Mathematical Sciences: Models for Phase Transitions

该项目的总体目标是了解和预测经过各种热或机械处理的晶体的表面结构和几何形状。首席研究员也对分析缺陷晶体的行为感兴趣。这些问题集中在材料科学家紧张工作的领域，但它们脱离了经典数学理论的框架。因此，实现这些目标不仅对工业和技术很重要，而且还有助于数学的进步，因为它需要操作最近开发的数学工具，也许还需要引入新的数学工具。

The general objective of this project is to understand and to predict the surface structures and geometries of crystals which have been subjected to various kinds of thermal or mechanical treatments. The principal investigator is also interested in analyzing the behavior of defective crystals. These problems concentrate on areas that are the subject of intense work of material scientists but they escape the framework of classical mathematical theories. Therefore, accomplishing these goals is not only important for the industry and technology but it also contributes to the advance of mathematics, since it requires manipulation of very recently developed mathematical tools and maybe the introduction of new ones.