Higher order Sobolev Spaces and polyharmonic boundary value problems in Carnot Groups

The main task of this work is to present a concise survey on the theory of certain function spaces in the contexts of Hörmander vector fields and Carnot Groups, and to discuss briefly an application to some polyharmonic boundary value problems on Carnot Groups of step 2.

Data analysis of collapse mechanisms of a 3D printed groin vault in shaking table testing

The aim of this novel experimental study is to investigate the behaviour of a 2m x 2m model of a masonry groin vault, which is built by the assembly of blocks made of a 3D-printed plastic skin filled with mortar. The choice of the groin vault is due to the large presence of this vulnerable roofing system in the historical heritage. Experimental tests on the shaking table are carried out to explore the vault response on two support boundary conditions, involving four lateral confinement modes. The data processing of markers displacement has allowed to examine the collapse mechanisms of the vault, based on the arches deformed shapes. There then follows a numerical evaluation, to provide the orders of magnitude of the displacements associated to the previous mechanisms. Given that these displacements are related to the arches shortening and elongation, the last objective is the definition of a critical elongation between two diagonal bricks and consequently of a diagonal portion. This study aims to continue the previous work and to take another step forward in the research of ground motion effects on masonry structures.

Exploiting the clustering of cosmic voids as a novel cosmological probe

The investigations of the large-scale structure of our Universe provide us with extremely powerful tools to shed light on some of the open issues of the currently accepted Standard Cosmological Model. Until recently, constraining the cosmological parameters from cosmic voids was almost infeasible, because the amount of data in void catalogues was not enough to ensure statistically relevant samples. The increasingly wide and deep fields in present and upcoming surveys have made the cosmic voids become promising probes, despite the fact that we are not yet provided with a unique and generally accepted definition for them. In this Thesis we address the two-point statistics of cosmic voids, in the very first attempt to model its features with cosmological purposes. To this end, we implement an improved version of the void power spectrum presented by Chan et al. (2014). We have been able to build up an exceptionally robust method to tackle with the void clustering statistics, by proposing a functional form that is entirely based on first principles. We extract our data from a suite of high-resolution N-body simulations both in the LCDM and alternative modified gravity scenarios. To accurately compare the data to the theory, we calibrate the model by accounting for a free parameter in the void radius that enters the theory of void exclusion. We then constrain the cosmological parameters by means of a Bayesian analysis. As far as the modified gravity effects are limited, our model is a reliable method to constrain the main LCDM parameters. By contrast, it cannot be used to model the void clustering in the presence of stronger modification of gravity. In future works, we will further develop our analysis on the void clustering statistics, by testing our model on large and high-resolution simulations and on real data, also addressing the void clustering in the halo distribution. Finally, we also plan to combine these constraints with those of other cosmological probes.