Mathematical Sciences: Variational Methods for Phase Transitions in Crystalline Structure

本项目的总体目标是研究连续介质理论背景下与相变相关的变分问题，使用连续介质力学（特别是热弹性）和变分法作为理论工具。正在考虑的主题包括：宏观性质的研究，这取决于一个构型的特定微观结构；固体晶体界面能对称不变性和本构关系的确定包含表面项的总能量泛函的最小化问题研究详细描述在孪晶中观察到的相界，并保护不同相的相对比例；具有内在热力学结构的表面及其相平衡的热静态研究光偏振效应；动力学方面，如确定界面表面在临界温度下的传播速度和传播过程中产生的热量。

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.