Mathematical Sciences: Elastodynamic Modelling of Stress Driven Phase Boundary Motion

相干相变导致具有特征的精细尺度结构。基于弹性能最小化的分析方法已经取得了相当大的成功，但它们也有明显的局限性。数值方法对于探索局部最小值，理解各种选择机制的作用，以及最重要的是建模动力学是绝对必要的。我们将继续发展一种基于非凸弹性能的新方法。弹性动力学和扩散驱动动力学都将被考虑。这项工作将利用串行和并行体系结构上的大规模计算。

Coherent phase transitions lead to characteristic fine scale structures. Analytic methods based on the minimization of elastic energy have had considerable success, but they also have notable limitations. Numerical methods are an absolute necessity for exploring local minimizers, for understanding the role of various selection mechanisms, and above all for modelling dynamics. We will continue the development of a new approach based on nonconvex elastic energies. Both elastodynamics and diffusion-driven dynamics will be considered. This work will make use of large-scale computation on both serial and parallel architectures.