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.

Probabilistic approaches in civil engineering: generation of random fields and structural identification with genetic algorithms

The inherent stochastic character of most of the physical quantities involved in engineering models has led to an always increasing interest for probabilistic analysis. Many approaches to stochastic analysis have been proposed. However, it is widely acknowledged that the only universal method available to solve accurately any kind of stochastic mechanics problem is Monte Carlo Simulation. One of the key parts in the implementation of this technique is the accurate and efficient generation of samples of the random processes and fields involved in the problem at hand. In the present thesis an original method for the simulation of homogeneous, multi-dimensional, multi-variate, non-Gaussian random fields is proposed. The algorithm has proved to be very accurate in matching both the target spectrum and the marginal probability. The computational efficiency and robustness are very good too, even when dealing with strongly non-Gaussian distributions. What is more, the resulting samples posses all the relevant, welldefined and desired properties of “translation fields”, including crossing rates and distributions of extremes. The topic of the second part of the thesis lies in the field of non-destructive parametric structural identification. Its objective is to evaluate the mechanical characteristics of constituent bars in existing truss structures, using static loads and strain measurements. In the cases of missing data and of damages that interest only a small portion of the bar, Genetic Algorithm have proved to be an effective tool to solve the problem.

Design and Computation of Warped Time-Frequency Transforms

In this work we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed mathematical model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is known to be analytically characterized and fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped non-smooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.

Lie symmetries in cortical inspired CNNs

Our scope in this thesis is to propose architectures of CNNs in such a way to model the early visual pathway, including the Lateral Geniculate Nucleus and the Horizontal Connectivity of the primary visual cortex. Moreover, we will show how cortically inspired architectures allow to perform contrast perceptual invariance as well as grouping and the emergence of visual percepts. Particularly, the LGN is modeled with a first layer l0 containing a single filter Ψ0 that pre-filters the image I. Since the RPs of the LGN cells can be modeled as a LoG, we expect to obtain a radially symmetric filter with a similar shape; to this end, we prove the rotational invariance of Ψ0 and we study the influence of this filter to the subsequent layer. Indeed, we compare the statistic distribution of the filters in the second layer l1 of our architecture with the statistic distribution of the RPs of V1 cells of a macaque. Then, we model the horizontal connectivity of V1 implementing a transition kernel K1 to the layer l1. In this setting, we study the vector fields and the association fields induced by the connectivity kernel K1. To this end, we first approximate the filters bank in l1 with a Gabor function and use the parameters just found to re-parameterize the kernel. Thanks to this step, the kernel is now re-parameterized into a sub-Riemmanian space R2 × S1. Now we are able to compare the vector and association fields induced by K1 with the models of the horizontal connectivity.

Wordline approach to higher spin fields

The main object of this thesis is the analysis and the quantization of spinning particle models which employ extended ”one dimensional supergravity” on the worldline, and their relation to the theory of higher spin fields (HS). In the first part of this work we have described the classical theory of massless spinning particles with an SO(N) extended supergravity multiplet on the worldline, in flat and more generally in maximally symmetric backgrounds. These (non)linear sigma models describe, upon quantization, the dynamics of particles with spin N/2. Then we have analyzed carefully the quantization of spinning particles with SO(N) extended supergravity on the worldline, for every N and in every dimension D. The physical sector of the Hilbert space reveals an interesting geometrical structure: the generalized higher spin curvature (HSC). We have shown, in particular, that these models of spinning particles describe a subclass of HS fields whose equations of motions are conformally invariant at the free level; in D = 4 this subclass describes all massless representations of the Poincar´e group. In the third part of this work we have considered the one-loop quantization of SO(N) spinning particle models by studying the corresponding partition function on the circle. After the gauge fixing of the supergravity multiplet, the partition function reduces to an integral over the corresponding moduli space which have been computed by using orthogonal polynomial techniques. Finally we have extend our canonical analysis, described previously for flat space, to maximally symmetric target spaces (i.e. (A)dS background). The quantization of these models produce (A)dS HSC as the physical states of the Hilbert space; we have used an iterative procedure and Pochhammer functions to solve the differential Bianchi identity in maximally symmetric spaces. Motivated by the correspondence between SO(N) spinning particle models and HS gauge theory, and by the notorious difficulty one finds in constructing an interacting theory for fields with spin greater than two, we have used these one dimensional supergravity models to study and extract informations on HS. In the last part of this work we have constructed spinning particle models with sp(2) R symmetry, coupled to Hyper K¨ahler and Quaternionic-K¨ahler (QK) backgrounds.

Development and characterization of non-oxide ceramic composites for mechanical and tribological applications

The main reasons for the attention focused on ceramics as possible structural materials are their wear resistance and the ability to operate with limited oxidation and ablation at temperatures above 2000°C. Hence, this work is devoted to the study of two classes of materials which can satisfy these requirements: silicon carbide -based ceramics (SiC) for wear applications and borides and carbides of transition metals for ultra-high temperatures applications (UHTCs). SiC-based materials: Silicon carbide is a hard ceramic, which finds applications in many industrial sectors, from heat production, to automotive engineering and metals processing. In view of new fields of uses, SiC-based ceramics were produced with addition of 10-30 vol% of MoSi2, in order to obtain electro conductive ceramics. MoSi2, indeed, is an intermetallic compound which possesses high temperature oxidation resistance, high electrical conductivity (21·10-6 Ω·cm), relatively low density (6.31 g/cm3), high melting point (2030°C) and high stiffness (440 GPa). The SiC-based ceramics were hot pressed at 1900°C with addition of Al2O3-Y2O3 or Y2O3-AlN as sintering additives. The microstructure of the composites and of the reference materials, SiC and MoSi2, were studied by means of conventional analytical techniques, such as X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (SEM-EDS). The composites showed a homogeneous microstructure, with good dispersion of the secondary phases and low residual porosity. The following thermo-mechanical properties of the SiC-based materials were measured: Vickers hardness (HV), Young’s modulus (E), fracture toughness (KIc) and room to high temperature flexural strength (σ). The mechanical properties of the composites were compared to those of two monolithic SiC and MoSi2 materials and resulted in a higher stiffness, fracture toughness and slightly higher flexural resistance. Tribological tests were also performed in two configurations disco-on-pin and slideron cylinder, aiming at studying the wear behaviour of SiC-MoSi2 composites with Al2O3 as counterfacing materials. The tests pointed out that the addition of MoSi2 was detrimental owing to a lower hardness in comparison with the pure SiC matrix. On the contrary, electrical measurements revealed that the addition of 30 vol% of MoSi2, rendered the composite electroconductive, lowering the electrical resistance of three orders of magnitude. Ultra High Temperature Ceramics: Carbides, borides and nitrides of transition metals (Ti, Zr, Hf, Ta, Nb, Mo) possess very high melting points and interesting engineering properties, such as high hardness (20-25 GPa), high stiffness (400-500 GPa), flexural strengths which remain unaltered from room temperature to 1500°C and excellent corrosion resistance in aggressive environment. All these properties place the UHTCs as potential candidates for the development of manoeuvrable hypersonic flight vehicles with sharp leading edges. To this scope Zr- and Hf- carbide and boride materials were produced with addition of 5-20 vol% of MoSi2. This secondary phase enabled the achievement of full dense composites at temperature lower than 2000°C and without the application of pressure. Besides the conventional microstructure analyses XRD and SEM-EDS, transmission electron microscopy (TEM) was employed to explore the microstructure on a small length scale to disclose the effective densification mechanisms. A thorough literature analysis revealed that neither detailed TEM work nor reports on densification mechanisms are available for this class of materials, which however are essential to optimize the sintering aids utilized and the processing parameters applied. Microstructural analyses, along with thermodynamics and crystallographic considerations, led to disclose of the effective role of MoSi2 during sintering of Zrand Hf- carbides and borides. Among the investigated mechanical properties (HV, E, KIc, σ from room temperature to 1500°C), the high temperature flexural strength was improved due to the protective and sealing effect of a silica-based glassy phase, especially for the borides. Nanoindentation tests were also performed on HfC-MoSi2 composites in order to extract hardness and elastic modulus of the single phases. Finally, arc jet tests on HfC- and HfB2-based composites confirmed the excellent oxidation behaviour of these materials under temperature exceeding 2000°C; no cracking or spallation occurred and the modified layer was only 80-90 μm thick.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Collective effects for the LHC injectors: non-ultrarelativistic approaches

The upgrade of the CERN accelerator complex has been planned in order to further increase the LHC performances in exploring new physics frontiers. One of the main limitations to the upgrade is represented by the collective instabilities. These are intensity dependent phenomena triggered by electromagnetic fields excited by the interaction of the beam with its surrounding. These fields are represented via wake fields in time domain or impedances in frequency domain. Impedances are usually studied assuming ultrarelativistic bunches while we mainly explored low and medium energy regimes in the LHC injector chain. In a non-ultrarelativistic framework we carried out a complete study of the impedance structure of the PSB which accelerates proton bunches up to 1.4 GeV. We measured the imaginary part of the impedance which creates betatron tune shift. We introduced a parabolic bunch model which together with dedicated measurements allowed us to point to the resistive wall impedance as the source of one of the main PSB instability. These results are particularly useful for the design of efficient transverse instability dampers. We developed a macroparticle code to study the effect of the space charge on intensity dependent instabilities. Carrying out the analysis of the bunch modes we proved that the damping effects caused by the space charge, which has been modelled with semi-analytical method and using symplectic high order schemes, can increase the bunch intensity threshold. Numerical libraries have been also developed in order to study, via numerical simulations of the bunches, the impedance of the whole CERN accelerator complex. On a different note, the experiment CNGS at CERN, requires high-intensity beams. We calculated the interpolating Hamiltonian of the beam for highly non-linear lattices. These calculations provide the ground for theoretical and numerical studies aiming to improve the CNGS beam extraction from the PS to the SPS.

Non-Linear Analysis and Design of Synchronous Bearingless Multiphase Permanent Magnet Machines and Drives

A two-dimensional model to analyze the distribution of magnetic fields in the airgap of a PM electrical machines is studied. A numerical algorithm for non-linear magnetic analysis of multiphase surface-mounted PM machines with semi-closed slots is developed, based on the equivalent magnetic circuit method. By using a modular structure geometry, whose the basic element can be duplicated, it allows to design whatever typology of windings distribution. In comparison to a FEA, permits a reduction in computing time and to directly changing the values of the parameters in a user interface, without re-designing the model. Output torque and radial forces acting on the moving part of the machine can be calculated. In addition, an analytical model for radial forces calculation in multiphase bearingless Surface-Mounted Permanent Magnet Synchronous Motors (SPMSM) is presented. It allows to predict amplitude and direction of the force, depending on the values of torque current, of levitation current and of rotor position. It is based on the space vectors method, letting the analysis of the machine also during transients. The calculations are conducted by developing the analytical functions in Fourier series, taking all the possible interactions between stator and rotor mmf harmonic components into account and allowing to analyze the effects of electrical and geometrical quantities of the machine, being parametrized. The model is implemented in the design of a control system for bearingless machines, as an accurate electromagnetic model integrated in a three-dimensional mechanical model, where one end of the motor shaft is constrained to simulate the presence of a mechanical bearing, while the other is free, only supported by the radial forces developed in the interactions between magnetic fields, to realize a bearingless system with three degrees of freedom. The complete model represents the design of the experimental system to be realized in the laboratory.

Vector meson photoproduction in ultra-peripheral heavy ion collisions with ALICE at the LHC

Ultra-relativistic heavy ions generate strong electromagnetic fields which offer the possibility to study γ-γ and γ-nucleus processes at the LHC in the so called ultra-peripheral collisions (UPC). The photoproduction of J/ψ vector mesons in UPC is sensitive to the gluon distribution of the interacting nuclei. In this thesis the study of coherent and incoherent J/ψ production in Pb-Pb collisions at √sNN = 2.76 TeV is described. The J/ψ has been measured via its leptonic decay in the rapidity range -0.9 < y < 0.9. The cross section for coherent and incoherent J/ψ are given. The results are compared to theoretical models for J/ψ production and the coherent cross section is found to be in good agreement with those models which include nuclear gluon shadowing consistent with EPS09 parametrization. In addition the cross section for the process γ γ→ e+e− has been measured and found to be in agreement with the STARLIGHT Monte Carlo predictions. The analysis has been published by the ALICE Collaboration in the European Physical Journal C, with one of its main plot depicted on the cover-front of the November 2013 issue.

Practical Management of the Endangered African Wild Dog (Lycaon Pictus): Implementation of Research Methodologies, Management Tools and Validation of Non-Invasive Endocrinology Applications

The porpoise of this study was to implement research methodologies and assess the effectiveness and impact of management tools to promote best practices for the long term conservation of the endangered African wild dog (Lycaon pictus). Different methods were included in the project framework to investigate and expand the applicability of these methodologies to free-ranging African wild dogs in the southern African region: ethology, behavioural endocrinology and ecology field methodologies were tested and implemented. Additionally, research was performed to test the effectiveness and implication of a contraceptive implant (Suprenolin) as a management tool for the species of a subpopulation hosted in fenced areas. Attention was especially given to social structure and survival of treated packs. This research provides useful tools and advances the applicability of these methods for field studies, standardizing and improving research instruments in the field of conservation biology and behavioural endocrinology. Results reported here provide effective methodologies to expand the applicability of non-invasive endocrine assessment to previously prohibited fields, and validation of sampling methods for faecal hormone analysis. The final aim was to fill a knowledge gap on behaviours of the species and provide a common ground for future researchers to apply non-invasive methods to this species research and to test the effectiveness of the contraception on a managed metapopulation.

La perdita di chance nel prisma del danno non patrimoniale

Il danno da perdita di chance rappresenta la categoria giuridica di cui la giurisprudenza si serve per ampliare i confini della tutela risarcitoria, in diversi casi in cui, alla stregua dell’impostazione dogmatica tradizionale, non potrebbe dirsi configurabile un danno-conseguenza (né sotto forma di danno emergente, né sotto forma di lucro cessante). Lo studio, una volta delimitato il campo dell’indagine e dato conto delle opinioni dottrinali sulla ricostruzione della figura, ha preso le mosse dall’illustrazione degli orientamenti della giurisprudenza, la quale, a partire dagli anni ’80 del secolo scorso, è andata via via applicando l’istituto nei settori del diritto del lavoro, della responsabilità professionale (in particolare dell’avvocato), e del danno alla persona (nel quale ultimo si è messo in luce come il danno da perdita di chance possa rivestire funzione unicamente descrittiva di tipologie di pregiudizio riconducibili alle “tradizionali” voci di danno). Nel secondo capitolo si è analiticamente esaminata la fattispecie del danno da perdita di chance, alla luce delle categorie e dei principi generali della responsabilità civile, vagliando i margini di “armonizzabilità” dell’istituto rispetto alle classificazioni in termini di danno emergente/lucro cessante, danno presente/futuro, danno-evento/danno-conseguenza, nonché rispetto alle regole sulla causalità, al requisito dell’ingiustizia del danno, e alle tecniche di liquidazione del danno. Nell’ultimo capitolo, si è proceduto, poi, a “calare” l’istituto del danno da perdita di chance nel “sottosettore” della responsabilità sanitaria, sottoponendo a verifica la “tenuta teorica” della sua “variante” non patrimoniale al cospetto della recente novella legislativa rappresentata dalla l. n. 24/17, nonché degli orientamenti giurisprudenziali che, negli ultimi due anni, hanno interessato i temi dell’onere della prova del nesso causale e dello stesso danno da perdita di chance non patrimoniale. A conclusione dello studio, si sono svolte, infine, alcune considerazioni sulle criticità che precludono un’armonica “riconduzione a sistema” dell’istituto, consigliandone il definitivo abbandono.

Application of Pulsed Electric Fields for the Modulation of Chemico-Physical Properties of Different Foods

Pulsed electric field technology is one of the most attractive new non-thermal technology thanks to its lower energy consumption and short treatment times. It consists of an electric treatment of short duration (from several ns to several ms) with electric field strengths from 0.1 to 80 kV/cm that lead to an increase in the permeability of the cell membrane. In this PhD thesis, PEF technology was investigated with the aim of improving mass transfer in plant and animal foods by using it alone or in combination with conventional food processes. Different methods of evaluating electroporation for optimizing PEF processing parameters were investigated. In this respect, the degree of membrane permeabilization in plant and animal food matrices was investigated using electrical impedance spectroscopy, current-voltage measurements and magnetic resonance imaging. The research findings provided useful insights and calls for critical choice of electroporation assessment methods for the selection of adequate PEF treatment conditions. It was outlined that the effect of electroporation is highly dependent on the properties of the food matrix and secondary phenomena occurring in the cell structure undergoing PEF treatment, such as the water re-distribution in the tissue due to the exchange of fluids between intra- and extra-cellular environments. This study also confirmed the great potential of combining PEF technology with conventional food processes, with the main purpose of improving the quality of the food material and accelerating the kinetics of mass transfers, in both plant and animal tissues. Consistent reduction of acrylamide formation in potato crisps was achieved by monitoring key PEF process parameters and subsequent manufacturing steps. Kiwifruit snacks showed a significant reduction in drying kinetics when pre-treated with PEF, while their quality was well maintained. Finally, the research results showed that PEF pre-treatments can shorten the brine process as well as the rehydration kinetics of fish muscles.

La moltiplicazione relazionale dei non imparentati. Un'etnografia delle attese di genitorialità e filiazione intorno alla categoria giuridica di "minore straniero non accompagnato" in Italia.

Sulla spinta dell’approvazione della legge italiana 47/2017 “Disposizioni in materia di misure di protezione dei minori stranieri non accompagnati”, questo lavoro è teso ad affrontare le complesse aspettative genitoriali e parentali sviluppatesi intorno al processo di categorizzazione MSNA di cui questa legge è diventata approdo giuridico. Le controverse aspettative di accompagnamento legatesi alla denominazione di “non accompagnato”, prese come aspetto scontato e assiomatico in molta parte della letteratura scientifica che utilizza l’acronimo, sono state qui intese come un nodo ambiguo e questionabile. Attraverso una ricerca e una metodologia antropologico-etnografica queste rappresentazioni contradditorie sono esplorate a partire da un “crocevia di campi” da queste interessati in un territorio amministrativo dell’Italia Settentrionale variamente frequentato tra 2018 e 2021. Insieme ad ambienti, metodi e sfide della ricerca locale, una prima sezione situa storicamente e contestualmente la categoria MSNA come fenomeno in sé piuttosto che come efficace espressione descrittiva di soggetti. Le due sezioni successive, dedicate rispettivamente alla neo-realtà di tutela volontaria e a quella di una comunità socio-educativa/di tipo familiare rivolta a persone di minore età, interrogano invece questi ambienti come spazi e tempi di elaborazione prima e negoziazione poi di rappresentazioni e pratiche relazionali e parentali molteplici.