseudo-convex CR manifolds, we look for an osculating Heisenberg structure in a neighborhood of a point in M, and we want this structure to change smoothly from a point to another. For that, we define Normal Coordinates and we study their properties. We also examinate different Normal Coordinates in the case of a real hypersurface with an induced CR structure. Finally, we define again the CR complex, its adjoint and the Laplacian operator on M. We study these new operators showing subelliptic estimates. For that, we don't need M to be pseudo-complex but we ask less, that is, the Z(q) and the Y(q) conditions. This provides local regularity theorems for Laplacian and show its hypoellipticity on M.

Thermal structure and dynamical modeling of a Mediterranean tropical-like cyclone

In the present work, a detailed analysis of a Mediterranean TLC occurred in January 2014 has been conducted. The author is not aware of other studies regarding this particular event at the publication of this thesis. In order to outline the cyclone evolution, observational data, including weather-stations data, satellite data, radar data and photographic evidence, were collected at first. After having identified the cyclone path and its general features, the GLOBO, BOLAM and MOLOCH NWP models, developed at ISAC-CNR (Bologna), were used to simulate the phenomenon. Particular attention was paid on the Mediterranean phase as well as on the Atlantic phase, since the cyclone showed a well defined precursor up to 3 days before the minimum formation in the Alboran Sea. The Mediterranean phase has been studied using different combinations of GLOBO, BOLAM and MOLOCH models, so as to evaluate the best model chain to simulate this kind of phenomena. The BOLAM and MOLOCH models showed the best performance, by adjusting the path erroneously deviated in the National Centre for Environmental Prediction (NCEP) and ECMWF operational models. The analysis of the cyclone thermal phase shown the presence of a deep-warm core structure in many cases, thus confirming the tropical-like nature of the system. Furthermore, the results showed high sensitivity to initial conditions in the whole lifetime of the cyclone, while the Sea Surface Temperature (SST) modification leads only to small changes in the Adriatic phase. The Atlantic phase has been studied using GLOBO and BOLAM model and with the aid of the same methodology already developed. After tracing the precursor, in the form of a low-pressure system, from the American East Coast to Spain, the thermal phase analysis was conducted. The parameters obtained showed evidence of a deep-cold core asymmetric structure during the whole Atlantic phase, while the first contact with the Mediterranean Sea caused a sudden transition to a shallow-warm core structure. The examination of Potential Vorticity (PV) 3-dimensional structure revealed the presence of a PV streamer that individually formed over Greenland and eventually interacted with the low-pressure system over the Spanish coast, favouring the first phase of the cyclone baroclinic intensification. Finally, the development of an automated system that tracks and studies the thermal phase of Mediterranean cyclones has been encouraged. This could lead to the forecast of potential tropical transition, against with a minimum computational investment.

Axion-like particles and the 3.5 keV line in 4D string models

This work is focused on axions and axion like particles (ALPs) and their possible relation with the 3.55 keV photon line detected, in recent years, from galaxy clusters and other astrophysical objects. We focus on axions that come from string compactification and we study the vacuum structure of the resulting low energy 4D N=1 supergravity effective field theory. We then provide a model which might explain the 3.55 keV line through the following processes. A 7.1 keV dark matter axion decays in two light axions, which, in turn, are transformed into photons thanks to the Primakoff effect and the existence of a kinetic mixing between two U(1)s gauge symmetries belonging respectively to the hidden and the visible sector. We present two models, the first one gives an outcome inconsistent with experimental data, while the second can yield the desired result.

Geometric versus Model Predictive Control based guidance algorithms for fixed-wing UAVs in the presence of very strong wind fields.

The recent years have witnessed increased development of small, autonomous fixed-wing Unmanned Aerial Vehicles (UAVs). In order to unlock widespread applicability of these platforms, they need to be capable of operating under a variety of environmental conditions. Due to their small size, low weight, and low speeds, they require the capability of coping with wind speeds that are approaching or even faster than the nominal airspeed. In this thesis, a nonlinear-geometric guidance strategy is presented, addressing this problem. More broadly, a methodology is proposed for the high-level control of non-holonomic unicycle-like vehicles in the presence of strong flowfields (e.g. winds, underwater currents) which may outreach the maximum vehicle speed. The proposed strategy guarantees convergence to a safe and stable vehicle configuration with respect to the flowfield, while preserving some tracking performance with respect to the target path. As an alternative approach, an algorithm based on Model Predictive Control (MPC) is developed, and a comparison between advantages and disadvantages of both approaches is drawn. Evaluations in simulations and a challenging real-world flight experiment in very windy conditions confirm the feasibility of the proposed guidance approach.