Homogenization of many particle systems

在这个项目中，我们计划研究通过场相互作用的大量粒子的动力学。两个典型的例子是奥斯特瓦尔德成熟，一个基本的过程在材料老化和颗粒沉降。在第一个阶段，我们严格地建立了奥斯特瓦尔德成熟中的筛选效应和粒子沉降中的临界样本量，其中可以排除粒子的碰撞。在第二阶段，我们的主要目的是了解奥斯特瓦尔德成熟过程中粒子间相关关系的发展，以及它们如何影响平均动力学。为此，我们将推导和分析几种类型的简化模型、单极子近似以及用于粒度分布两点统计的平均场模型。

In this project we plan to study the dynamics of a large number of particles which interact through a field. The two model examples are Ostwald Ripening, a fundamental process in the aging of materials and particle sedimentation. In the first period we have rigorously established the screening effect in Ostwald Ripening and the critical sample size in particle sedimentation where collisions of particles can be excluded. Our main aim in the second period will be to understand the development of correlations between particles in Ostwald Ripening and how they influence the average dynamics. For that we will derive and analyse several type of reduced models, monopole approximations as well as mean-field models for the two-point statistics of the particel size distribution.