Economic and Environmental Optimization of Ornamental Stone Block Cutting with a 3D Algorithm

This thesis focuses on finding the optimum block cutting dimensions in terms of the environmental and economic factors by using a 3D algorithm for a limestone quarry in Foggia, Italy. The environmental concerns of quarrying operations are mainly: energy consumption, material waste, and pollution. The main economic concerns are the block recovery, the selling prices, and the production costs. Fractures adversely affect the block recovery ratio. With a fracture model, block production can be optimized. In this research, the waste volume produced by quarrying was minimised to increase the recovery ratio and ensure economic benefits. SlabCutOpt is a software developed at DICAM–University of Bologna for block cutting optimization which tests different cutting angles on the x-y-z planes to offer up alternative cutting methods. The program tests several block sizes and outputs the optimal result for each entry. By using SlabCutOpt, ten different block dimensions were analysed, the results indicated the maximum number of non-intersecting blocks for each dimension. After analysing the outputs, the block named number 1 with the dimensions ‘1mx1mx1m’ had the highest recovery ratio as 43% and the total Relative Money Value (RMV) with a value of 22829. Dimension number 1, also had the lowest waste volume, with a value of 3953.25 m3, for the total bench. For cutting the total bench volume of 6932.25m3, the diamond wire cutter had the lowest dust emission values for the block with the dimension ‘2mx2mx2m’, with a value of 24m3. When compared with the Eco-Label standards, block dimensions having surface area values lower than 15m2, were found to fit the natural resource waste criteria of the label, as the threshold required 25% of minimum recovery [1]. Due to the relativity of production costs, together with the Eco-Label threshold, the research recommends the selection of the blocks with a surface area value between 6m2 and 14m2.

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.