Mathematical Modelling, Simulation and Statistical Analysis of Crystallization processes

In this thesis a specific birth and growth process is analyzed; namely a mass crystallization process, where growth is driven by supersaturation only. Based on purely physical grounds, a multifronts moving boundary model is derived and a non-linear condition for the concentration arises on the boundary. The deterministic growth model is completed by considering stochastic nucleations in space and time. A new formulation of the deterministic process based on the Schwartz distributions is proposed. This formulation is well adapted for a numerical solution in a multi-fronts framework and a fixed grid, since it gives a global description of the evolution of all the crystals in a single equation. Simulations are performed for different sets of values of the physical parameters, also for extreme cases where real experiments would be unfeasible. The coupling of the growth dynamics with the evolution of the underlying field of the concentration of matter finally causes the stochastic geometry of the crystals. By collecting observations from independent simulations, the relationship between the physical parameters of the model and the final morphology of the system is analyzed. Finally, the inverse problem of estimation of the initial concentration, given a target final distribution of sizes, is solved by applying functional data analysis techniques. The rigorous mathematical description of the crystallization phenomena and the morphological analysis give the possibility to experimentalists to design optimal experiments and to foresee the behaviour of the system.