Non-Gaussianities from a sudden change in the inflaton speed of sound

Il concetto di inflazione e' stato introdotto nei primi anni ’80 per risolvere alcuni problemi del modello cosmologico standard, quali quello dell’orizzonte e quello della piattezza. Le predizioni dei piu' semplici modelli inflazionari sono in buon accordo con le osservazioni cosmologiche piu'recenti, che confermano sezioni spaziali piatte e uno spettro di fluttuazioni primordiali con statistica vicina a quella gaussiana. I piu' recenti dati di Planck, pur in ottimo accordo con una semplice legge di potenza per lo spettro a scale k > 0.08 Mpc−1 , sembrano indicare possibili devi- azioni a scale maggiori, seppur non a un livello statisticamente significativo a causa della varianza cosmica. Queste deviazioni nello spettro possono essere spiegate da modelli inflazionari che includono una violazione della condizione di lento rotolamento (slow-roll ) e che hanno precise predizioni per lo spettro. Per uno dei primi modelli, caratterizzato da una discontinuita' nella derivata prima del potenziale proposto da Starobinsky, lo spettro ed il bispettro delle fluttuazioni primordiali sono noti analiticamente. In questa tesi estenderemo tale modello a termini cinetici non standard, calcolandone analiticamente il bispettro e confrontando i risultati ottenuti con quanto presente in letteratura. In particolare, l’introduzione di un termine cinetico non standard permettera' di ottenere una velocita' del suono per l’inflatone non banale, che consentira' di estendere i risultati noti, riguardanti il bispettro, per questo modello. Innanzitutto studieremo le correzioni al bispettro noto in letteratura dovute al fatto che in questo caso la velocita' del suono e' una funzione dipendente dal tempo; successivamente, cercheremo di calcolare analiticamente un ulteriore contributo al bispettro proporzionale alla derivata prima della velocita' del suono (che per il modello originale e' nullo).

A multi-objective genetic algorithm optimisation using variable speed pumps in water distribution systems

Due to its practical importance and inherent complexity, the optimisation of distribution networks for supplying drinking water has been the subject of extensive study for the past 30 years. The optimization is governed by sizing the pipes in the water distribution network (WDN) and / or optimises specific parts of the network such as pumps, tanks etc. or try to analyse and optimise the reliability of a WDN. In this thesis, the author has analysed two different WDNs (Anytown City and Cabrera city networks), trying to solve and optimise a multi-objective optimisation problem (MOOP). The main two objectives in both cases were the minimisation of Energy Cost (€) or Energy consumption (kWh), along with the total Number of pump switches (TNps) during a day. For this purpose, a decision support system generator for Multi-objective optimisation used. Its name is GANetXL and has been developed by the Center of Water System in the University of Exeter. GANetXL, works by calling the EPANET hydraulic solver, each time a hydraulic analysis has been fulfilled. The main algorithm used, was a second-generation algorithm for multi-objective optimisation called NSGA_II that gave us the Pareto fronts of each configuration. The first experiment that has been carried out was the network of Anytown city. It is a big network with a pump station of four fixed speed parallel pumps that are boosting the water dynamics. The main intervention was to change these pumps to new Variable speed driven pumps (VSDPs), by installing inverters capable to diverse their velocity during the day. Hence, it’s been achieved great Energy and cost savings along with minimisation in the number of pump switches. The results of the research are thoroughly illustrated in chapter 7, with comments and a variety of graphs and different configurations. The second experiment was about the network of Cabrera city. The smaller WDN had a unique FS pump in the system. The problem was the same as far as the optimisation process was concerned, thus, the minimisation of the energy consumption and in parallel the minimisation of TNps. The same optimisation tool has been used (GANetXL).The main scope was to carry out several and different experiments regarding a vast variety of configurations, using different pump (but this time keeping the FS mode), different tank levels, different pipe diameters and different emitters coefficient. All these different modes came up with a large number of results that were compared in the chapter 8. Concluding, it should be said that the optimisation of WDNs is a very interested field that has a vast space of options to deal with. This includes a large number of algorithms to choose from, different techniques and configurations to be made and different support system generators. The researcher has to be ready to “roam” between these choices, till a satisfactory result will convince him/her that has reached a good optimisation point.