GRK 1128: Analysis, Numerics, and Optimisation of Multiphase Problems

在不同的科学领域中出现了多阶段的系统。它们的数学建模、分析、数值处理和优化需要新的方法来处理例如非局部效应或不同的尺度。研究训练组的目的是加强和传播对相变过程中的形态变化、晶体中颗粒结构的粗化、金属薄膜的外延生长、混合流体的多相平衡、空气动力学中的亚音速/超音速飞行转变和其他多相现象的理解。研究训练组的重点是开发和教授数学技术和算法，以处理多相问题中出现的非线性偏微分方程组和不等式。尽管博士生可能毕业于工程或科学专业，但他们被期望在应用数学方面有很强的背景。该计划吸引了大量的国际学者来柏林，因此以英语进行。洪堡大学数学系在偏微分方程式(PDE)的基础数学方面保持着深厚的传统。最近任命的三名主席在应用分析、偏微分方程的数值计算和非线性优化等关键领域补充了这一优势。来自柏林魏尔斯特拉斯应用分析和随机研究所(WIAS)的几位兼职教授和其他一些资深科学家完成了对多阶段问题的研究专长。此外，还与柏林地区的其他大学、研究实验室和科学机构开展合作。

Systems with multiple phases arise in various scientific fields. Their mathematical modelling, analysis, numerical treatment, and optimisation requires novel approaches to deal for example with nonlocal effects or varying scales. The aim of the Research Training Group is to enhance and to disseminate the understanding of morphological changes during phase transformations, coarsening of grain structures in crystals, epitactial growth of thin metallic films, multiphase equilibria of mixed fluids, subsonic/supersonic flight transitions in aerodynamics, and other multiphase phenomena.The Research Training Group focuses on the development and teaching of mathematical techniques and algorithms for the treatment of nonlinear partial differential equations and inequalities arising in multiple phase problems. Doctoral candidates are expected to have a strong background in applied mathematics though they may have graduated in engineering or sciences. The programme is attracting a significant number of international fellows to Berlin and is therefore conducted in English.The department of mathematics of Humboldt University maintains a strong tradition in the fundamental mathematics of partial differential equations (PDE). The recent appointment of three chairs has complemented this strength in the key areas of applied analysis, numerics of PDEs, and nonlinear optimisation. Several adjunct professors and some other senior scientists from Weierstrass Institute for Applied Analysis and Stochastics (WIAS) in Berlin complete the research expertise on multiphase problems. There is also cooperation with other universities and research laboratories and scientific institutions in the Berlin area.