AI 中文总结
该研究从微观随机模型出发构建增殖活性物质的连续介质理论，以主动布朗虫模型为例验证，揭示了活性与种群动力学相互作用驱动集体运动的机制。
AI 中文摘要
我们从经历出生、死亡和非局域竞争的自驱动粒子的微观随机模型出发，构建了增殖活性物质的连续介质理论。从主方程开始，我们推导了粒子密度和极化场的平均场演化方程，并通过冯·米塞斯假设闭合所得的层级，提供了适用于广泛类别的增殖活性系统的耦合流体动力学描述。作为应用，我们研究了最近提出的主动布朗虫（Active Brownian Bug）模型，该模型中即使没有明确的对齐相互作用也会出现群集形式。线性稳定性分析预测了图灵和霍普夫不稳定性，其分析阈值与数值模拟结果一致。该连续介质模型再现了底层粒子系统的主要动力学状态，包括均匀态、稳态周期团簇和相干传播的群集态。这些结果为增殖活性物质建立了通用的连续介质框架，并为由活性与种群动力学相互作用驱动的集体运动提供了物理解释。
英文摘要
We develop a continuum theory for proliferating active matter starting from a microscopic stochastic model of self-propelled particles undergoing birth, death, and nonlocal competition. Beginning from the master equation, we derive mean-field evolution equations for the particle density and polarization fields and close the resulting hierarchy through a von Mises ansatz, providing a coupled hydrodynamic description applicable to a broad class of proliferating active systems. As an application, we study the recently introduced Active Brownian Bug model, in which the form of flocking emerges despite the absence of explicit alignment interactions. Linear stability analysis predicts both Turing and Hopf instabilities, whose analytical thresholds agree with numerical simulations. The continuum model reproduces the principal dynamical regimes of the underlying particle system, including homogeneous states, stationary periodic clusters, and coherently propagating flocking states. These results establish a general continuum framework for proliferating active matter and provide a physical interpretation of collective motion driven by the interplay between activity and population dynamics.
Comments22 pages, 10 figures, 7 videos
