Homogenization of many particle systems

许多粒子系统的均质化

• 批准号: 5275222
• 负责人: Professorin Dr. Barbara Niethammer
• 金额: --
• 依托单位: Max-Planck-Institut für Mathematik in den Naturwissenschaften (MIS)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2000
• 资助国家: 德国
• 起止时间: 1999-12-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5275222?language=en
• 关键词: Homogenization; many; particle; systems

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.

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。两个模型的例子是奥斯特瓦尔德熟化，一个基本的过程中的材料老化和颗粒沉降。在第一阶段，我们严格地建立了奥斯特瓦尔德熟化中的筛选效应和颗粒沉降中的临界样品尺寸，其中可以排除颗粒的碰撞。我们在第二阶段的主要目标是了解奥斯特瓦尔德熟化过程中粒子之间的相关性的发展，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，近似，以及平均场模型的两点统计的颗粒尺寸分布。