Analysis and design considerations of resonator arrays for inductive power transfer systems

In the frame of inductive power transfer (IPT) systems, arrays of magnetically coupled resonators have received increasing attention as they are cheap and versatile due to their simple structure. They consist of magnetically coupled coils, which resonate with their self-capacitance or lumped capacitive networks. Of great industrial interest are planar resonator arrays used to power a receiver that can be placed at any position above the array. A thorough circuit analysis has been carried out, first starting from traditional two-coil IPT devices. Then, resonator arrays have been introduced, with particular attention to the case of arrays with a receiver. To evaluate the system performance, a circuit model based on original analytical formulas has been developed and experimentally validated. The results of the analysis also led to the definition of a new doubly-fed array configuration with a receiver that can be placed above it at any position. A suitable control strategy aimed at maximising the transmitted power and the efficiency has been also proposed. The study of the array currents has been carried out resorting to the theory of magneto-inductive waves, allowing useful insight to be highlighted. The analysis has been completed with a numerical and experimental study on the magnetic field distribution originating from the array. Furthermore, an application of the resonator array as a position sensor has been investigated. The position of the receiver is estimated through the measurement of the array input impedance, for which an original analytical expression has been also obtained. The application of this sensing technique in an automotive dynamic IPT system has been discussed. The thesis concludes with an evaluation of the possible applications of two-dimensional resonator arrays in IPT systems. These devices can be used to improve system efficiency and transmitted power, as well as for magnetic field shielding.

Potential theory on metric spaces

This work revolves around potential theory in metric spaces, focusing on applications of dyadic potential theory to general problems associated to functional analysis and harmonic analysis. In the first part of this work we consider the weighted dual dyadic Hardy's inequality over dyadic trees and we use the Bellman function method to characterize the weights for which the inequality holds, and find the optimal constant for which our statement holds. We also show that our Bellman function is the solution to a stochastic optimal control problem. In the second part of this work we consider the problem of quasi-additivity formulas for the Riesz capacity in metric spaces and we prove formulas of quasi-additivity in the setting of the tree boundaries and in the setting of Ahlfors-regular spaces. We also consider a proper Harmonic extension to one additional variable of Riesz potentials of functions on a compact Ahlfors-regular space and we use our quasi-additivity formula to prove a result of tangential convergence of the harmonic extension of the Riesz potential up to an exceptional set of null measure

The combinatorics of Hilbert-Poincaré series of matroids

In this thesis we explore the combinatorial properties of several polynomials arising in matroid theory. Our main motivation comes from the problem of computing them in an efficient way and from a collection of conjectures, mainly the real-rootedness and the monotonicity of their coefficients with respect to weak maps. Most of these polynomials can be interpreted as Hilbert--Poincaré series of graded vector spaces associated to a matroid and thus some combinatorial properties can be inferred via combinatorial algebraic geometry (non-negativity, palindromicity, unimodality); one of our goals is also to provide purely combinatorial interpretations of these properties, for example by redefining these polynomials as poset invariants (via the incidence algebra of the lattice of flats); moreover, by exploiting the bases polytopes and the valuativity of these invariants with respect to matroid decompositions, we are able to produce efficient closed formulas for every paving matroid, a class that is conjectured to be predominant among all matroids. One last goal is to extend part of our results to a higher categorical level, by proving analogous results on the original graded vector spaces via abelian categorification or on equivariant versions of these polynomials.

Dalla Sintesi di Leganti Polimerici alla Realizzazione di Adesivi da Parquet

This final report is part of a research project by Kerakoll S.P.A aimed to the realization and optimization of hybrid adhesive for the parquet using hybrid polyurethane silanizated (STPU). Hybrid polymers belong to polyurethane polymers which undergo an hybridization process where the classic isocyanate groups are converted into a alkoxysilylether terminated chain. The aim of this thesis was to realize hybrid polymers with specific proprieties compared to the indexes wanted by the company; another goal of this project was to use this polymers STPU to realize adhesive for the parquet which should be competitive in the adhesive market. All activities were carried out in a chemistry laboratory with specific tools for the synthesis of polymers and characterization of the finals products. The study led to two prototypes; the second was obtained thanks to the use of the experimental design procedure known as DOE (Design Of Experiment), a recently acquired approach by the company, which allows the rationalization of the formulas and the creation of a database that can be extended and implemented indefinitely.