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).

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.

"Influence of lower-limb joint models on subject-specific musculoskeletal model predictions during gait" ( "modelli muscoloscheletrici personalizzati dell'arto inferiore: Analisi dell'effetto della modellazione dei giunti sulla predizione dei carichi agenti sul sistema scheletrico durante il cammino").

The aim of the present thesis was to investigate the influence of lower-limb joint models on musculoskeletal model predictions during gait. We started our analysis by using a baseline model, i.e., the state-of-the-art lower-limb model (spherical joint at the hip and hinge joints at the knee and ankle) created from MRI of a healthy subject in the Medical Technology Laboratory of the Rizzoli Orthopaedic Institute. We varied the models of knee and ankle joints, including: knee- and ankle joints with mean instantaneous axis of rotation, universal joint at the ankle, scaled-generic-derived planar knee, subject-specific planar knee model, subject-specific planar ankle model, spherical knee, spherical ankle. The joint model combinations corresponding to 10 musculoskeletal models were implemented into a typical inverse dynamics problem, including inverse kinematics, inverse dynamics, static optimization and joint reaction analysis algorithms solved using the OpenSim software to calculate joint angles, joint moments, muscle forces and activations, joint reaction forces during 5 walking trials. The predicted muscle activations were qualitatively compared to experimental EMG, to evaluate the accuracy of model predictions. Planar joint at the knee, universal joint at the ankle and spherical joints at the knee and at the ankle produced appreciable variations in model predictions during gait trials. The planar knee joint model reduced the discrepancy between the predicted activation of the Rectus Femoris and the EMG (with respect to the baseline model), and the reduced peak knee reaction force was considered more accurate. The use of the universal joint, with the introduction of the subtalar joint, worsened the muscle activation agreement with the EMG, and increased ankle and knee reaction forces were predicted. The spherical joints, in particular at the knee, worsened the muscle activation agreement with the EMG. A substantial increase of joint reaction forces at all joints was predicted despite of the good agreement in joint kinematics with those of the baseline model. The introduction of the universal joint had a negative effect on the model predictions. The cause of this discrepancy is likely to be found in the definition of the subtalar joint and thus, in the particular subject’s anthropometry, used to create the model and define the joint pose. We concluded that the implementation of complex joint models do not have marked effects on the joint reaction forces during gait. Computed results were similar in magnitude and in pattern to those reported in literature. Nonetheless, the introduction of planar joint model at the knee had positive effect upon the predictions, while the use of spherical joint at the knee and/or at the ankle is absolutely unadvisable, because it predicted unrealistic joint reaction forces.

Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Angular momentum of S0 galaxies

The aim of this thesis is to study the angular momentum of a sample of S0 galaxies. In the quest to understand whether the formation of S0 galaxies is more closely linked to that of ellipticals or that of spirals, our goal is to compare the amount of their specific angular momentum as a function of stellar mass with respect to spirals. Through kinematic comparison between these different classes of galaxies we aim to understand if a scenario of passive evolution, in which the galaxy’s gas is consumed and the star formation is quenched, can be considered as plausible mechanism to explain the transformation from spirals to S0s. In order to derive the structural and photometric parameters of galaxy sub-components we performed a bulge-disc decomposition of optical images using GALFIT. The stellar kinematic of the galaxies was measured using integral field spectroscopic data from CALIFA survey. The development of new original software, based on a Monte Carlo Markov Chain algorithm, allowed us to obtain the values of the line of sight velocity and velocity dispersion of disc and bulge components. The result that we obtained is that S0 discs have a distribution of stellar specific angular momentum that is in full agreement with that of spiral discs, so the mechanism of simple fading can be considered as one of the most important for transformation from spirals to S0s.

Characterization of ENSO changes under idealised radiative forcing in an intermediate complexity general circulation model

Intermediate-complexity general circulation models are a fundamental tool to investigate the role of internal and external variability within the general circulation of the atmosphere and ocean. The model used in this thesis is an intermediate complexity atmospheric general circulation model (SPEEDY) coupled to a state-of-the-art modelling framework for the ocean (NEMO). We assess to which extent the model allows a realistic simulation of the most prominent natural mode of variability at interannual time scales: El-Niño Southern Oscillation (ENSO). To a good approximation, the model represents the ENSO-induced Sea Surface Temperature (SST) pattern in the equatorial Pacific, despite a cold tongue-like bias. The model underestimates (overestimates) the typical ENSO spatial variability during the winter (summer) seasons. The mid-latitude response to ENSO reveals that the typical poleward stationary Rossby wave train is reasonably well represented. The spectral decomposition of ENSO features a spectrum that lacks periodicity at high frequencies and is overly periodic at interannual timescales. We then implemented an idealised transient mean state change in the SPEEDY model. A warmer climate is simulated by an alteration of the parametrized radiative fluxes that corresponds to doubled carbon dioxide absorptivity. Results indicate that the globally averaged surface air temperature increases of 0.76 K. Regionally, the induced signal on the SST field features a significant warming over the central-western Pacific and an El-Niño-like warming in the subtropics. In general, the model features a weakening of the tropical Walker circulation and a poleward expansion of the local Hadley cell. This response is also detected in a poleward rearrangement of the tropical convective rainfall pattern. The model setting that has been here implemented provides a valid theoretical support for future studies on climate sensitivity and forced modes of variability under mean state changes.

Optimization of aqueous Zn-ion batteries

MnHCF was synthesized by simple co-precipitation method. In this work we investigate the electrochemical behavior of manganese hexacyanoferrate in zinc sulfate (ZnSO4), ZnSO4+MnSO4 and zinc triflate (Zn(OTF)2) aqueous electrolytes. Electrochemical tests were performed by both El-cell which is designed for reflection investigation and coin cell. In cyclic voltammetry curves, we observed redox peaks of both Fe3+/2+ and Mn3+/2+ pairs. The results based on current shows that the capacity of battery is controlled by diffusion process in aqueous electrolyte system. MnHCF undergoes severe dissolution and zinc displacement during cycling. Compared to ZnSO4, anions of Zn (OTF)2 electrolyte are strongly adsorbed on the electrolyte surface, in turn hindering the water oxidation reaction and reducing the decomposition of MnHCF. The MnHCF/Zn battery using 3M Zn (OTF)2 delivers a specific capacity of 41 mAhg-1 at 50 mAg-1 while by using 3M ZnSO4+1M MnSO4 the specific capacity reaches to 400 mAhg-1 for the pure sample and around 250 mAhg-1 for the MnHCF+A. Our results suggest that the anions in the aqueous electrolyte are of great importance to optimize the electrochemical performance of metal hexacyanoferrates. The pre-addition of MnSO4 into ZnSO4 solution is capable of easing the Mn2+ dissolution from the cathode.