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.

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.

Dynamic characterisation of four nine-story large-panel R.C. buildings in Bishkek (Kyrgyzstan): A comparison between experimental ambient vibration analysis and numerical finite element modeling

With the outlook of improving seismic vulnerability assessment for the city of Bishkek (Kyrgyzstan), the global dynamic behaviour of four nine-storey r.c. large-panel buildings in elastic regime is studied. The four buildings were built during the Soviet era within a serial production system. Since they all belong to the same series, they have very similar geometries both in plan and in height. Firstly, ambient vibration measurements are performed in the four buildings. The data analysis composed of discrete Fourier transform, modal analysis (frequency domain decomposition) and deconvolution interferometry, yields the modal characteristics and an estimate of the linear impulse response function for the structures of the four buildings. Then, finite element models are set up for all four buildings and the results of the numerical modal analysis are compared with the experimental ones. The numerical models are finally calibrated considering the first three global modes and their results match the experimental ones with an error of less then 20%.

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.

X-ray analysis of local mid-infrared selected Compton-thick AGN candidates

Cosmic X-ray background synthesis models (Gilli 2007) require a significant fraction of obscured AGN, some of which are expected to be heavily obscured (Compton-thick), but the number density of observationally found obscured sources is still an open issue (Vignali 2010, 2014). This thesis work takes advantage of recent NuSTAR data and is based on a multiwavelength research approach. Gruppioni et al. 2016 compared the AGN bolometric luminosity, for a sample of local 12 micron Seyfert galaxies, derived from the SED decomposition to the same quantity obtained by the 2-10 keV luminosity (IPAC-NED). A difference up to two orders of magnitude resulted between these quantities for some sources. Thus, the intrinsic X-ray luminosity obtained correcting for the obscuration may be underestimated. In this thesis we have tested this hypothesis by re-analysing the X-ray spectra of three of the sources (UGC05101, NGC1194 and NGC3079), for which observations from NuSTAR and Chandra and/or XMM-Newton were available. This is meant to extend our analysis to energies above 10 keV and thus estimate the AGN column density as reliable as possible. For spectral fitting we made use of both the commonly used XSPEC package and the two very recent MYtorus and BNtorus physical models. The available wide bandpass allowed us to achieve new and more solid insights into the X-ray spectral properties of these sources. The measured absorption column densities are highly suggestive of heavy obscuration. Once corrected the X-ray AGN luminosity for the obscuration estimated through our spectral analysis, we compared the L(X) values in the 2-10 keV band with those derived from the MIR band, by means of the relation by Gandhi, 2009. As expected, the values derived from this relation are in good agreement with those we measured, indicating that the column densities were underestimated in the previous literature works.