Large-scale Network Analysis on Distributed Architectures

Questa dissertazione esamina le sfide e i limiti che gli algoritmi di analisi di grafi incontrano in architetture distribuite costituite da personal computer. In particolare, analizza il comportamento dell'algoritmo del PageRank così come implementato in una popolare libreria C++ di analisi di grafi distribuiti, la Parallel Boost Graph Library (Parallel BGL). I risultati qui presentati mostrano che il modello di programmazione parallela Bulk Synchronous Parallel è inadatto all'implementazione efficiente del PageRank su cluster costituiti da personal computer. L'implementazione analizzata ha infatti evidenziato una scalabilità negativa, il tempo di esecuzione dell'algoritmo aumenta linearmente in funzione del numero di processori. Questi risultati sono stati ottenuti lanciando l'algoritmo del PageRank della Parallel BGL su un cluster di 43 PC dual-core con 2GB di RAM l'uno, usando diversi grafi scelti in modo da facilitare l'identificazione delle variabili che influenzano la scalabilità. Grafi rappresentanti modelli diversi hanno dato risultati differenti, mostrando che c'è una relazione tra il coefficiente di clustering e l'inclinazione della retta che rappresenta il tempo in funzione del numero di processori. Ad esempio, i grafi Erdős–Rényi, aventi un basso coefficiente di clustering, hanno rappresentato il caso peggiore nei test del PageRank, mentre i grafi Small-World, aventi un alto coefficiente di clustering, hanno rappresentato il caso migliore. Anche le dimensioni del grafo hanno mostrato un'influenza sul tempo di esecuzione particolarmente interessante. Infatti, si è mostrato che la relazione tra il numero di nodi e il numero di archi determina il tempo totale.

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.

Design of an indirectly fired gas turbine integrated with an organic rankine cycle unit for combined heat and power production

In the last years, the European countries have paid increasing attention to renewable sources and greenhouse emissions. The Council of the European Union and the European Parliament have established ambitious targets for the next years. In this scenario, biomass plays a prominent role since its life cycle produces a zero net carbon dioxide emission. Additionally, biomass can ensure plant operation continuity thanks to its availability and storage ability. Several conventional systems running on biomass are available at the moment. Most of them are performant either in the large-scale or in the small power range. The absence of an efficient system on the small-middle scale inspired this thesis project. The object is an innovative plant based on a wet indirectly fired gas turbine (WIFGT) integrated with an organic Rankine cycle (ORC) unit for combined heat and power production. The WIFGT is a performant system in the small-middle power range; the ORC cycle is capable of giving value to low-temperature heat sources. Their integration is investigated in this thesis with the aim of carrying out a preliminary design of the components. The targeted plant output is around 200 kW in order not to need a wide cultivation area and to avoid biomass shipping. Existing in-house simulation tools are used: They are adapted to this purpose. Firstly the WIFGT + ORC model is built; Zero-dimensional models of heat exchangers, compressor, turbines, furnace, dryer and pump are used. Different fluids are selected but toluene and benzene turn out to be the most suitable. In the indirectly fired gas turbine a pressure ratio around 4 leads to the highest efficiency. From the thermodynamic analysis the system shows an electric efficiency of 38%, outdoing other conventional plants in the same power range. The combined plant is designed to recover thermal energy: Water is used as coolant in the condenser. It is heated from 60°C up to 90°C, ensuring the possibility of space heating. Mono-dimensional models are used to design the heat exchange equipment. Different types of heat exchangers are chosen depending on the working temperature. A finned-plate heat exchanger is selected for the WIFGT heat transfer equipment due to the high temperature, oxidizing and corrosive environment. A once-through boiler with finned tubes is chosen to vaporize the organic fluid in the ORC. A plate heat exchanger is chosen for the condenser and recuperator. A quasi-monodimensional model for single-stage axial turbine is implemented to design both the WIFGT and the ORC turbine. The system simulation after the components design shows an electric efficiency around 34% with a decrease by 10% compared to the zero-dimensional analysis. The work exhibits the system potentiality compared to the existing plants from both technical and economic point of view.