Study of the second hyperpolarizability of poly(3-alkylthiophenes) using the third-harmonic scattering technique

During the past years, the considerable need in the domain of communications for more potent photonic devices has focused the research activities into the nonlinear optical (NLO) materials which can be used for modern optical switches. In this regard, a lot of research activities are focused on the organic materials and conjugated polymers which offer more advantages compared to the inorganic ones. On this matter, poly(3-alkylthiophene) (P3AT), an organic conjugated polymer, can be investigated as potential optical material with in particular the focus on the NLO properties such as the first- and second-hyperpolarizability, β and γ respectively. The activities carried out at the Laboratory of Polymer Synthesis of the KU Leuven, during the master's thesis work, focused on the study of conjugated polymers in order to evaluate their NLO properties for the future purpose of applications in optical systems. In particular, three series of polythiophenes functionalized with an alkyl side chain in the 3-position were synthesized: poly(3-hexylthiophene) (P3HT), poly[3-(2-ethylhexyl)thiophene] (P3EHT) and random copolymer of the two regio-isomers of P3HT. They were made in order to study the influence of molar mass, branching and regio-irregularity on the γ-value. The Kumada catalyst transfer condensative polymerization (KCTCP) and the Pd(RuPhos)-protocol were used for the polymerizations in order to have control over the molar mass of the growing chain and consequently to obtain well-defined and reproducible materials. The P3AT derivatives obtained were characterized by gel permeation chromatography (GPC), spectroscopic techniques (1H-NMR, UV-Vis) and the γ-value was investigated using the third-harmonic scattering (THS) technique. In particular, the THS technique is useful to investigate the optical behavior of the series of polymers in solution.

A next-to-leading order calculation of the impact of primordial magnetic fields into cosmological observables

In this thesis, we perform a next-to-leading order calculation of the impact of primordial magnetic fields (PMF) into the evolution of scalar cosmological perturbations and the cosmic microwave background (CMB) anisotropy. Magnetic fields are everywhere in the Universe at all scales probed so far, but their origin is still under debate. The current standard picture is that they originate from the amplification of initial seed fields, which could have been generated as PMFs in the early Universe. The most robust way to test their presence and constrain their features is to study how they impact on key cosmological observables, in particular the CMB anisotropies. The standard way to model a PMF is to consider its contribution (quadratic in the magnetic field) at the same footing of first order perturbations, under the assumptions of ideal magneto-hydrodynamics and compensated initial conditions. In the perspectives of ever increasing precision of CMB anisotropies measurements and of possible uncounted non-linear effects, in this thesis we study effects which go beyond the standard assumptions. We study the impact of PMFs on cosmological perturbations and CMB anisotropies with adiabatic initial conditions, the effect of Alfvén waves on the speed of sound of perturbations and possible non-linear behavior of baryon overdensity for PMFs with a blue spectral index, by modifying and improving the publicly available Einstein-Boltzmann code SONG, which has been written in order to take into account all second-order contributions in cosmological perturbation theory. One of the objectives of this thesis is to set the basis to verify by an independent fully numerical analysis the possibility to affect recombination and the Hubble constant.

An optimal control tool for trajectory generation of autonomous drones

In the recent years, autonomous aerial vehicles gained large popularity in a variety of applications in the field of automation. To accomplish various and challenging tasks the capability of generating trajectories has assumed a key role. As higher performances are sought, traditional, flatness-based trajectory generation schemes present their limitations. In these approaches the highly nonlinear dynamics of the quadrotor is, indeed, neglected. Therefore, strategies based on optimal control principles turn out to be beneficial, since in the trajectory generation process they allow the control unit to best exploit the actual dynamics, and enable the drone to perform quite aggressive maneuvers. This dissertation is then concerned with the development of an optimal control technique to generate trajectories for autonomous drones. The algorithm adopted to this end is a second-order iterative method working directly in continuous-time, which, under proper initialization, guarantees quadratic convergence to a locally optimal trajectory. At each iteration a quadratic approximation of the cost functional is minimized and a decreasing direction is then obtained as a linear-affine control law, after solving a differential Riccati equation. The algorithm has been implemented and its effectiveness has been tested on the vectored-thrust dynamical model of a quadrotor in a realistic simulative setup.