Analysis of the Kohn Laplacian on the Heisenberg Group and on Cauchy-Riemann Manifolds

The purpose of this study is to analyse the regularity of a differential operator, the Kohn Laplacian, in two settings: the Heisenberg group and the strongly pseudoconvex CR manifolds. The Heisenberg group is defined as a space of dimension 2n+1 with a product. It can be seen in two different ways: as a Lie group and as the boundary of the Siegel UpperHalf Space. On the Heisenberg group there exists the tangential CR complex. From this we define its adjoint and the Kohn-Laplacian. Then we obtain estimates for the Kohn-Laplacian and find its solvability and hypoellipticity. For stating L^p and Holder estimates, we talk about homogeneous distributions. In the second part we start working with a manifold M of real dimension 2n+1. We say that M is a CR manifold if some properties are satisfied. More, we say that a CR manifold M is strongly pseudoconvex if the Levi form defined on M is positive defined. Since we will show that the Heisenberg group is a model for the strongly pseudo-convex CR manifolds, we look for an osculating Heisenberg structure in a neighborhood of a point in M, and we want this structure to change smoothly from a point to another. For that, we define Normal Coordinates and we study their properties. We also examinate different Normal Coordinates in the case of a real hypersurface with an induced CR structure. Finally, we define again the CR complex, its adjoint and the Laplacian operator on M. We study these new operators showing subelliptic estimates. For that, we don't need M to be pseudo-complex but we ask less, that is, the Z(q) and the Y(q) conditions. This provides local regularity theorems for Laplacian and show its hypoellipticity on M.

Influence of free-radical functionalization on non-woven filtering media for medical application

Nowadays the leukodepletion is one of the most important processes done on the blood in order to reduce the risk of transfusion diseases. It can be performed through different techniques but the most popular one is the filtration due to its simplicity and efficiency. This work aims at improving a current commercial product, by developing a new filter based on Fenton-type reaction to cross-link a hydrogel on to the base material. The filters for leukodepletion are preferably made through the melt flow technique resulting in a non-woven tissue; the functionalization should increase the stability of the filter restricting the extraction of substances to minimum amount when in contact with blood. Through the modification the filters can acquire new properties including wettability, surface charge and good resistance to the extractions. The most important for leukodepletion is the surface charge due to the nature of the filtration process. All the modified samples results have been compared to the commercial product. Three different polymers (A, B and C) have been studied for the filter modifications and every modified filter has been tested in order to determine its properties.

Spatial-temporal variability of the benthic communities in Ravenna harbour using Autonomous Reef Monitoring Structures (ARMS) with focus on Non-Indigenous Species (NIS)

A Non-Indigenous Species (NIS) is defined as an organism, introduced outside its natural past or present range of distribution by humans, that successfully survives, reproduces, and establish in the new environment. Harbors and tourist marinas are considered NIS hotspots, as they are departure and arrival points for numerous vessels and because of the presence of free artificial substrates, which facilitate colonization by NIS. To early detect the arrival of new NIS, monitoring benthic communities in ports is essential. Autonomous Reef Monitoring Structures (ARMS) are standardized passive collectors that are used to assess marine benthic communities. Here we use an integrative approach based on multiple 3-month ARMS deployment (from April 2021 to October 2022) to characterize the benthic communities (with a focus on NIS) of two sites: a commercial port (Harbor) and a touristic Marina (Marina) of Ravenna. The colonizing sessile communities were assessed using percentage coverage of the taxa trough image analyses and vagile fauna (> 2 mm) was identified morphologically using a stereomicroscope and light microscope. Overall, 97 taxa were identified and 19 of them were NIS. All NIS were already observed in port environments in the Mediterranean Sea, but for the first time the presence of the polychaete Schistomeringos cf. japonica (Annenkova, 1937) was observed; however molecular analysis is needed to confirm its identity. Harbor and Marina host significantly different benthic communities, with significantly different abundance depending on the sampling period. While the differences between sites are related to their different environmental characteristic and their anthropogenic pressures, differences among times seems related to the different life cycle of the main abundant species. This thesis evidenced that ARMS, together with integrative taxonomic approaches, represent useful tools to early detect NIS and could be used for a long-term monitoring of their presence.

Heat kernel and worldline path integrals for the Proca theory

In this thesis we study the heat kernel, a useful tool to analyze various properties of different quantum field theories. In particular, we focus on the study of the one-loop effective action and the application of worldline path integrals to derive perturbatively the heat kernel coefficients for the Proca theory of massive vector fields. It turns out that the worldline path integral method encounters some difficulties if the differential operator of the heat kernel is of non-minimal kind. More precisely, a direct recasting of the differential operator in terms of worldline path integrals, produces in the classical action a non-perturbative vertex and the path integral cannot be solved. In this work we wish to find ways to circumvent this issue and to give a suggestion to solve similar problems in other contexts.

Effects of Paramuricea clavata (Risso, 1826) (Anthozoa: Plexauridae) forests on settlement of benthic species: an experimental approach

Rationale: Coralligenous habitat is considered the second most important subtidal “hot spot” of species diversity in the Mediterranean Sea after the Posidonia oceanica meadows. It can be defined as a typical Mediterranean biogenic hard bottom, mainly produced by the accumulation of calcareous encrusting algae that, together with other builder organisms, form a multidimensional framework with a high micro-spatial variability. The development of this habitat depends on physical factors (i.e. light, hydrodynamism, nutrients, etc.), but also biologic interactions can play a relevant role in structuring the benthic assemblages. This great environmental heterogeneity allows several different assemblages to coexist in a reduced space. One of the most beautiful is that characterised by the Mediterranean gorgonian Paramuricea clavata (Risso, 1826) that can contribute to above 40% of total biomass of the community and brings significant structural complexity into the coralligenous habitat. In sites moderately exposed to waves and currents, P. clavata can form high-density populations (up to 60 colonies m-2) between 20 – 70 m in depth. Being a suspension feeder, where it forms dense populations, P. clavata plays a significant role in transferring energy from planktonic to benthic system. The effects of the branched colonies of P. clavata could be comparable to those of the forests on land. They can affect the micro scale hydrodynamism and light, promoting or inhibiting the growth of other species. Unfortunately, gorgonians are threatened by several anthropogenic disturbance factors (i.e. fishing, pollution, tourism) and by climatic anomalies, linked to the global changes, that are responsible of thermal stress, development of mucilage and enhanced pathogens activity, leading to mass mortality events in last decades. Till now, the possible effects of gorgonian forest loss are largely unknown. Our goal was to analyse the ecological role of these sea fan forests on the coralligenous benthic assemblages. Experimental setup and main results: The influence of P. clavata in the settlement and recruitment of epibenthic organisms was analysed by a field experiment carried out in two randomly selected places: Tavolara island and Portofino promontory. The experiment consisted in recreate the presence and absence of the gorgonian forest on recruitment panels, arranged in four plots per type (forested and non-forested), interspersed each other, and deployed at the same depth. On every forested panel 3 gorgonian colonies about 20 cm height were grafted with the use of Eppendorf tubes and epoxy resin bicomponent simulating a density of 190 sea fans per m-2. This density corresponds to a mean biomass of 825 g DW m-2,3 which is of the same order of magnitude of the natural high-density populations. After about 4 months, the panels were collected and analysed in laboratory in order to estimate the percent cover of all the species that have colonized the substrata. The gorgonian forest effects were tested by multivariate and univariate permutational analyses of the variance (PERMANOVA). Recruited assemblages largely differed between the two study sites, probably due to different environmental conditions including water quality and turbidity. On overall, the presence of P. clavata reduced the settlement and recruitment of several algae: the shadow caused by the gorgonian might reduce light availability and therefore their growth. This effect might be greater in places where the waters are on average more clear, since at Portofino it is less visible and could be masked by the high turbidity of the water. The same pattern was registered for forams, more abundant outside gorgonian forest, probably linked with algal distribution, shadowing effect or alimentary competition. The last one hypothesis could be valid also for serpulids polychaetes that growth mainly on non-forested panels. An opposite trend, was showed by a species of bryozoan and by an hydroid that is facilitated by the presence of P. clavata, probably because it attenuates irradiance level and hydrodynamism. Species diversity was significantly reduced by the presence of P. clavata forests at both sites. This seems in contrast with what we expected, but the result may be influenced by the large algal component on non-forested panels. The analysis confirmed the presence of differences in the species diversity among plots and between sites respectively due to natural high variability of the coralligenous system and to different local environment conditions. The reduction of species diversity due to the presence of gorgonians appeared related to a worst evenness rather than to less species richness. With our experiment it is demonstrated that the presence of P. clavata forests can significantly alter local coralligenous assemblages patterns, promoting or inhibiting the recruitment of some species, modifying trophic relationships and adding heterogeneity and complexity to the habitat. Moreover, P. clavata could have a stabilising effect on the coralligenous assemblages.

Climatological analysis of temperature and salinity fields in the Mediterranean sea

A climatological field is a mean gridded field that represents the monthly or seasonal trend of an ocean parameter. This instrument allows to understand the physical conditions and physical processes of the ocean water and their impact on the world climate. To construct a climatological field, it is necessary to perform a climatological analysis on an historical dataset. In this dissertation, we have constructed the temperature and salinity fields on the Mediterranean Sea using the SeaDataNet 2 dataset. The dataset contains about 140000 CTD, bottles, XBT and MBT profiles, covering the period from 1900 to 2013. The temperature and salinity climatological fields are produced by the DIVA software using a Variational Inverse Method and a Finite Element numerical technique to interpolate data on a regular grid. Our results are also compared with a previous version of climatological fields and the goodness of our climatologies is assessed, according to the goodness criteria suggested by Murphy (1993). Finally the temperature and salinity seasonal cycle for the Mediterranean Sea is described.

Methodologies for attitude determination from MEMS sensors in vehicles

The focus of the thesis is the application of different attitude’s determination algorithms on data evaluated with MEMS sensor using a board provided by University of Bologna. MEMS sensors are a very cheap options to obtain acceleration, and angular velocity. The use of magnetometers based on Hall effect can provide further data. The disadvantage is that they have a lot of noise and drift which can affects the results. The different algorithms that have been used are: pitch and roll from accelerometer, yaw from magnetometer, attitude from gyroscope, TRIAD, QUEST, Magdwick, Mahony, Extended Kalman filter, Kalman GPS aided INS. In this work the algorithms have been rewritten to fit perfectly with the data provided from the MEMS sensor. The data collected by the board are acceleration on the three axis, angular velocity on the three axis, magnetic fields on the three axis, and latitude, longitude, and altitude from the GPS. Several tests and comparisons have been carried out installing the electric board on different vehicles operating in the air and on ground. The conclusion that can be drawn from this study is that the Magdwich filter is the best trade-off between computational capabilities required and results obtained. If attitude angles are obtained from accelerometers, gyroscopes, and magnetometer, inconsistent data are obtained for cases where high vibrations levels are noticed. On the other hand, Kalman filter based algorithms requires a high computational burden. TRIAD and QUEST algorithms doesn’t perform as well as filters.