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.

Characterization Of Single Use Reactor Used For The Manufacturing Of Formulated Products Within The Pharmaceutical Industry

Mixing is a fundamental unit operation in the pharmaceutical industry to ensure consistent product quality across different batches. It is usually carried out in mechanically stirred tanks, with a large variety of designs according to the process requirements. A key aspect of pharmaceutical manufacturing is the extensive and meticulous cleaning of the vessels between runs to prevent the risk of contamination. Single-use reactors represent an increasing trend in the industry since they do not require cleaning and sterilization, reducing the need for utilities such as steam to sterilize equipment and the time between production batches. In contrast to traditional stainless steel vessels, single-use reactors consist of a plastic bag used as a vessel and disposed of after use. This thesis aims to characterize the fluid dynamics features and the mixing performance of a commercially available single-use reactor. The characterization employs a combination of various experimental techniques. The analysis starts with the visual observation of the liquid behavior inside the vessel, focusing on the vortex shape evolution at different impeller speeds. The power consumption is then measured using a torque meter to quantify the power number. Particle Image Velocimetry (PIV) is employed to investigate local fluid dynamics properties such as mean flow field and mean and rms velocity profiles. The same experimental setup of PIV is exploited for another optical measurement technique, the Planar Laser-Induced Fluorescence (PLIF). The PLIF measurements complete the characterization of the reactor with the qualitative visualization of the turbulent flow and the quantitative assessment of the system performance through the mixing time. The results confirm good mixing performances for the single-use reactor over the investigated impeller speeds and reveal that the filling volume plays a significant role in the fluid dynamics of the system.