Constraining mass and shape of galaxy clusters through large scale structures

The mass estimation of galaxy clusters is a crucial point for modern cosmology, and can be obtained by several different techniques. In this work we discuss a new method to measure the mass of galaxy clusters connecting the gravitational potential of the cluster with the kinematical properties of its surroundings. We explore the dynamics of the structures located in the region outside virialized cluster, We identify groups of galaxies, as sheets or filaments, in the cluster outer region, and model how the cluster gravitational potential perturbs the motion of these structures from the Hubble fow. This identification is done in the redshift space where we look for overdensities with a filamentary shape. Then we use a radial mean velocity profile that has been found as a quite universal trend in simulations, and we fit the radial infall velocity profile of the overdensities found. The method has been tested on several cluster-size haloes from cosmological N-body simulations giving results in very good agreement with the true values of virial masses of the haloes and orientation of the sheets. We then applied the method to the Coma cluster and even in this case we found a good correspondence with previous. It is possible to notice a mass discrepancy between sheets with different alignments respect to the center of the cluster. This difference can be used to reproduce the shape of the cluster, and to demonstrate that the spherical symmetry is not always a valid assumption. In fact, if the cluster is not spherical, sheets oriented along different axes should feel a slightly different gravitational potential, and so give different masses as result of the analysis described before. Even this estimation has been tested on cosmological simulations and then applied to Coma, showing the actual non-sphericity of this cluster.

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.

Investigation of petabyte-scale data transfer performances with PhEDEx for the CMS experiment

PhEDEx, the CMS transfer management system, during the first LHC Run has moved about 150 PB and currently it is moving about 2.5 PB of data per week over the Worldwide LHC Computing Grid (WLGC). It was designed to complete each transfer required by users at the expense of the waiting time necessary for its completion. For this reason, after several years of operations, data regarding transfer latencies has been collected and stored into log files containing useful analyzable informations. Then, starting from the analysis of several typical CMS transfer workflows, a categorization of such latencies has been made with a focus on the different factors that contribute to the transfer completion time. The analysis presented in this thesis will provide the necessary information for equipping PhEDEx in the future with a set of new tools in order to proactively identify and fix any latency issues. PhEDEx, il sistema di gestione dei trasferimenti di CMS, durante il primo Run di LHC ha trasferito all’incirca 150 PB ed attualmente trasferisce circa 2.5 PB di dati alla settimana attraverso la Worldwide LHC Computing Grid (WLCG). Questo sistema è stato progettato per completare ogni trasferimento richiesto dall’utente a spese del tempo necessario per il suo completamento. Dopo svariati anni di operazioni con tale strumento, sono stati raccolti dati relativi alle latenze di trasferimento ed immagazzinati in log files contenenti informazioni utili per l’analisi. A questo punto, partendo dall’analisi di una ampia mole di trasferimenti in CMS, è stata effettuata una suddivisione di queste latenze ponendo particolare attenzione nei confronti dei fattori che contribuiscono al tempo di completamento del trasferimento. L’analisi presentata in questa tesi permetterà di equipaggiare PhEDEx con un insieme di utili strumenti in modo tale da identificare proattivamente queste latenze e adottare le opportune tattiche per minimizzare l’impatto sugli utenti finali.