Homogenization of many particle systems

在这个项目中，我们计划研究大量粒子通过场相互作用的动力学。这两个模型的例子是Ostwald熟化，这是材料老化和颗粒沉淀的基本过程。在第一阶段，我们严格地建立了Ostwald熟化中的屏蔽效应和颗粒沉降中可以排除颗粒碰撞的临界样本量。我们在第二阶段的主要目标将是了解Ostwald成熟过程中粒子之间的关联的发展，以及它们如何影响平均动力学。为此，我们将推导和分析粒子尺寸分布的两点统计的几种简化模型、单极近似以及平均场模型。

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.