Mathematical Sciences: Variational Methods for Phase Transitions in Crystalline Structure

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The general objective of this project is to study variational problems associated with phase transitions in the context of continuum theory, using as theoretical tools Continuum Mechanics (specifically Thermoelasticity) and the Calculus of Variations. The topics under consideration include: the study of macroscopic properties which depend on the particular microstructure of a configuration; determination of symmetry invariances and constitutive relations appropriate to interfacial energies for solid crystals; the study of minimization problems for the total energy functional obtained by the inclusion of surface terms; to give a detailed description of the phase boundaries observed in twinned crystals and to protect the relative proportions of different phases; the study of surfaces endowed with an intrinsic thermodynamic structure and thermostatics of phase equilibria; the effect of light polarization; dynamical aspects, such as the determination of the speed of propagation of the interfacial surface at the critical temperature and the heat generated during this propagation.