Multiple scales in phase separating systems with elastic misfit

本项目的目的是通过建立、分析和关联与弹性失配过程中固有的不同长度尺度相对应的模型来研究弹性失配合金的形态变化。计划分析在不同长度尺度上形成的这些现象的模型之间的关系。在这里，我们将特别研究弹性修正的Cahn-Hilliard模型和尖锐界面模型之间的关系。此外，我们希望了解颗粒演化的统计行为，例如将研究平均颗粒尺寸的增长率。不同的长度尺度和弹性相互作用对固体薄膜的生长也很重要。问题将是：(In)薄膜表面的稳定性、粗化和数值模拟。此外，我们还将考虑这些具有弹性效应的相分离问题中宏观和介观模型的有效数值方法。适当的时间步长格式和空间上的自适应多层有限元使得具有适度多粒子的Cahn-Hilliard模型具有足够的分辨率。对于具有非常多粒子的系统，我们将研究带有粒子形状和相互作用类型限制的尖锐界面模型的多极子类型方法。对生长速率和颗粒环境的结构进行了统计评估。

It is the aim of this project to study morphological changes in alloys with elastic misfit by developing, analyzing and relating models corresponding to different length scales inherent in this process. It is planed to analyze the relationship of models for these phenomena that are formulated on different length scales. Here, in particular the relation between the elastically modified Cahn-Hilliard model and sharp interface models will be studied. Furthermore, we want to understand the statistical behaviour of the evolution of particles, e.g. growth rates for the average particle size will be studied. Different length scales and elastic interactions are also important in the growth of thin solid films. Issues will be: (in)stability of the film surface, coarsening and numerical simulations. Furthermore, we will consider efficient numerical methods for the macroscopic as well as the mesoscopic model in these phase separation problems with elastic effects. Appropriate time step schemes and adaptive multilevel finite elements in space enable the adequate resolution of Cahn-Hilliard models with moderately many particles. Multipole type methods for the sharp interface model, with build in restrictions on the particle shape and interaction type will be studied for systems with very many particles. Statistical evaluations of growth rates and the structure of the particle environment are indended.