论文标题
稀释硬球气体动力学的簇扩展
Cluster expansion for a dilute hard sphere gas dynamics
论文作者
论文摘要
在[7]中，已经开发了一种群集扩展方法来研究玻尔兹曼方程周围硬球动力学的波动。该方法对经验度量的指数力矩提供了精确的控制，从中可以推断出波动的玻尔兹曼方程和大偏差估计值。 [7]中的群集扩展是在BBGKY层次结构级别实现的，该层次结构是研究确定性动力学的标准工具[11]。在本文中，我们介绍了一种替代方法，其中将群集扩展直接应用于粒子系统的实际轨迹上。这为在低密度极限中对硬球动力学的研究提供了新的视角，从而可以恢复[7]中获得的结果，并描述粒子轨迹的实际聚类。
In [7], a cluster expansion method has been developed to study the fluctuations of the hard sphere dynamics around the Boltzmann equation. This method provides a precise control on the exponential moments of the empirical measure, from which the fluctuating Boltzmann equation and large deviation estimates have been deduced. The cluster expansion in [7] was implemented at the level of the BBGKY hierarchy, which is a standard tool to investigate the deterministic dynamics [11]. In this paper, we introduce an alternative approach, in which the cluster expansion is applied directly on real trajectories of the particle system. This offers a fresh perspective on the study of the hard sphere dynamics in the low density limit, allowing to recover the results obtained in [7], and also to describe the actual clustering of particle trajectories.
