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.

Generic wind estimation and compensation based on residual generators and higher-order sliding mode schemes

This master thesis proposes a solution to the approach problem in case of unknown severe microburst wind shear for a fixed-wing aircraft, accounting for both longitudinal and lateral dynamics. The adaptive controller design for wind rejection is also addressed, exploiting the wind estimation provided by suitable estimators. It is able to successfully complete the final approach phase even in presence of wind shear, and at the same time aerodynamic envelope protection is retained. The adaptive controller for wind compensation has been designed by a backstepping approach and feedback linearization for time-varying systems. The wind shear components have been estimated by higher-order sliding mode schemes. At the end of this work the results are provided, an autonomous final approach in presence of microburst is discussed, performances are analyzed, and estimation of the microburst characteristics from telemetry data is examined.

Statistical mechanics of polymer models: rigorous results and applications

Monomer-dimer models are amongst the models in statistical mechanics which found application in many areas of science, ranging from biology to social sciences. This model describes a many-body system in which monoatomic and diatomic particles subject to hard-core interactions get deposited on a graph. In our work we provide an extension of this model to higher-order particles. The aim of our work is threefold: first we study the thermodynamic properties of the newly introduced model. We solve analytically some regular cases and find that, differently from the original, our extension admits phase transitions. Then we tackle the inverse problem, both from an analytical and numerical perspective. Finally we propose an application to aggregation phenomena in virtual messaging services.