具有取向相互作用的自驱动粒子的连续极限
Continuum limit of self-driven particles with orientation interaction
摘要：
我们认为离散Couzin-Vicsek算法（CVA），它描述了动物社会，如鱼群之间的相互作用。在这篇文章中，我们提出了一个动力学（平均场）版本的CVA模型，并提供其正式的宏观限制。最终的宏观模型包含了个体密度的守恒方程和平均速度指向矢的非守恒方程，并被证明是双曲线的。推导是基于引入一个非传统的概念的碰撞算子的碰撞不变量。
英文摘要：
We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator.
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