AI 中文总结
研究大量刚性球浸没粘性流体的运动问题，提出基于簇概念的新方法，可提高小半径球数量临界值，还能使球在特定极限下随流体流动，即便有引力作用。
AI 中文摘要
我们针对大量浸没在粘性流体中的刚体运动问题开发了一种新方法。主要思路是簇的概念，即一组单个刚性物体，它们以某种方式分组甚至连接，使得它们对系统整体运动的集体影响类似于单个物体。新方法的应用包括：一是提高小半径球数量的临界值，使其云团对由不可压缩纳维 - 斯托克斯方程表示的极限系统无影响；二是即使施加引力，在半径趋于零且数量增加的渐近极限中，球也会跟随流体流动。
英文摘要
We develop a new approach to the problem of the motion of a large number of rigid bodies immersed in a viscous fluid. The leading idea is the concept of cluster - a collection of individual rigid objects that may be grouped or even connected in such a way that their collective impact on the bulk motion of the system is similar to that of a single body. The applications of the new approach include: 1. Improving the critical value of the number of balls of small radius such that their cloud has no impact on the limit system represented by the incompressible Navier--Stokes equations. 2. The balls follow the fluid flow in the asymptotic limit of vanishing radius and increasing number even if a gravitational force is imposed.
