Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities

In this thesis, numerical methods aiming at determining the eigenfunctions, their adjoint and the corresponding eigenvalues of the two-group neutron diffusion equations representing any heterogeneous system are investigated. First, the classical power iteration method is modified so that the calculation of modes higher than the fundamental mode is possible. Thereafter, the Explicitly-Restarted Arnoldi method, belonging to the class of Krylov subspace methods, is touched upon. Although the modified power iteration method is a computationally-expensive algorithm, its main advantage is its robustness, i.e. the method always converges to the desired eigenfunctions without any need from the user to set up any parameter in the algorithm. On the other hand, the Arnoldi method, which requires some parameters to be defined by the user, is a very efficient method for calculating eigenfunctions of large sparse system of equations with a minimum computational effort. These methods are thereafter used for off-line analysis of the stability of Boiling Water Reactors. Since several oscillation modes are usually excited (global and regional oscillations) when unstable conditions are encountered, the characterization of the stability of the reactor using for instance the Decay Ratio as a stability indicator might be difficult if the contribution from each of the modes are not separated from each other. Such a modal decomposition is applied to a stability test performed at the Swedish Ringhals-1 unit in September 2002, after the use of the Arnoldi method for pre-calculating the different eigenmodes of the neutron flux throughout the reactor. The modal decomposition clearly demonstrates the excitation of both the global and regional oscillations. Furthermore, such oscillations are found to be intermittent with a time-varying phase shift between the first and second azimuthal modes.

Extracting evolutionary information from the spectral decomposition of early-type galaxies.

Holding the major share of stellar mass in galaxies and being also old and passively evolving, early-type galaxies (ETGs) are the primary probes in investigating these various evolution scenarios, as well as being useful means to provide insights on cosmological parameters. In this thesis work I focused specifically on ETGs and on their capability in constraining galaxy formation and evolution; in particular, the principal aims were to derive some of the ETGs evolutionary parameters, such as age, metallicity and star formation history (SFH) and to study their age-redshift and mass-age relations. In order to infer galaxy physical parameters, I used the public code STARLIGHT: this program provides a best fit to the observed spectrum from a combination of many theoretical models defined in user-made libraries. the comparison between the output and input light-weighted ages shows a good agreement starting from SNRs of ∼ 10, with a bias of ∼ 2.2% and a dispersion 3%. Furthermore, also metallicities and SFHs are well reproduced. In the second part of the thesis I performed an analysis on real data, starting from Sloan Digital Sky Survey (SDSS) spectra. I found that galaxies get older with cosmic time and with increasing mass (for a fixed redshift bin); absolute light-weighted ages, instead, result independent from the fitting parameters or the synthetic models used. Metallicities, instead, are very similar from each other and clearly consistent with the ones derived from the Lick indices. The predicted SFH indicates the presence of a double burst of star formation. Velocity dispersions and extinctiona are also well constrained, following the expected behaviours. As a further step, I also fitted single SDSS spectra (with SNR∼ 20), to verify that stacked spectra gave the same results without introducing any bias: this is an important check, if one wants to apply the method at higher z, where stacked spectra are necessary to increase the SNR. Our upcoming aim is to adopt this approach also on galaxy spectra obtained from higher redshift Surveys, such as BOSS (z ∼ 0.5), zCOSMOS (z 1), K20 (z ∼ 1), GMASS (z ∼ 1.5) and, eventually, Euclid (z 2). Indeed, I am currently carrying on a preliminary study to estabilish the applicability of the method to lower resolution, as well as higher redshift (z 2) spectra, just like the Euclid ones.

Catalytic decomposition of formic acid using supported metal nanoparticles

Upgrade of hydrogen to valuable fuel is a central topic in modern research due to its high availability and low price. For the difficulties in hydrogen storage, different pathways are still under investigation. A promising way is in the liquid-phase chemical hydrogen storage materials, because they can lead to greener transformation processes with the on line development of hydrogen for fuel cells. The aim of my work was the optimization of catalysts for the decomposition of formic acid made by sol immobilisation method (a typical colloidal method). Formic acid was selected because of the following features: it is a versatile renewable reagent for green synthesis studies. The first aim of my research was the synthesis and optimisation of Pd nanoparticles by sol-immobilisation to achieve better catalytic performances and investigate the effect of particle size, oxidation state, role of stabiliser and nature of the support. Palladium was chosen because it is a well-known active metal for the catalytic decomposition of formic acid. Noble metal nanoparticles of palladium were immobilized on carbon charcoal and on titania. In the second part the catalytic performance of the “homemade” catalyst Pd/C to a commercial Pd/C and the effect of different monometallic and bimetallic systems (AuxPdy) in the catalytic formic acid decomposition was investigated. The training period for the production of this work was carried out at the University of Cardiff (Group of Dr. N. Dimitratos).

Study of Co-based hydrotalcite-derived mixed metal oxides partially modified with silver as potential catalysts for N2O decomposition

Co-Al-Ox mixed metal oxides partially modified with Cu or Mg, as well as Ag were successfully prepared, characterized and evaluated as potential catalysts for the N2O decomposition. The materials were characterized by the following techniques: X-Ray Diffraction, Thermogravimetric Analysis (TGA), N2 Physisorption, Hydrogen Temperature-Programmed Reduction (H2-TPR), and X-ray photoelectron spectroscopy (XPS). Ag-modified HT-derived mixed oxides showed enhanced activity compared to the undoped materials, the optimum composition was found for (1 wt.% Ag)CHT-Co3Al. The catalyst characterization studies suggested that the improved catalytic activity of Ag-promoted catalysts were mainly because of the altered redox properties of the materials.

Rational algorithms for the decomposition of Feynman integrals via intersection theory

The decomposition of Feynman integrals into a basis of independent master integrals is an essential ingredient of high-precision theoretical predictions, that often represents a major bottleneck when processes with a high number of loops and legs are involved. In this thesis we present a new algorithm for the decomposition of Feynman integrals into master integrals with the formalism of intersection theory. Intersection theory is a novel approach that allows to decompose Feynman integrals into master integrals via projections, based on a scalar product between Feynman integrals called intersection number. We propose a new purely rational algorithm for the calculation of intersection numbers of differential $n-$forms that avoids the presence of algebraic extensions. We show how expansions around non-rational poles, which are a bottleneck of existing algorithms for intersection numbers, can be avoided by performing an expansion in series around a rational polynomial irreducible over $\mathbb{Q}$, that we refer to as $p(z)-$adic expansion. The algorithm we developed has been implemented and tested on several diagrams, both at one and two loops.

On the Iwasawa decomposition

La decomposizione di Iwasawa è una particolare decomposizione di un gruppo di Lie semisemplice G in cui i fattori sono sottogruppi chiusi di G. In questa tesi si analizza nello specifico la decomposizione di Iwasawa del gruppo SL(2,R), dandone alcune rilevanti applicazioni algebriche e topologiche (Capitolo 2). Alcune di queste sono ad esempio l'omeomorfismo di SL(2,R) con l'interno di un toro solido e l'esistenza di un unico omomorfismo continuo (quello banale) da SL(2,R) al gruppo additivo di R. Vengono poi studiate le classi di coniugio degli elementi di SL(2,R) in termini dei sottogruppi che compaiono nella decomposizione di Iwasawa e l'azione di SL(2,R) sul semipiano superiore del piano complesso, da cui è possibile ricavare una dimostrazione alternativa della decomposizione di Iwasawa. Il Capitolo 1 raccoglie il materiale introduttivo utile ad una lettura autocontenuta della tesi; in particolare vengono introdotti i gruppi topologici GL(n,F) e SL(n,F) (dove F indica un campo), l'azione di un gruppo su un insieme e l'esponenziale di matrici. Infine nel Capitolo 3 viene estesa la dimostrazione della decomposizione di Iwasawa ai gruppi SL(n,R) e SL(n,C).