Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

Cosmological perturbations in generalized theories of gravity

The first part of the thesis concerns the study of inflation in the context of a theory of gravity called "Induced Gravity" in which the gravitational coupling varies in time according to the dynamics of the very same scalar field (the "inflaton") driving inflation, while taking on the value measured today since the end of inflation. Through the analytical and numerical analysis of scalar and tensor cosmological perturbations we show that the model leads to consistent predictions for a broad variety of symmetry-breaking inflaton's potentials, once that a dimensionless parameter entering into the action is properly constrained. We also discuss the average expansion of the Universe after inflation (when the inflaton undergoes coherent oscillations about the minimum of its potential) and determine the effective equation of state. Finally, we analyze the resonant and perturbative decay of the inflaton during (p)reheating. The second part is devoted to the study of a proposal for a quantum theory of gravity dubbed "Horava-Lifshitz (HL) Gravity" which relies on power-counting renormalizability while explicitly breaking Lorentz invariance. We test a pair of variants of the theory ("projectable" and "non-projectable") on a cosmological background and with the inclusion of scalar field matter. By inspecting the quadratic action for the linear scalar cosmological perturbations we determine the actual number of propagating degrees of freedom and realize that the theory, being endowed with less symmetries than General Relativity, does admit an extra gravitational degree of freedom which is potentially unstable. More specifically, we conclude that in the case of projectable HL Gravity the extra mode is either a ghost or a tachyon, whereas in the case of non-projectable HL Gravity the extra mode can be made well-behaved for suitable choices of a pair of free dimensionless parameters and, moreover, turns out to decouple from the low-energy Physics.

Semantic-based middleware solutions to support context-aware service provisioning in pervasive environments

The dynamicity and heterogeneity that characterize pervasive environments raise new challenges in the design of mobile middleware. Pervasive environments are characterized by a significant degree of heterogeneity, variability, and dynamicity that conventional middleware solutions are not able to adequately manage. Originally designed for use in a relatively static context, such middleware systems tend to hide low-level details to provide applications with a transparent view on the underlying execution platform. In mobile environments, however, the context is extremely dynamic and cannot be managed by a priori assumptions. Novel middleware should therefore support mobile computing applications in the task of adapting their behavior to frequent changes in the execution context, that is, it should become context-aware. In particular, this thesis has identified the following key requirements for novel context-aware middleware that existing solutions do not fulfil yet. (i) Middleware solutions should support interoperability between possibly unknown entities by providing expressive representation models that allow to describe interacting entities, their operating conditions and the surrounding world, i.e., their context, according to an unambiguous semantics. (ii) Middleware solutions should support distributed applications in the task of reconfiguring and adapting their behavior/results to ongoing context changes. (iii) Context-aware middleware support should be deployed on heterogeneous devices under variable operating conditions, such as different user needs, application requirements, available connectivity and device computational capabilities, as well as changing environmental conditions. Our main claim is that the adoption of semantic metadata to represent context information and context-dependent adaptation strategies allows to build context-aware middleware suitable for all dynamically available portable devices. Semantic metadata provide powerful knowledge representation means to model even complex context information, and allow to perform automated reasoning to infer additional and/or more complex knowledge from available context data. In addition, we suggest that, by adopting proper configuration and deployment strategies, semantic support features can be provided to differentiated users and devices according to their specific needs and current context. This thesis has investigated novel design guidelines and implementation options for semantic-based context-aware middleware solutions targeted to pervasive environments. These guidelines have been applied to different application areas within pervasive computing that would particularly benefit from the exploitation of context. Common to all applications is the key role of context in enabling mobile users to personalize applications based on their needs and current situation. The main contributions of this thesis are (i) the definition of a metadata model to represent and reason about context, (ii) the definition of a model for the design and development of context-aware middleware based on semantic metadata, (iii) the design of three novel middleware architectures and the development of a prototypal implementation for each of these architectures, and (iv) the proposal of a viable approach to portability issues raised by the adoption of semantic support services in pervasive applications.

Development and testing of innovative methodologies for modelling and control of normal and knocking combustion and implementation of novel rapid prototyping solutions

The thesis work deals with topics that led to the development of innovative control-oriented models and control algorithms for modern gasoline engines. Knock in boosted spark ignition engines is the widest topic discussed in this document because it remains one of the most limiting factors for maximizing combustion efficiency in this kind of engine. First chapter is thus focused on knock and a wide literature review is proposed to summarize the preliminary knowledge that even represents the background and the reference for discussed activities. Most relevant results achieved during PhD course in the field of knock modelling and control are then presented, describing every control-oriented model that led to the development of an adaptive model-based combustion control system. The complete controller has been developed in the context of the collaboration with Ferrari GT and it allowed to completely redefine the knock intensity evaluation as well as the combustion phase control. The second chapter is focused on the activity related to a prototyping Port Water Injection system that has been developed and tested on a turbocharged spark ignition engine, within the collaboration with Magneti Marelli. Such system and the effects of injected water on the combustion process were then modeled in a 1-D simulation environment (GT Power). Third chapter shows the development and validation of a control-oriented model for the real-time calculation of exhaust gas temperature that represents another important limitation to the performance increase in modern boosted engines. Indeed, modelling of exhaust gas temperature and thermocouple behavior are themes that play a key role in the optimization of combustion and catalyst efficiency.

Vision-Based Solutions for Human-Robot Collaboration in Industrial Workcells

Industrial robots are both versatile and high performant, enabling the flexible automation typical of the modern Smart Factories. For safety reasons, however, they must be relegated inside closed fences and/or virtual safety barriers, to keep them strictly separated from human operators. This can be a limitation in some scenarios in which it is useful to combine the human cognitive skill with the accuracy and repeatability of a robot, or simply to allow a safe coexistence in a shared workspace. Collaborative robots (cobots), on the other hand, are intrinsically limited in speed and power in order to share workspace and tasks with human operators, and feature the very intuitive hand guiding programming method. Cobots, however, cannot compete with industrial robots in terms of performance, and are thus useful only in a limited niche, where they can actually bring an improvement in productivity and/or in the quality of the work thanks to their synergy with human operators. The limitations of both the pure industrial and the collaborative paradigms can be overcome by combining industrial robots with artificial vision. In particular, vision can be exploited for a real-time adjustment of the pre-programmed task-based robot trajectory, by means of the visual tracking of dynamic obstacles (e.g. human operators). This strategy allows the robot to modify its motion only when necessary, thus maintain a high level of productivity but at the same time increasing its versatility. Other than that, vision offers the possibility of more intuitive programming paradigms for the industrial robots as well, such as the programming by demonstration paradigm. These possibilities offered by artificial vision enable, as a matter of fact, an efficacious and promising way of achieving human-robot collaboration, which has the advantage of overcoming the limitations of both the previous paradigms yet keeping their strengths.

Wireless solutions for the industrial internet of things

The fourth industrial revolution is paving the way for Industrial Internet of Things applications where industrial assets (e.g., robotic arms, valves, pistons) are equipped with a large number of wireless devices (i.e., microcontroller boards that embed sensors and actuators) to enable a plethora of new applications, such as analytics, diagnostics, monitoring, as well as supervisory, and safety control use-cases. Nevertheless, current wireless technologies, such as Wi-Fi, Bluetooth, and even private 5G networks, cannot fulfill all the requirements set up by the Industry 4.0 paradigm, thus opening up new 6G-oriented research trends, such as the use of THz frequencies. In light of the above, this thesis provides (i) a broad overview of the main use-cases, requirements, and key enabling wireless technologies foreseen by the fourth industrial revolution, and (ii) proposes innovative contributions, both theoretical and empirical, to enhance the performance of current and future wireless technologies at different levels of the protocol stack. In particular, at the physical layer, signal processing techniques are being exploited to analyze two multiplexing schemes, namely Affine Frequency Division Multiplexing and Orthogonal Chirp Division Multiplexing, which seem promising for high-frequency wireless communications. At the medium access layer, three protocols for intra-machine communications are proposed, where one is based on LoRa at 2.4 GHz and the others work in the THz band. Different scheduling algorithms for private industrial 5G networks are compared, and two main proposals are described, i.e., a decentralized scheme that leverages machine learning techniques to better address aperiodic traffic patterns, and a centralized contention-based design that serves a federated learning industrial application. Results are provided in terms of numerical evaluations, simulation results, and real-world experiments. Several improvements over the state-of-the-art were obtained, and the description of up-and-running testbeds demonstrates the feasibility of some of the theoretical concepts when considering a real industry plant.

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.