发表机构
Dalhousie University; University of British Columbia（达尔豪斯大学; 不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究基于随机智能体模型推导连续极限的四阶非线性偏微分方程，解析求解团簇密度与群速度，并验证行波团簇的存在及速度与离散模型高度一致。
AI 中文摘要
我们模拟了在趋化性或流体输运存在的情况下，细胞聚集形成团簇的定向运动。从Galante & Levy (2013)、Chavy-Waddy & Kolokolnikov (2016)的基于随机智能体模型（ABM）出发，我们考虑了两种模型变体：（I）个体的定向运动，或（II）个体在单一方向上的隐式偏向。在两种情况下，我们推导出四阶非线性偏微分方程（PDE），作为Chavy-Waddy & Kolokolnikov (2016)模型的连续极限的推广。一个精确的解析解随后描述了团簇密度分布以及群速度，我们识别了行波团簇存在的参数区间。在两种模型中，离散模型与PDE的精确解之间观察到极好的一致性，包括行波团簇的存在性及其速度。
英文摘要
We model directed motion of cells that aggregate into a cluster in the presence of chemotaxis or fluid transport. Starting from a stochastic agent-based model (ABM) of Galante \& Levy (2013), Chavy-Waddy \& Kolokolnikov (2016), we consider two model variants, with (I) directed motion of individuals, or (II) implicit individual bias in one direction. In both cases, we derive fourth order nonlinear PDEs representing the continuum limits of the models as a generalization of Chavy-Waddy \& Kolokolnikov (2016). An exact analytic solution then describes cluster density profile as well as the group velocity, and we identify the regimes where the travelling cluster exists. Excellent agreement is observed between the discrete models and the exact solutions of the PDEs in both models, including the existence and speed of the travelling cluster.
