标题： 蜂群运动动力学中的临界相变可以使用二维细胞自动机进行建模 显示英文标题

标题： A critical phase transition in bee movement dynamics can be modeled using a 2D cellular automata

摘要： 许多动物物种（包括昆虫）的集体行为表现出无标度行为，这表明了临界（二阶）相变的特征。 先前的研究在蜜蜂的行为中发现了这种现象，最显著的是空间和时间上的长程相关性。 此外，已经证明蜂巢中的蜜蜂活动表现出阻塞过程的特征。 我们接着提出一个离散模型，该模型忠实地再现了数据中的一些关键特征——如关联长度的发散和阻塞簇的无标度分布。 对于真实数据和模型，都展示了关联长度对控制参数——密度的依赖关系。 最后，我们简要讨论了该模型提供的见解对理解昆虫集体行为的贡献。 显示英文摘要

摘要： The collective behavior of numerous animal species, including insects, exhibits scale-free behavior indicative of the critical (second-order) phase transition. Previous research uncovered such phenomena in the behavior of honeybees, most notably the long-range correlations in space and time. Furthermore, it was demonstrated that the bee activity in the hive manifests the hallmarks of the jamming process. We follow up by presenting a discrete model of the system that faithfully replicates some of the key features found in the data - such as the divergence of correlation length and scale-free distribution of jammed clusters. The dependence of the correlation length on the control parameter - density is demonstrated for both the real data and the model. We conclude with a brief discussion on the contribution of the insights provided by the model to our understanding of the insects' collective behavior.