Models for the assessment of resilience in water distribution networks

The following thesis work focuses on the use and implementation of advanced models for measuring the resilience of water distribution networks. In particular, the functions implemented in GRA Tool, a software developed by the University of Exeter (UK), and the functions of the Toolkit of Epanet 2.2 were investigated. The study of the resilience and failure, obtained through GRA Tool and the development of the methodology based on the combined use of EPANET 2.2 and MATLAB software, was tested in a first phase, on a small-sized literature water distribution network, so that the variability of the results could be perceived more clearly and with greater immediacy, and then, on a more complex network, that of Modena. In the specific, it has been decided to go to recreate a mode of failure deferred in time, one proposed by the software GRA Tool, that is failure to the pipes, to make a comparison between the two methodologies. The analysis of hydraulic efficiency was conducted using a synthetic and global network performance index, i.e., Resilience index, introduced by Todini in the years 2000-2016. In fact, this index, being one of the parameters with which to evaluate the overall state of "hydraulic well-being" of a network, has the advantage of being able to act as a criterion for selecting any improvements to be made on the network itself. Furthermore, during these analyzes, was shown the analytical development undergone over time by the formula of the Resilience Index. The final intent of this thesis work was to understand by what means to improve the resilience of the system in question, as the introduction of the scenario linked to the rupture of the pipelines was designed to be able to identify the most problematic branches, i.e., those that in the event of a failure it would entail greater damage to the network, including lowering the Resilience Index.

Hidden Schrödinger symmetry in FLRW and Bianchi I minisuperspace models of cosmology and black holes Schwarzschild dynamics

A broad sector of literature focuses on the relationship between fluid dynamics and gravitational systems. This thesis presents results that suggest the existence of a new kind of fluid/gravity duality not based on the holographic principle. The goal is to provide tools that allow us to systematically unearth hidden symmetries for reduced models of cosmology. The focus is on the field space of these models, i.e. the superspace. In fact, conformal isometries of the supermetric leave geodesics in the field space unaltered; this leads to symmetries of the models. An innovative aspect is the use of the Eisenhart-Duval’s lift. Using this method, systems constrained by a potential can be treated as free ones. Moreover, charges explicitly dependent on time, i.e. dynamical, can be found. A detailed analysis is carried out on three basic models of homogenous cosmology: i) flat Friedmann-Lemaître-Robertson-Walker’s isotropic universe filled with a massless scalar field; ii) Schwarzschild’s black hole mechanics and its extension to vacuum (A)dS gravity; iii) Bianchi’s anisotropic type I universe with a massless scalar field. The results show the presence of a hidden Schrödinger’s symmetry which, being intrinsic to both Navier-Stokes’ and Schrödinger’s equations, indicates a correspondence between cosmology and hydrodynamics. Furthermore, the central extension of this algebra explicitly relates two concepts. The first is the number of particles coming from the fluid picture; while the second is the ratio between the IR and UV cutoffs that weighs how much a theory has of “classical” over “quantum”. This suggests a spacetime that emerges from an underlying world which is described by quantum building blocks. These quanta statistically conspire to appear as gravitational phenomena from a macroscopic point of view.