从基于智能体的动力学到水母群集的动力学理论
From agent-based dynamics to a kinetic theory of jellyfish swarms
AI总结：
本文从水母运动的主动粒子模型推导出连续动力学理论，通过福克-普朗克框架和流体动力学闭合，为预测大规模水母群集形成与演化提供了理论基础。
AI中文摘要：
在海上观察到的大规模水母群集可延伸数十公里，包含数百万个体，然而控制其形成和大尺度动力学的机制仍知之甚少。基于智能体的模型提供了一个框架，用于根据水母对洋流和环境线索的响应来描述这种动力学，但当扩展到与海洋环流相关的大种群和空间尺度时，计算上变得不可行。在此，我们从水母运动的主动粒子模型推导出一个连续的动力学理论。所得的福克-普朗克框架包含了预定流场的输运、随机重定向、直接相互作用和刺激转向，允许通过耦合场来表示化学信号。我们进一步利用快速取向动力学与慢速空间动力学之间的分离，为大群集推导出一个流体动力学闭合，得到一个适用于海洋流模型实现的简化密度方程。该框架提供了一条从个体行为机制到水母种群连续描述的途径，并为利用观测和原位测量约束模型参数奠定了基础。该方法为未来在真实海洋流中大规模水母群集形成和演化的数值预测提供了理论基础。
英文摘要：
Massive jellyfish swarms observed at sea can extend over tens of kilometres and contain millions of individuals, yet the mechanisms governing their formation and large-scale dynamics remain poorly understood. Agent-based models provide a framework for describing this dynamics based on jellyfish responses to ocean currents and environmental cues, but become computationally prohibitive when extended to large populations and spatial scales relevant to ocean circulation. Here we derive a continuous kinetic theory from an active-particle model of jellyfish motion. The resulting Fokker-Planck framework incorporates transport by prescribed currents, stochastic reorientation, direct interactions and stimulated steering, allowing chemical signalling to be represented through a coupled field. We further derive a hydrodynamic closure for large swarms by exploiting the separation between fast orientational and slow spatial dynamics, yielding a reduced density equation suitable for implementation in ocean-current models. This framework provides a route from individual behavioural mechanisms to continuum descriptions of jellyfish populations and establishes a basis for constraining model parameters using observations and in-situ measurements. This approach offers a theoretical foundation for future numerical prediction of large jellyfish swarm formation and evolution in realistic ocean flows.
