活跃人群
Active Crowds
摘要：
本章重点介绍拥挤环境中的活动粒子（或代理）的数学建模。我们讨论了文献中发现的几个微观模型和各自的宏观偏微分方程的粒子密度的推导。宏观模型具有共同的特征，如交叉扩散或简并迁移率。然后，我们将宏观模型的多样性转化为统一的结构，并找出潜在的相似性和差异。此外，我们还讨论了边界效应及其在生命科学和社会科学中的可能应用。这是通过数值模拟来补充的，这些模拟突出了不同边界条件的影响。
英文摘要：
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential equations for the particle density. The macroscopic models share common features, such as cross diffusion or degenerate mobilities. We then take the diversity of macroscopic models to a uniform structure and work out potential similarities and differences. Moreover, we discuss boundary effects and possible applications in life and social sciences. This is complemented by numerical simulations that highlight the effects of different boundary conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
