Dynamics of coastal aquifers: data-driven forecasting and risk analysis

This work is focused on the study of saltwater intrusion in coastal aquifers, and in particular on the realization of conceptual schemes to evaluate the risk associated with it. Saltwater intrusion depends on different natural and anthropic factors, both presenting a strong aleatory behaviour, that should be considered for an optimal management of the territory and water resources. Given the uncertainty of problem parameters, the risk associated with salinization needs to be cast in a probabilistic framework. On the basis of a widely adopted sharp interface formulation, key hydrogeological problem parameters are modeled as random variables, and global sensitivity analysis is used to determine their influence on the position of saltwater interface. The analyses presented in this work rely on an efficient model reduction technique, based on Polynomial Chaos Expansion, able to combine the best description of the model without great computational burden. When the assumptions of classical analytical models are not respected, and this occurs several times in the applications to real cases of study, as in the area analyzed in the present work, one can adopt data-driven techniques, based on the analysis of the data characterizing the system under study. It follows that a model can be defined on the basis of connections between the system state variables, with only a limited number of assumptions about the "physical" behaviour of the system.

Dynamics of undeactuated cable-driven parallel robots

This thesis focuses on the dynamics of underactuated cable-driven parallel robots (UACDPRs), including various aspects of robotic theory and practice, such as workspace computation, parameter identification, and trajectory planning. After a brief introduction to CDPRs, UACDPR kinematic and dynamic models are analyzed, under the relevant assumption of inextensible cables. The free oscillatory motion of the end-effector (EE), which is a unique feature of underactuated mechanisms, is studied in detail, from both a kinematic and a dynamic perspective. The free (small) oscillations of the EE around equilibria are proved to be harmonic and the corresponding natural oscillation frequencies are analytically computed. UACDPR workspace computation and analysis are then performed. A new performance index is proposed for the analysis of the influence of actuator errors on cable tensions around equilibrium configurations, and a new type of workspace, called tension-error-insensitive, is defined as the set of poses that a UACDPR EE can statically attain even in presence of actuation errors, while preserving tensions between assigned (positive) bounds. EE free oscillations are then employed to conceive a novel procedure aimed at identifying the EE inertial parameters. This approach does not require the use of force or torque measurements. Moreover, a self-calibration procedure for the experimental determination of UACDPR initial cable lengths is developed, which consequently enables the robot to automatically infer the EE initial pose at machine start-up. Lastly, trajectory planning of UACDPRs is investigated. Two alternative methods are proposed, which aim at (i) reducing EE oscillations even when model parameters are uncertain or (ii) eliminate EE oscillations in case model parameters are perfectly known. EE oscillations are reduced in real-time by dynamically scaling a nominal trajectory and filtering it with an input shaper, whereas they can be eliminated if an off-line trajectory is computed that accounts for the system internal dynamics.

Computer simulation of ordering and dynamics in liquid crystals in the bulk and close to the surface

The aim of this PhD thesis is to investigate the orientational and dynamical properties of liquid crystalline systems, at molecular level and using atomistic computer simulations, to reach a better understanding of material behavior from a microscopic point view. In perspective this should allow to clarify the relation between the micro and macroscopic properties with the objective of predicting or confirming experimental results on these systems. In this context, we developed four different lines of work in the thesis. The first one concerns the orientational order and alignment mechanism of rigid solutes of small dimensions dissolved in a nematic phase formed by the 4-pentyl,4 cyanobiphenyl (5CB) nematic liquid crystal. The orientational distribution of solutes have been obtained with Molecular Dynamics Simulation (MD) and have been compared with experimental data reported in literature. we have also verified the agreement between order parameters and dipolar coupling values measured in NMR experiments. The MD determined effective orientational potentials have been compared with the predictions of Maier­Saupe and Surface tensor models. The second line concerns the development of a correct parametrization able to reproduce the phase transition properties of a prototype of the oligothiophene semiconductor family: sexithiophene (T6). T6 forms two crystalline polymorphs largely studied, and possesses liquid crystalline phases still not well characterized, From simulations we detected a phase transition from crystal to liquid crystal at about 580 K, in agreement with available experiments, and in particular we found two LC phases, smectic and nematic. The crystal­smectic transition is associated to a relevant density variation and to strong conformational changes of T6, namely the molecules in the liquid crystal phase easily assume a bent shape, deviating from the planar structure typical of the crystal. The third line explores a new approach for calculating the viscosity in a nematic through a virtual exper- iment resembling the classical falling sphere experiment. The falling sphere is replaced by an hydrogenated silicon nanoparticle of spherical shape suspended in 5CB, and gravity effects are replaced by a constant force applied to the nanoparticle in a selected direction. Once the nanoparticle reaches a constant velocity, the viscosity of the medium can be evaluated using Stokes' law. With this method we successfully reproduced experimental viscosities and viscosity anisotropy for the solvent 5CB. The last line deals with the study of order induction on nematic molecules by an hydrogenated silicon surface. Gaining predicting power for the anchoring behavior of liquid crystals at surfaces will be a very desirable capability, as many properties related to devices depend on molecular organization close to surfaces. Here we studied, by means of atomistic MD simulations, the flat interface between an hydrogenated (001) silicon surface in contact with a sample of 5CB molecules. We found a planar anchoring of the first layers of 5CB where surface interactions are dominating with respect to the mesogen intermolecular interactions. We also analyzed the interface 5CB­vacuum, finding a homeotropic orientation of the nematic at this interface.

The language of action. How language translates the dynamics of our actions.

The general aim of the thesis was to investigate how and to what extent the characteristics of action organization are reflected in language, and how they influence language processing and understanding. Even though a huge amount of research has been devoted to the study of the motor effects of language, this issue is very debated in literature. Namely, the majority of the studies have focused on low-level motor effects such as effector-relatedness of action, whereas only a few studies have started to systematically investigate how specific aspects of action organization are encoded and reflected in language. After a review of previous studies on the relationship between language comprehension and action (chapter 1) and a critical discussion of some of them (chapter 2), the thesis is composed by three experimental chapters, each devoted to a specific aspect of action organization. Chapter 3 presents a study designed with the aim to disentangle the effective time course of the involvement of the motor system during language processing. Three kinematics experiments were designed in order to determine whether and, at which stage of motor planning and execution effector-related action verbs influence actions executed with either the same or a different effector. Results demonstrate that the goal of an action can be linguistically re-activated, producing a modulation of the motor response. In chapter 4, a second study investigates the interplay between the role of motor perspective (agent) and the organization of action in motor chains. More specifically, this kinematics study aims at deepening how goal can be translated in language, using as stimuli simple sentences composed by a pronoun (I, You, He/She) and a verb. Results showed that the perspective activated by the pronoun You reflects the motor pattern of the “agent” combined with the chain structure of the verb. These data confirm an early involvement of the motor system in language processing, suggesting that it is specifically modulated by the activation of the agent’s perspective. In chapter 5, the issue of perspective is specifically investigated, focusing on its role in language comprehension. In particular, this study aimed at determining how a specific perspective (induced for example by a personal pronoun) modulates motor behaviour during and after language processing. A classical compatibility effect (the Action-sentence compatibility effect) has been used to this aim. In three behavioural experiments the authors investigated how the ACE is modulated by taking first or third person perspective. Results from these experiments showed that the ACE effect occurs only when a first-person perspective is activated by the sentences used as stimuli. Overall, the data from this thesis contributed to disentangle several aspects of how action organization is translated in language, and then reactivated during language processing. This constitutes a new contribution to the field, adding lacking information on how specific aspects such as goal and perspective are linguistically described. In addition, these studies offer a new point of view to understand the functional implications of the involvement of the motor system during language comprehension, specifically from the point of view of our social interactions.

Dynamic identification of structures: experimental assessment of modal parameteres through methods in frequency domain, in time-frequency domain and model updating

Among the experimental methods commonly used to define the behaviour of a full scale system, dynamic tests are the most complete and efficient procedures. A dynamic test is an experimental process, which would define a set of characteristic parameters of the dynamic behaviour of the system, such as natural frequencies of the structure, mode shapes and the corresponding modal damping values associated. An assessment of these modal characteristics can be used both to verify the theoretical assumptions of the project, to monitor the performance of the structural system during its operational use. The thesis is structured in the following chapters: The first introductive chapter recalls some basic notions of dynamics of structure, focusing the discussion on the problem of systems with multiply degrees of freedom (MDOF), which can represent a generic real system under study, when it is excited with harmonic force or in free vibration. The second chapter is entirely centred on to the problem of dynamic identification process of a structure, if it is subjected to an experimental test in forced vibrations. It first describes the construction of FRF through classical FFT of the recorded signal. A different method, also in the frequency domain, is subsequently introduced; it allows accurately to compute the FRF using the geometric characteristics of the ellipse that represents the direct input-output comparison. The two methods are compared and then the attention is focused on some advantages of the proposed methodology. The third chapter focuses on the study of real structures when they are subjected to experimental test, where the force is not known, like in an ambient or impact test. In this analysis we decided to use the CWT, which allows a simultaneous investigation in the time and frequency domain of a generic signal x(t). The CWT is first introduced to process free oscillations, with excellent results both in terms of frequencies, dampings and vibration modes. The application in the case of ambient vibrations defines accurate modal parameters of the system, although on the damping some important observations should be made. The fourth chapter is still on the problem of post processing data acquired after a vibration test, but this time through the application of discrete wavelet transform (DWT). In the first part the results obtained by the DWT are compared with those obtained by the application of CWT. Particular attention is given to the use of DWT as a tool for filtering the recorded signal, in fact in case of ambient vibrations the signals are often affected by the presence of a significant level of noise. The fifth chapter focuses on another important aspect of the identification process: the model updating. In this chapter, starting from the modal parameters obtained from some environmental vibration tests, performed by the University of Porto in 2008 and the University of Sheffild on the Humber Bridge in England, a FE model of the bridge is defined, in order to define what type of model is able to capture more accurately the real dynamic behaviour of the bridge. The sixth chapter outlines the necessary conclusions of the presented research. They concern the application of a method in the frequency domain in order to evaluate the modal parameters of a structure and its advantages, the advantages in applying a procedure based on the use of wavelet transforms in the process of identification in tests with unknown input and finally the problem of 3D modeling of systems with many degrees of freedom and with different types of uncertainty.

Influence of nitrogen and soil physical characteristics on belowground carbon flux dynamics of woody plants

At ecosystem level soil respiration (Rs) represents the largest carbon (C) flux after gross primary productivity, being mainly generated by root respiration (autotrophic respiration, Ra) and soil microbial respiration (heterotrophic respiration, Rh). In the case of terrestrial ecosystems, soils contain the largest C-pool, storing twice the amount of C contained in plant biomass. Soil organic matter (SOM), representing the main C storage in soil, is decomposed by soil microbial community. This process produces CO2 which is mainly released as Rh. It is thus relevant to understand how microbial activity is influenced by environmental factors like soil temperature, soil moisture and nutrient availability, since part of the CO2 produced by Rh, directly increases atmospheric CO2 concentration and therefore affects the phenomenon of climate change. Among terrestrial ecosystems, agricultural fields have traditionally been considered as sources of atmospheric CO2. In agricultural ecosystems, in particular apple orchards, I identified the role of root density, soil temperature, soil moisture and nitrogen (N) availability on Rs and on its two components, Ra and Rh. To do so I applied different techniques to separate Rs in its two components, the ”regression technique” and the “trenching technique”. I also studied the response of Ra to different levels of N availability, distributed either in a uniform or localized way, in the case of Populus tremuloides trees. The results showed that Rs is mainly driven by soil temperature, to which it is positively correlated, that high levels of soil moisture have inhibiting effects, and that N has a negligible influence on total Rs, as well as on Ra. Further I found a negative response of Rh to high N availability, suggesting that microbial decomposition processes in the soil are inhibited by the presence of N. The contribution of Ra to Rs was of 37% on average.

Dynamics and control issues of multi-rotor platforms

This thesis deals with the analytic study of dynamics of Multi--Rotor Unmanned Aerial Vehicles. It is conceived to give a set of mathematical instruments apt to the theoretical study and design of these flying machines. The entire work is organized in analogy with classical academic texts about airplane flight dynamics. First, the non--linear equations of motion are defined and all the external actions are modeled, with particular attention to rotors aerodynamics. All the equations are provided in a form, and with personal expedients, to be directly exploitable in a simulation environment. This has requited an answer to questions like the trim of such mathematical systems. All the treatment is developed aiming at the description of different multi--rotor configurations. Then, the linearized equations of motion are derived. The computation of the stability and control derivatives of the linear model is carried out. The study of static and dynamic stability characteristics is, thus, addressed, showing the influence of the various geometric and aerodynamic parameters of the machine and in particular of the rotors. All the theoretic results are finally utilized in two interesting cases. One concerns the design of control systems for attitude stabilization. The linear model permits the tuning of linear controllers gains and the non--linear model allows the numerical testing. The other case is the study of the performances of an innovative configuration of quad--rotor aircraft. With the non--linear model the feasibility of maneuvers impossible for a traditional quad--rotor is assessed. The linear model is applied to the controllability analysis of such an aircraft in case of actuator block.

Statistical Analysis and Modelling Aspects of Thermally Driven Turbulence

The present work aims to provide a deeper understanding of thermally driven turbulence and to address some modelling aspects related to the physics of the flow. For this purpose, two idealized systems are investigated by Direct Numerical Simulation: the rotating and non-rotating Rayleigh-Bénard convection. The preliminary study of the flow topologies shows how the coherent structures organise into different patterns depending on the rotation rate. From a statistical perspective, the analysis of the turbulent kinetic energy and temperature variance budgets allows to identify the flow regions where the production, the transport, and the dissipation of turbulent fluctuations occur. To provide a multi-scale description of the flows, a theoretical framework based on the Kolmogorov and Yaglom equations is applied for the first time to the Rayleigh-Bénard convection. The analysis shows how the spatial inhomogeneity modulates the dynamics at different scales and wall-distances. Inside the core of the flow, the space of scales can be divided into an inhomogeneity-dominated range at large scales, an inertial-like range at intermediate scales and a dissipative range at small scales. This classic scenario breaks close to the walls, where the inhomogeneous mechanisms and the viscous/diffusive processes are important at every scale and entail more complex dynamics. The same theoretical framework is extended to the filtered velocity and temperature fields of non-rotating Rayleigh-Bénard convection. The analysis of the filtered Kolmogorov and Yaglom equations reveals the influence of the residual scales on the filtered dynamics both in physical and scale space, highlighting the effect of the relative position between the filter length and the crossover that separates the inhomogeneity-dominated range from the quasi-homogeneous range. The assessment of the filtered and residual physics results to be instrumental for the correct use of the existing Large-Eddy Simulation models and for the development of new ones.

Musical tension in harmonic intervals: behavioral and neural correlates

Musical tension is what drives our emotional experience in music listening. However, the specific role of the musical elements involved in tension-resolution perception remains largely unclear. This dissertation aims to advance the understanding of tension perception dynamics related to sensory consonance-dissonance. The first experiment aimed to design and validate a new crossmodal proprioceptive device for tension rating that overcomes some of the limitations of known tools. As a result, a psychophysical equation for the matching of physical force and psychological force was presented. The same tool was subsequently used in the second and third experiments to collect ratings of perceived tension and movement in harmonic musical intervals and standard noises. Besides, a visual analog scale (VAS) was used to allow a comparison of these two methods. The results confirmed the close relationship between sensory dissonance and perceived tension. Moreover, stimuli in the higher pitch register were perceived as more tense, confirming the primary role of pitch as a mediator of tension. The comparison between ratings obtained with the proprioceptive device and the VAS highlighted the tendency to give higher tension ratings using the VAS compared to the proprioceptive device. In the last experiment, brain electrical activity was recorded during the presentation of short tension-resolution patterns created using the most tense (perfect unison, fourth, and fifth) and the least tense harmonic intervals (augmented fourth, minor second, and inverted major seventh) to understand how consonance-dissonance can convey meaningful information on perceived tension-resolution. Results showed overall larger effects during the ‘resolution’ condition compare to the ‘tension induction’ condition, indicating that the resolution of harmonic instability towards a state of stability may be more salient than its opposite. A late positive component (LPC) was elicited, possibly reflecting deeper processing of tension-related meaning within a minimal harmonic context.

Simulation of photoinduced processes in organic chromophores: mapping photochemically relevant states for accurate dynamics

The simulation of ultrafast photoinduced processes is a fundamental step towards the understanding of the underlying molecular mechanism and interpretation/prediction of experimental data. Performing a computer simulation of a complex photoinduced process is only possible introducing some approximations but, in order to obtain reliable results, the need to reduce the complexity must balance with the accuracy of the model, which should include all the relevant degrees of freedom and a quantitatively correct description of the electronic states involved in the process. This work presents new computational protocols and strategies for the parameterisation of accurate models for photochemical/photophysical processes based on state-of-the-art multiconfigurational wavefunction-based methods. The required ingredients for a dynamics simulation include potential energy surfaces (PESs) as well as electronic state couplings, which must be mapped across the wide range of geometries visited during the wavepacket/trajectory propagation. The developed procedures allow to obtain solid and extended databases reducing as much as possible the computational cost, thanks to, e.g., specific tuning of the level of theory for different PES regions and/or direct calculation of only the needed components of vectorial quantities (like gradients or nonadiabatic couplings). The presented approaches were applied to three case studies (azobenzene, pyrene, visual rhodopsin), all requiring an accurate parameterisation but for different reasons. The resulting models and simulations allowed to elucidate the mechanism and time scale of the internal conversion, reproducing or even predicting new transient experiments. The general applicability of the developed protocols to systems with different peculiarities and the possibility to parameterise different types of dynamics on an equal footing (classical vs purely quantum) prove that the developed procedures are flexible enough to be tailored for each specific system, and pave the way for exact quantum dynamics with multiple degrees of freedom.

Analytical methods for modeling elastic metasurfaces

This dissertation aims at developing advanced analytical tools able to model surface waves propagating in elastic metasurfaces. In particular, four different objectives are defined and pursued throughout this work to enrich the description of the metasurface dynamics. First, a theoretical framework is developed to describe the dispersion properties of a seismic metasurface composed of discrete resonators placed on a porous medium considering part of it fully saturated. Such a model combines classical elasticity theory, Biot’s poroelasticity and an effective medium approach to describe the metasurface dynamics and its coupling with the poroelastic substrate. Second, an exact formulation based on the multiple scattering theory is developed to extend the two-dimensional classical Lamb’s problem to the case of an elastic half-space coupled to an arbitrary number of discrete surface resonators. To this purpose, the incident wavefield generated by a harmonic source and the scattered field generated by each resonator are calculated. The substrate wavefield is then obtained as solutions of the coupled problem due to the interference of the incident field and the multiple scattered fields of the oscillators. Third, the above discussed formulation is extended to three-dimensional contexts. The purpose here is to investigate the dynamic behavior and the topological properties of quasiperiodic elastic metasurfaces. Finally, the multiple scattering formulation is extended to model flexural metasurfaces, i.e., an array of thin plates. To this end, the resonant plates are modeled by means of their equivalent impedance, derived by exploiting the Kirchhoff plate theory. The proposed formulation permits the treatment of a general flexural metasurface, with no limitation on the number of plates and the configuration taken into account. Overall, the proposed analytical tools could pave the way for a better understanding of metasurface dynamics and their implementation in engineered devices.

Oceanic Near-inertial internal waves generation, propagation and interaction with mesoscale dynamics

Oceans play a key role in the climate system, being the largest heat sinks on Earth. Part of the energy balance of ocean circulation is driven by the Near-inertial internal waves (NIWs). Strong NIWs are observed during a multi-platform, multi-disciplinary and multi-scale campaign led by the NATO-STO CMRE in autumn 2017 in the Ligurian Sea (northwestern Mediterranean Sea). The objectives of this work are as follows: characterise the studied area at different scales; study the NIWs generation and their propagation; estimate the NIWs properties; study the interaction between NIWs and mesoscale structures. This work provides, to the author’s knowledge, the first characterization of NIWs in the Mediterranean Sea. The near-surface NIWs observed at the fixed moorings are locally generated by wind bursts while the deeper waves originate in other regions and arrive at the moorings several days later. Most of the observed NIWs energy propagates downward with a mean vertical group velocity of (2.2±0.3) ⋅10-4 m s-1. On average, the NIWs have an amplitude of 0.13 m s-1 and mean horizontal and vertical wavelengths of 43±25 km and 125±35 m, while shorter wavelengths are observed at the near-coastal mooring, 36±2 km and 33±2 m, respectively. Most of the observed NIWs are blue shifted and reach a value 9% higher than the local inertial frequency. Only two observed NIWs are characterised by a redshift (up to 3% lower than the local inertial frequency). In support of the in situ observations, a high resolution numerical model is implemented using NEMO (Madec et al., 2019). Results show that anticyclones (cyclones) shift the frequency of NIWs to lower (higher) frequencies with respect to the local inertial frequency. Anticyclones facilitate the downward propagation of NIW energy, while cyclones dampen it. Absence of NIWs energy within an anticyclone is also investigated.

Spectral asymptotic properties of semi-regular non-commutative harmonic oscillators

The study carried out in this thesis is devoted to spectral analysis of systems of PDEs related also with quantum physics models. Namely, the research deals with classes of systems that contain certain quantum optics models such as Jaynes-Cummings, Rabi and their generalizations that describe light-matter interaction. First we investigate the spectral Weyl asymptotics for a class of semiregular systems, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch. Actually, the asymptotics by Doll, Gannot and Wunsch is more precise (that is why we call it refined) than the classical result by Helffer and Robert, but deals with a less general class of systems, since the authors make an hypothesis on the measure of the subset of the unit sphere on which the tangential derivatives of the X-Ray transform of the semiprincipal symbol vanish to infinity order. Abstract Next, we give a meromorphic continuation of the spectral zeta function for semiregular differential systems with polynomial coefficients, generalizing the results by Ichinose and Wakayama and Parmeggiani. Finally, we state and prove a quasi-clustering result for a class of systems including the aforementioned quantum optics models and we conclude the thesis by showing a Weyl law result for the Rabi model and its generalizations.