多群体：多尺度集体行为系统中的涌现动力学
Multi-flocks: emergent dynamics in systems with multi-scale collective behavior
摘要：
我们研究了多尺度描述的大时间集体行为的代理驱动的对齐。由此产生的多群动力学自然出现与现实的初始配置组成的多个空间尺度，这反过来又在不同的时间尺度的峰值。我们推导出一个“主方程”，它描述了一个复杂的多羊群聚集由两个成分：（一）快速内部羊群通信;（二）一个缓慢的（-呃）群间通信。后者是由宏观可观的特征放大的问题。我们扩展了目前的单群理论，证明了一系列的结果，描述率的多群集与自然依赖的通信强度。代理为基础的，动力学和流体动力学的描述被认为是，特别强调放在离散和宏观的描述。
英文摘要：
We study the multi-scale description of large-time collective behavior of agents driven by alignment. The resulting multi-flock dynamics arises naturally with realistic initial configurations consisting of multiple spatial scaling, which in turn peak at different time scales. We derive a `master-equation' which describes a complex multi-flock congregations governed by two ingredients: (i) a fast inner-flock communication; and (ii) a slow(-er) inter-flock communication. The latter is driven by macroscopic observables which feature the up-scaling of the problem. We extend the current mono-flock theory, proving a series of results which describe rates of multi-flocking with natural dependencies on communication strengths. Both agent-based, kinetic, and hydrodynamic descriptions are considered, with particular emphasis placed on the discrete and macroscopic descriptions.
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