Cone penetration testing to assess slope stability in the 1979 Nice landslide area (Ligurian Margin, SE France)

In the landslide-prone area near the Nice international airport, southeastern France, an interdisciplinary approach is applied to develop realistic lithological/geometrical profiles and geotechnical/strength sub-seafloor models. Such models are indispensable for slope stability assessments using limit equilibrium or finite element methods. Regression analyses, based on the undrained shear strength (su) of intact gassy sediments are used to generate a sub-seafloor strength model based on 37 short dynamic and eight long static piezocone penetration tests, and laboratory experiments on one Calypso piston and 10 gravity cores. Significant strength variations were detected when comparing measurements from the shelf and the shelf break, with a significant drop in su to 5.5 kPa being interpreted as a weak zone at a depth between 6.5 and 8.5 m below seafloor (mbsf). Here, a 10% reduction of the in situ total unit weight compared to the surrounding sediments is found to coincide with coarse-grained layers that turn into a weak zone and detachment plane for former and present-day gravitational, retrogressive slide events, as seen in 2D chirp profiles. The combination of high-resolution chirp profiles and comprehensive geotechnical information allows us to compute enhanced 2D finite element slope stability analysis with undrained sediment response compared to previous 2D numerical and 3D limit equilibrium assessments. Those models suggest that significant portions (detachment planes at 20 m or even 55 mbsf) of the Quaternary delta and slope apron deposits may be mobilized. Given that factors of safety are equal or less than 1 when further considering the effect of free gas, a high risk for a landslide event of considerable size off Nice international airport is identified

Existence and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system over moving domains

This dissertation concerns the well-posedness of the Navier-Stokes-Smoluchowski system. The system models a mixture of fluid and particles in the so-called bubbling regime. The compressible Navier-Stokes equations governing the evolution of the fluid are coupled to the Smoluchowski equation for the particle density at a continuum level. First, working on fixed domains, the existence of weak solutions is established using a three-level approximation scheme and based largely on the Lions-Feireisl theory of compressible fluids. The system is then posed over a moving domain. By utilizing a Brinkman-type penalization as well as penalization of the viscosity, the existence of weak solutions of the Navier-Stokes-Smoluchowski system is proved over moving domains. As a corollary the convergence of the Brinkman penalization is proved. Finally, a suitable relative entropy is defined. This relative entropy is used to establish a weak-strong uniqueness result for the Navier-Stokes-Smoluchowski system over moving domains, ensuring that strong solutions are unique in the class of weak solutions.

Kinetic study of solid phase demineralization by weak acids in one-step enzymatic bio-refinery of shrimp cuticles

We describe a one-step bio-refinery process for shrimp composites by-products. Its originality lies in a simple rapid (6 h) biotechnological cuticle fragmentation process that recovers all major compounds (chitins, peptides and minerals in particular calcium). The process consists of a controlled exogenous enzymatic proteolysis in a food-grade acidic medium allowing chitin purification (solid phase), and recovery of peptides and minerals (liquid phase). At a pH of between 3.5 and 4, protease activity is effective, and peptides are preserved. Solid phase demineralization kinetics were followed for phosphoric, hydrochloric, acetic, formic and citric acids with pKa ranging from 2.1 to 4.76. Formic acid met the initial aim of (i) 99 % of demineralization yield and (ii) 95 % deproteinization yield at a pH close to 3.5 and a molar ratio of 1.5. The proposed one-step process is proven to be efficient. To formalize the necessary elements for the future optimization of the process, two models to predict shell demineralization kinetics were studied, one based on simplified physical considerations and a second empirical one. The first model did not accurately describe the kinetics for times exceeding 30 minutes, the empirical one performed adequately.

Gravitational Waves: completeness and connectedness by geodesics

Only few months ago some physicists gave the official announcement that gravitational waves exist, but, from a geometrical point of view, they have always been ``real objects'' and their properties have been widely investigated. The aim of this talk is introducing generalized plane waves and discussing some of their properties such as geodesic connectedness and geodesic completeness.

WEAK ISOMETRIES OF HAMMING SPACES

In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rn. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean cube, that is, the binary Hamming space. We attempted to generalize some of their methods to the non-boolean case. The 4th chapter has our new results and is split into two major contributions. Our first contribution shows if n=p or p < n2, then every weak isometry of Hnq that preserves distance p is an isometry. Our second contribution gives a possible method to check if a weak isometry is an isometry using linear algebra and graph theory.

Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

Weak reasoning argumentative theory. A dialogical approach for the discovery of philosophy in high schools

In the literature on philosophical practices, despite the crucial role that argumentation plays in these activities, no specific argumentative theories have ever been proposed to assist the figure of the facilitator in conducting philosophical dialogue and to enhance student’s critical thinking skills. The dissertation starts from a cognitive perspective that challenges the classic Cartesian notion of rationality by focusing on limits and biases of human reasoning. An argumentative model (WRAT – Weak Reasoning Argumentative Theory) is then outlined in order to respond to the needs of philosophical dialogue. After justifying the claim that this learning activity, among other inductive methodologies, is the most suitable for critical thinking education, I inquired into the specific goal of ‘arguing’ within this context by means of the tools provided by Speech Act Theory: the speaker’s intention is to construct new knowledge by questioning her own and other’s beliefs. The model proposed has been theorized on this assumption, starting from which the goals, and, in turn, the related norms, have been pinpointed. In order to include all the epistemic attitudes required to accomplish the complex task of arguing in philosophical dialogue, I needed to integrate two opposed cognitive accounts, Dual Process Theory and Evolutionary Approach, that, although they provide incompatible descriptions of reasoning, can be integrated to provide a normative account of argumentation. The model, apart from offering a theoretical contribution to argumentation studies, is designed to be applied to the Italian educational system, in particular to classes in technical and professional high schools belonging to the newly created network Inventio. This initiative is one of the outcomes of the research project by the same name, which also includes an original Syllabus, research seminars, a monitoring action and publications focused on introducing philosophy, in the form of workshop activities, into technical and professional schools.

Unveiling the expansion history of the universe with cosmic chronometers and gravitational waves

This Thesis explores two novel and independent cosmological probes, Cosmic Chronometers (CCs) and Gravitational Waves (GWs), to measure the expansion history of the Universe. CCs provide direct and cosmology-independent measurements of the Hubble parameter H(z) up to z∼2. In parallel, GWs provide a direct measurement of the luminosity distance without requiring additional calibration, thus yielding a direct measurement of the Hubble constant H0=H(z=0). This Thesis extends the methodologies of both of these probes to maximize their scientific yield. This is achieved by accounting for the interplay of cosmological and astrophysical parameters to derive them jointly, study possible degeneracies, and eventually minimize potential systematic effects. As a legacy value, this work also provides interesting insights into galaxy evolution and compact binary population properties. The first part presents a detailed study of intermediate-redshift passive galaxies as CCs, with a focus on the selection process and the study of their stellar population properties using specific spectral features. From their differential aging, we derive a new measurement of the Hubble parameter H(z) and thoroughly assess potential systematics. In the second part, we develop a novel methodology and pipeline to obtain joint cosmological and astrophysical population constraints using GWs in combination with galaxy catalogs. This is applied to GW170817 to obtain a measurement of H0. We then perform realistic forecasts to predict joint cosmological and astrophysical constraints from black hole binary mergers for upcoming gravitational wave observatories and galaxy surveys. Using these two probes we provide an independent reconstruction of H(z) with direct measurements of H0 from GWs and H(z) up to z∼2 from CCs and demonstrate that they can be powerful independent probes to unveil the expansion history of the Universe.

Galaxy cluster cosmology in KiDS, Planck, and Euclid surveys

In this Thesis, we present a series of works that encompass the fundamental steps of cosmological analyses based on galaxy clusters, spanning from mass calibration to deriving cosmological constraints through counts and clustering. Firstly, we focus on the 3D two-point correlation function (2PCF) of the galaxy cluster sample by Planck Collaboration XXVII (2016). The masses of these clusters are expected to be underestimated, as they are derived from a scaling relation calibrated through X-ray observations. We derived a mass bias which disagrees with simulation predictions, consistent with what derived by Planck Collaboration VI (2020). Furthermore, in this Thesis we analyse the cluster counts and 2PCF, respectively, of the photometric galaxy cluster sample developed by Maturi et al. (2019), based on the third data release of KiDS (KiDS-DR3, de Jong et al. 2017). We derived constraints on fundamental cosmological parameters which are consistent and competitive, in terms of uncertainties, with other state-of-the-art cosmological analyses. Then, we introduce a novel approach to establish galaxy colour-redshift relations for cluster weak-lensing analyses, regardless of the specific photometric bands in use. This method optimises the selection completeness of cluster background galaxies while maintaining a defined purity threshold. Based on the galaxy sample by Bisigello et al. (2020), we calibrated two colour selections, one relying on the ground-based griz bands, and the other including the griz and Euclid YJH bands. In addition, we present the preliminary work on the weak-lensing mass calibration of the clusters detected by Maturi et al. (in prep.) in the fourth data release of KiDS (KiDS-1000, Kuijken et al. 2019). This mass calibration will enable the cosmological analyses based on cluster counts and clustering, from which we expect remarkable improvements in the results compared to those derived in KiDS-DR3.

Lipschitz regularity for weak solutions of parabolic p-Laplacian type equations in certain subriemannian structures

The main aim of the thesis is to prove the local Lipschitz regularity of the weak solutions to a class of parabolic PDEs modeled on the parabolic p-Laplacian. This result is well known in the Euclidean case and recently has been extended in the Heisenberg group, while higher regularity results are not known in subriemannian parabolic setting. In this thesis we will consider vector fields more general than those in the Heisenberg setting, introducing some technical difficulties. To obtain our main result we will use a Moser-like iteration. Due to the non linearity of the equation, we replace the usual parabolic cylinders with new ones, whose dimension also depends on the L^p norm of the solution. In addition, we deeply simplify the iterative procedure, using the standard Sobolev inequality, instead of the parabolic one.

Fermion masses, leptogenesis and gravitational waves in SO(10)

Grand Unification Theories (GUTs) predict the unification of three of the fundamental forces and are a possible extension of the Standard Model, some of them predict neutrino mass and baryon asymmetry. We consider a minimal non-supersymmetric $SO(10)$ GUT model that can reproduce the observed fermionic masses and mixing parameters of the Standard Model. We calculate the scales of spontaneous symmetry breaking from the GUT to the Standard Model gauge group using two-loop renormalisation group equations. This procedure determines the proton decay rate and the scale of $U(1)_{B-L}$ breaking, which generates cosmic strings, and the right-handed neutrino mass scales. Consequently, the regions of parameter space where thermal leptogenesis is viable are identified and correlated with the fermion masses and mixing, the neutrinoless double beta decay rate, the proton decay rate, and the gravitational wave signal resulting from the network of cosmic strings. We demonstrate that this framework, which can explain the Standard Model fermion masses and mixing and the observed baryon asymmetry, will be highly constrained by the next generation of gravitational wave detectors and neutrino oscillation experiments which will also constrain the proton lifetime

Gravitational waves as dark sirens: an astrophysical and cosmological analysis

Despite the success of the ΛCDM model in describing the Universe, a possible tension between early- and late-Universe cosmological measurements is calling for new independent cosmological probes. Amongst the most promising ones, gravitational waves (GWs) can provide a self-calibrated measurement of the luminosity distance. However, to obtain cosmological constraints, additional information is needed to break the degeneracy between parameters in the gravitational waveform. In this thesis, we exploit the latest LIGO-Virgo-KAGRA Gravitational Wave Transient Catalog (GWTC-3) of GW sources to constrain the background cosmological parameters together with the astrophysical properties of Binary Black Holes (BBHs), using information from their mass distribution. We expand the public code MGCosmoPop, previously used for the application of this technique, by implementing a state-of-the-art model for the mass distribution, needed to account for the presence of non-trivial features, i.e. a truncated power law with two additional Gaussian peaks, referred to as Multipeak. We then analyse GWTC-3 comparing this model with simpler and more commonly adopted ones, both in the case of fixed and varying cosmology, and assess their goodness-of-fit with different model selection criteria, and their constraining power on the cosmological and population parameters. We also start to explore different sampling methods, namely Markov Chain Monte Carlo and Nested Sampling, comparing their performances and evaluating the advantages of both. We find concurring evidence that the Multipeak model is favoured by the data, in line with previous results, and show that this conclusion is robust to the variation of the cosmological parameters. We find a constraint on the Hubble constant of H0 = 61.10+38.65−22.43 km/s/Mpc (68% C.L.), which shows the potential of this method in providing independent constraints on cosmological parameters. The results obtained in this work have been included in [1].

Spectral distortions of the cosmic microwave background and small-scale gravitational waves as new windows on the Early Universe

In this thesis, we explore constraints which can be put on the primordial power spectrum of curvature perturbations beyond the scales probed by anisotropies of the cosmic microwave background and galaxy surveys. We exploit present and future measurements of CMB spectral distortions, and their synergy with CMB anisotropies, as well existing and future upper limits on the stochastic background of gravitational waves. We derive for the first time phenomenological templates that fit small-scale bumps in the primordial power spectrum generated in multi-field models of inflation. By using such templates, we study for the first time imprints of primordial peaks on anisotropies and spectral distortions of the cosmic microwave background and we investigate their contribution to the stochastic background of gravitational waves. Through a Monte Carlo Markov Chain analysis we infer for the first time the constraints on the amplitude, the width and the location of such bumps using Planck and FIRAS data. We also forecast how a future spectrometer like PIXIE could improve FIRAS boundaries. The results derived in this thesis have implications for the possibility of primordial black holes from inflation.