论文标题
群体制造中多机构系统的Fokker-Planck建模：渐近分析和数值结果
Fokker-Planck modeling of many-agent systems in swarm manufacturing: asymptotic analysis and numerical results
论文作者
论文摘要
在本文中，我们研究了一种新型的Fokker-Planck型模型，该模型旨在通过表征大量代理的动力学来模仿制造过程。特别是，我们描述了一个与目标域相互作用的多机构系统，使每个代理/粒子都被目标域的质量中心吸引，目的是均匀覆盖该区域。为此，我们首先引入了一个带有不连续通量的平均场模型，其较大的时间行为使得稳态在全球连续且在域的连接部分上是均匀的。我们证明，一个扩散系数可以保证给定的质量部分进入目标域，并且它是独一无二的。此外，通过重新制定涉及非稳定扩散函数的初始问题，提供了1D中平衡的收敛。通过最近引入的fokker-Planck方程的结构保存方法来探索2D的扩展。
In this paper we study a novel Fokker-Planck-type model that is designed to mimic manufacturing processes through the dynamics characterizing a large set of agents. In particular, we describe a many-agent system interacting with a target domain in such a way that each agent/particle is attracted by the center of mass of the target domain with the aim to uniformly cover this zone. To this end, we first introduce a mean-field model with discontinuous flux whose large time behavior is such that the steady state is globally continuous and uniform over a connected portion of the domain. We prove that a diffusion coefficient that guarantees that a given portion of mass enters in the target domain exists and that it is unique. Furthermore, convergence to equilibrium in 1D is provided through a reformulation of the initial problem involving a nonconstant diffusion function. The extension to 2D is explored numerically by means of recently introduced structure preserving methods for Fokker-Planck equations.
