Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Sistemi liquido cristallini complessi: simulazioni al calcolatore e studi ESR

The aim of this PhD thesis was to study at a microscopic level different liquid crystal (LC) systems, in order to determine their physical properties, resorting to two distinct methodologies, one involving computer simulations, and the other spectroscopic techniques, in particular electron spin resonance (ESR) spectroscopy. By means of the computer simulation approach we tried to demonstrate this tool effectiveness for calculating anisotropic static properties of a LC material, as well as for predicting its behaviour and features. This required the development and adoption of suitable molecular models based on a convenient intermolecular potentials reflecting the essential molecular features of the investigated system. In particular, concerning the simulation approach, we have set up models for discotic liquid crystal dimers and we have studied, by means of Monte Carlo simulations, their phase behaviour and self­-assembling properties, with respect to the simple monomer case. Each discotic dimer is described by two oblate Gay­Berne ellipsoids connected by a flexible spacer, modelled by a harmonic "spring" of three different lengths. In particular we investigated the effects of dimerization on the transition temperatures, as well as on the characteristics of molecular aggregation displayed and the relative orientational order. Moving to the experimental results, among the many experimental techniques that are typically employed to evaluate LC system distinctive features, ESR has proved to be a powerful tool in microscopic scale investigation of the properties, structure, order and dynamics of these materials. We have taken advantage of the high sensitivity of the ESR spin probe technique to investigate increasingly complex LC systems ranging from devices constituted by a polymer matrix in which LC molecules are confined in shape of nano- droplets, as well as biaxial liquid crystalline elastomers, and dimers whose monomeric units or lateral groups are constituted by rod-like mesogens (11BCB). Reflection-mode holographic-polymer dispersed liquid crystals (H-PDLCs) are devices in which LCs are confined into nanosized (50­-300 nm) droplets, arranged in layers which alternate with polymer layers, forming a diffraction grating. We have determined the configuration of the LC local director and we have derived a model of the nanodroplet organization inside the layers. Resorting also to additional information on the nanodroplet size and shape distribution provided by SEM images of the H-PDLC cross-section, the observed director configuration has been modeled as a bidimensional distribution of elongated nanodroplets whose long axis is, on the average, parallel to the layers and whose internal director configuration is a uniaxial quasi- monodomain aligned along the nanodroplet long axis. The results suggest that the molecular organization is dictated mainly by the confinement, explaining, at least in part, the need for switching voltages significantly higher and the observed faster turn-off times in H-PDLCs compared to standard PDLC devices. Liquid crystal elastomers consist in cross-linked polymers, in which mesogens represent the monomers constituting the main chain or the laterally attached side groups. They bring together three important aspects: orientational order in amorphous soft materials, responsive molecular shape and quenched topological constraints. In biaxial nematic liquid crystalline elastomers (BLCEs), two orthogonal directions, rather than the one of normal uniaxial nematic, can be controlled, greatly enhancing their potential value for applications as novel actuators. Two versions of a side-chain BLCEs were characterized: side­-on and end­-on. Many tests have been carried out on both types of LCE, the main features detected being the lack of a significant dynamical behaviour, together with a strong permanent alignment along the principal director, and the confirmation of the transition temperatures already determined by DSC measurements. The end­-on sample demonstrates a less hindered rotation of the side group mesogenic units and a greater freedom of alignment to the magnetic field, as already shown by previous NMR studies. Biaxial nematic ESR static spectra were also obtained on the basis of Molecular Dynamics generated biaxial configurations, to be compared to the experimentally determined ones, as a mean to establish a possible relation between biaxiality and the spectral features. This provides a concrete example of the advantages of combining the computer simulation and spectroscopic approaches. Finally, the dimer α,ω-bis(4'-cyanobiphenyl-4-yl)undecane (11BCB), synthesized in the "quest" for the biaxial nematic phase has been analysed. Its importance lies in the dimer significance as building blocks in the development of new materials to be employed in innovative technological applications, such as faster switching displays, resorting to the easier aligning ability of the secondary director in biaxial phases. A preliminary series of tests were performed revealing the population of mesogenic molecules as divided into two groups: one of elongated straightened conformers sharing a common director, and one of bent molecules, which display no order, being equally distributed in the three dimensions. Employing this model, the calculated values show a consistent trend, confirming at the same time the transition temperatures indicated by the DSC measurements, together with rotational diffusion tensor values that follow closely those of the constituting monomer 5CB.

Dynamic stabilization of Rayleigh-Taylor instability of ablation fronts in inertial confinement fusion

One of the most important problems in inertial confinement fusion is how to find a way to mitigate the onset of the Rayleigh-Taylor instability which arises in the ablation front during the compression. In this thesis it is studied in detail the possibility of using for such a purpose the well-known mechanism of dynamic stabilization, already applied to other dynamical systems such as the inverted pendulum. In this context, a periodic acceleration superposed to the background gravity generates a vertical vibration of the ablation front itself. The effects of different driving modulations (Dirac deltas and square waves) are analyzed from a theoretical point of view, with a focus on stabilization of ion beam driven ablation fronts, and a comparison is made, in order to look for optimization.

Modellazione Tridimensionale del Processo di Combustione di un Razzo a Propellente Solido

La regolazione dei sistemi di propulsione a razzo a propellente solido (Solid Rocket Motors) ha da sempre rappresentato una delle principali problematiche legate a questa tipologia di motori. L’assenza di un qualsiasi genere di controllo diretto del processo di combustione del grano solido, fa si che la previsione della balistica interna rappresenti da sempre il principale strumento utilizzato sia per definire in fase di progetto la configurazione ottimale del motore, sia per analizzare le eventuali anomalie riscontrate in ambito sperimentale. Variazioni locali nella struttura del propellente, difettosità interne o eterogeneità nelle condizioni di camera posso dare origine ad alterazioni del rateo locale di combustione del propellente e conseguentemente a profili di pressione e di spinta sperimentali differenti da quelli previsti per via teorica. Molti dei codici attualmente in uso offrono un approccio piuttosto semplificato al problema, facendo per lo più ricorso a fattori correttivi (fattori HUMP) semi-empirici, senza tuttavia andare a ricostruire in maniera più realistica le eterogeneità di prestazione del propellente. Questo lavoro di tesi vuole dunque proporre un nuovo approccio alla previsione numerica delle prestazioni dei sistemi a propellente solido, attraverso la realizzazione di un nuovo codice di simulazione, denominato ROBOOST (ROcket BOOst Simulation Tool). Richiamando concetti e techiche proprie della Computer Grafica, questo nuovo codice è in grado di ricostruire in processo di regressione superficiale del grano in maniera puntuale, attraverso l’utilizzo di una mesh triangolare mobile. Variazioni locali del rateo di combustione posso quindi essere facilmente riprodotte ed il calcolo della balistica interna avviene mediante l’accoppiamento di un modello 0D non-stazionario e di uno 1D quasi-stazionario. L’attività è stata svolta in collaborazione con l’azienda Avio Space Division e il nuovo codice è stato implementato con successo sul motore Zefiro 9.

Estimation of Quasi-Rational DSGE Models

Small-scale dynamic stochastic general equilibrium have been treated as the benchmark of much of the monetary policy literature, given their ability to explain the impact of monetary policy on output, inflation and financial markets. One cause of the empirical failure of New Keynesian models is partially due to the Rational Expectations (RE) paradigm, which entails a tight structure on the dynamics of the system. Under this hypothesis, the agents are assumed to know the data genereting process. In this paper, we propose the econometric analysis of New Keynesian DSGE models under an alternative expectations generating paradigm, which can be regarded as an intermediate position between rational expectations and learning, nameley an adapted version of the "Quasi-Rational" Expectatations (QRE) hypothesis. Given the agents' statistical model, we build a pseudo-structural form from the baseline system of Euler equations, imposing that the length of the reduced form is the same as in the `best' statistical model.

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.

Mode-I fracture parameters of quasi-brittle materials: direct evaluation using DIC and relationship with Mode-II interfacial parameters

The objective of this thesis is the investigation of the Mode-I fracture mechanics parameters of quasi-brittle materials to shed light onto the influence of the width and size of the specimen on the fracture response of notched beams. To further the knowledge on the fracture process, 3D digital image correlation (DIC) was employed. A new method is proposed to determine experimentally the critical value of the crack opening, which is then used to determine the size of the fracture process zone (FPZ). In addition, the Mode-I fracture mechanics parameters are compared with the Mode-II interfacial properties of composites materials that feature as matrices the quasi-brittle materials studied in Mode-I conditions. To investigate the Mode II fracture parameters, single-lap direct shear tests are performed. Notched concrete beams with six cross-sections has been tested using a three-point bending (TPB) test set-up (Mode-I fracture mechanics). Two depths and three widths of the beam are considered. In addition to concrete beams, alkali-activated mortar beams (AAMs) that differ by the type and size of the aggregates have been tested using the same TPB set-up. Two dimensions of AAMs are considered. The load-deflection response obtained from DIC is compared with the load-deflection response obtained from the readings of two linear variable displacement transformers (LVDT). Load responses, peak loads, strain profiles along the ligament from DIC, fracture energy and failure modes of TPB tests are discussed. The Mode-II problem is investigated by testing steel reinforced grout (SRG) composites bonded to masonry and concrete elements under single-lap direct shear tests. Two types of anchorage systems are proposed for SRG reinforced masonry and concrete element to study their effectiveness. An indirect method is proposed to find the interfacial properties, compare them with the Mode-I fracture properties of the matrix and to model the effect of the anchorage.

The United Nations 'quasi-prosecutorial' investigative mechanisms: assessing a new institutional model in the international criminal justice landscape

This work aims to provide a theoretical examination of three recently created bodies of the United Nations mandated to investigate the alleged international crimes committed in Syria (IIIM), Iraq (UNITAD) and Myanmar (IIMM). Established as a compromise solution in the paralysis of international criminal jurisdictions, these essentially overlapping entities have been depicted as a ‘new generation’ of UN investigative mechanisms. While non-judicial in nature, they depart indeed from traditional commissions of inquiry in several respects due to their increased criminal or ‘quasi-prosecutorial’ character. After clarifying their legal basis and different mandating authorities, a comparative institutional analysis is thus carried out in order to ascertain whether these ‘mechanisms’ can be said to effectively represent a new institutional model. Through an in-depth assessment of their mandates, the thesis is also intended to outline both the strengths and the criticalities of these organs. Given their aim to facilitate criminal proceedings by sharing information and case files, it is suggested that more attention shall be paid to the position of the person under investigation. To this end, some proposals are made in order to enhance the mechanisms’ frameworks, especially from the angle of procedural safeguards. As a third aspect, the cooperation with judicial authorities is explored, in order to shed light on the actors involved, the relevant legal instruments and the possible obstacles, in particular from a human rights perspective. Ultimately, drawing from the detected issues, the thesis seeks to identify some lessons learned which could be taken into account in case of creation of new ad hoc investigative mechanisms or of a permanent institution of this kind.

Far muovere, lasciar morire. Analisi delle politiche di confinamento e mobilita dei profughi siriani in Libano.

L’obiettivo di questa analisi è di coniugare la ricostruzione dei processi di assoggettamento che producono i copioni entro cui prende forma la soggettività dei profughi siriani, con la ricostruzione delle problematizzazioni alla base dei sistemi di controllo e gestione della circolazione regolare. Secondo l’UNHCR, tra il 2012 e il 2016 quasi un milione e mezzo di profughi siriani si è stabilita in Libano nel tentativo di sottrarsi all’intensificarsi del conflitto tra il regime di Assad e il fronte variegato di milizie ribelli. Questa popolazione in esilio si è confrontata con le politiche di amministrazione e controllo della loro presenza dispiegate dall’assemblaggio tra istituzioni locali e internazionali: in particolare, i governi libanesi che si sono avvicendati dal 2013 hanno progressivamente implementato interventi di inclusione differenziale della popolazione di profughi, relegandone la maggioranza in uno stato di marginalità e precarietà esistenziale. Di conseguenza, per molti di loro provare ad accedere a forme di mobilità regolare si impone come uno dei pochi percorsi possibili per ottenere il riconoscimento di un livello minimo di esistenza legittima. L’analisi sviluppata in questo elaborato si basa su una ricerca etnografica condotta in Libano nella regione dell’Akkar tra il 2019 e il 2020, a cui è stata associato uno studio dell’infrastruttura tecnico-politica dei Corridoi Umanitari, un programma per la mobilità dei profughi avviato nel biennio 2016-2017, grazie alla collaborazione tra autorità italiane e una serie di associazioni religiose attive in Italia.