Mean curvature flow in SE (2) and applications to visual perception

Our goal in this thesis is to provide a result of existence of the degenerate non-linear, non-divergence PDE which describes the mean curvature flow in the Lie group SE(2) equipped with a sub-Riemannian metric. The research is motivated by problems of visual completion and models of the visual cortex.

Caratterizzazione della Risposta Idrologica alle Precipitazioni nella Zona d’Innesco di un Debris Flow in Area Dolomitica (Bacino di Pezovico, Cortina d’Ampezzo, BL)

Il presente lavoro riguarda lo studio delle colate detritiche, fenomeno che rappresenta un importante argomento di studio sia per la sua caratterizzazione e analisi a livello scientifico che per attuare una corretta pianificazione e gestione del territorio. Nell’ambiente alpino, ed in particolare nell’area Dolomitica, le colate detritiche rappresentano un fenomeno complesso, le cui caratteristiche di velocità ed intensità, congiuntamente alla difficile previsione temporale, determinano l’alto grado di pericolosità che espone a rischi elevati infrastrutture e persone. Il monitoraggio delle colate detritiche assume quindi una notevole importanza nella determinazione delle condizioni idrologiche e morfologiche che inducono la generazione e la propagazione di tali fenomeni. Il presente lavoro ha come obiettivo la caratterizzazione della risposta idrologica nella zona d’innesco di un canale detritico, localizzato nella Conca Ampezzana. La caratterizzazione è stata definita attraverso l’analisi dei dati ottenuti dal monitoraggio eseguito mediante una stazione di rilevamento appositamente progettata e realizzata.

Multiphase flow in porous media: meta-modeling techniques for sensitivity analysis and risk assessment

One of the biggest challenges that contaminant hydrogeology is facing, is how to adequately address the uncertainty associated with model predictions. Uncertainty arise from multiple sources, such as: interpretative error, calibration accuracy, parameter sensitivity and variability. This critical issue needs to be properly addressed in order to support environmental decision-making processes. In this study, we perform Global Sensitivity Analysis (GSA) on a contaminant transport model for the assessment of hydrocarbon concentration in groundwater. We provide a quantification of the environmental impact and, given the incomplete knowledge of hydrogeological parameters, we evaluate which are the most influential, requiring greater accuracy in the calibration process. Parameters are treated as random variables and a variance-based GSA is performed in a optimized numerical Monte Carlo framework. The Sobol indices are adopted as sensitivity measures and they are computed by employing meta-models to characterize the migration process, while reducing the computational cost of the analysis. The proposed methodology allows us to: extend the number of Monte Carlo iterations, identify the influence of uncertain parameters and lead to considerable saving computational time obtaining an acceptable accuracy.

Galactic fountain flows in high-resolution hydrodynamical simulations of galaxy disks

Feedback from the most massive components of a young stellar cluster deeply affects the surrounding ISM driving an expanding over-pressured hot gas cavity in it. In spiral galaxies these structures may have sufficient energy to break the disk and eject large amount of material into the halo. The cycling of this gas, which eventually will fall back onto the disk, is known as galactic fountains. We aim at better understanding the dynamics of such fountain flow in a Galactic context, frame the problem in a more dynamic environment possibly learning about its connection and regulation to the local driving mechanism and understand its role as a metal diffusion channel. The interaction of the fountain with a hot corona is hereby analyzed, trying to understand the properties and evolution of the extraplanar material. We perform high resolution hydrodynamical simulations with the moving-mesh code AREPO to model the multi-phase ISM of a Milky Way type galaxy. A non-equilibrium chemical network is included to self consistently follow the evolution of the main coolants of the ISM. Spiral arm perturbations in the potential are considered so that large molecular gas structures are able to dynamically form here, self shielded from the interstellar radiation field. We model the effect of SN feedback from a new-born stellar cluster inside such a giant molecular cloud, as the driving force of the fountain. Passive Lagrangian tracer particles are used in conjunction to the SN energy deposition to model and study diffusion of freshly synthesized metals. We find that both interactions with hot coronal gas and local ISM properties and motions are equally important in shaping the fountain. We notice a bimodal morphology where most of the ejected gas is in a cold $10^4$ K clumpy state while the majority of the affected volume is occupied by a hot diffuse medium. While only about 20\% of the produced metals stay local, most of them quickly diffuse through this hot regime to great scales.

Use of isotopes for studying nitrogen processes in a wetland within the Venice Lagoon watershed

The present study is based on the use of isotopes for evaluating the efficiency of nutrients removal of a wetland, in particular nitrogen and nitrates, also between the different habitats present in the wetland. Nutrients like nitrogen and phosphorus, normally distributed as fertilizers, are among the principal causes of diffuse pollution. This is particularly important in the Adriatic Sea, which is frequently subjected to eutrophication phenomena. So it is very crucial requalification of wetland, in which there are naturally depurative processes such as denitrification and plant uptake, which allow the reduction of pollutant loads that flow in water bodies. In this study nutrient reduction is analyzed in the wetland of the Comuna drain, which waters flow in the Venice lagoon. Chemical and isotopical analyses were performed on samples of water, vegetation, soil and sediments taken in the wetlands of the Comuna drain in four different periods of the year and on data of nitrogen and phosphorus concentration obtained by the LASA of the University of Padova. Values of total nitrogen and nitrates were obtained in order to evaluate the reduction within the different systems of the wetland. Instead, the isotopic values of nitrogen and carbon were used to evaluate which process influence more nitrogen reduction and to understand the origin of the nutrient, if it is from fertilizers, waste water or sewage. To conclude, the most important process in the wetland of the Comuna drain is plant uptake, in facts the bigger percentage of nitrogen reduction was in the period of vegetative growth. So it is important the study of isotopes in plant tissues and water residence time, whose increase would allow a greater reduction of nutrients.

Contributo sperimentale alla ridefinizione della diffusione in parete della camera di prova della galleria del vento Dallara

Joseph Nicolas Cugnot built the first primitive car in 1769 and approximately one hundred year later the first automotive race took place. Thanks to this, for the first time the aerodynamics principles began to be applied to cars. The aerodynamic study of a car is important to improve the performance on the road, or on the track. It purposely enhances the stability in the turns and increases the maximum velocity. However, it is also useful, decrease the fuel consumption, in order to reduce the pollution. Given that cars are a very complex body, the aerodynamic study cannot be conducted following an analytical method, but it is possible, in general, to choose between two different approaches: the numerical or the experimental one. The results of numerical studies depend on the computers’ potential and on the method use to implement the mathematical model. Today, the best way to perform an aerodynamic study is still experimental, which means that in the first phase of the design process the study is performed in a wind tunnel and in later phases directly on track. The automotive wind tunnels are singular mainly due to the test chamber, which typically contains a ground simulation system. The test chamber can have different types of walls: open walls, closed walls, adaptive walls or slotted walls. The best solution is to use the slotted walls because they minimize the interference between the walls and the streamlines, the interaction between the flow and the environment, and also to contain the overall costs. Furthermore, is necessary minimize the boundary layer at the walls, without accelerating the flow, in order to provide the maximum section of homogeneous flow. This thesis aims at redefining the divergent angle of the Dallara Automobili S.P.A. wind tunnel’s walls, in order to improve the overall homogeneity. To perform this study it was necessary to acquire the pressure data of the boundary layer, than it was created the profile of the boundary layer velocity and, to minimize the experimental errors, it was calculated the displacement thickness. The results obtained shows, even if the instrument used to the experiment was not the best one, that the boundary layer thickness could be minor in case of a low diffusion angle. So it is convenient to perform another experiment with a most sensitive instrument to verified what is the better wall configuration.