A 300 million year-long history. The metamorphic evolution of the Northern Apennine Variscan basement

The Variscan basement of Northern Apennines (Northern Italy) is a polymetamorphic portion of continental crust. This thesis investigated the metamorphic history of this basement occurring in the Cerreto Pass, in the Pontremoli well, and in the Pisani Mountains. The study comprised fieldwork, petrography and microstructural analysis, determination of the bulk rock and mineral composition, thermodynamic modelling, conventional geothermobarometry, monazite chemical dating and Ar/Ar dating of muscovite. The reconstructed metamorphic evolution of the selected samples allowed to define a long-lasting metamorphic history straddling the Variscan and Alpine orogenesis. Some general petrological issues generally found in low- to medium-grade metapelites were also tackled: (i) With middle-grade micaschist it is possible to reconstruct a complete P-T-D path by combining microstructural analysis and thermodynamic modelling. Prekinematic white mica may preserve Mg-rich cores related to the pre-peak stage. Mn-poor garnet rim records the peak metamorphism. Na-rich mylonitic white mica, the XFe of chlorite and the late paragenesis may constrain the retrograde stage. (ii) Metapelites may contain coronitic microstructures of apatite + Th-silicate, allanite and epidote around unstable monazite grains. Chemistry and microstructure of Th-rich monazite relics surrounded by this coronitic microstructure may suggest that monazite mineral was inherited and underwent partial dissolution and fluid-aided replacement by REE-accessory minerals at 500-600°C and 5-7 kbar. (iii) Fish-shaped white mica is not always a (prekinematic) mica-fish. Observed at high-magnification BSE images it may consist of several white mica formed during a mylonitic stage. Hence, the asymmetric foliation boudin is a suitable microstructure to obtain geochronological information about the shearing stage. (iv) Thermodynamic modelling of a hematite-rich metasedimentary rock fails to reproduce the observed mineral compositions when the bulk Fe2O3 is neglected or determined through titration. The mismatch between observed and computed mineral compositions and assemblage is resolved by tuning the effective ferric iron content by P-XFe2O3 diagrams.

An equilibrium approach to modelling social interaction

The aim of this work is to put forward a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. After showing the formal equivalence linking econometric multinomial logit models to equilibrium statical mechanics, a multi- population generalization of the Curie-Weiss model for ferromagnets is considered as a starting point in developing a model capable of describing sudden shifts in aggregate human behaviour. Existence of the thermodynamic limit for the model is shown by an asymptotic sub-additivity method and factorization of correlation functions is proved almost everywhere. The exact solution for the model is provided in the thermodynamical limit by nding converging upper and lower bounds for the system's pressure, and the solution is used to prove an analytic result regarding the number of possible equilibrium states of a two-population system. The work stresses the importance of linking regimes predicted by the model to real phenomena, and to this end it proposes two possible procedures to estimate the model's parameters starting from micro-level data. These are applied to three case studies based on census type data: though these studies are found to be ultimately inconclusive on an empirical level, considerations are drawn that encourage further refinements of the chosen modelling approach, to be considered in future work.