论文标题
在狭窄的Vicsek羊群模型中缩放无混乱的混乱
Scale free chaos in the confined Vicsek flocking model
论文作者
论文摘要
Vicsek模型涵盖了主动干物质的范式。通过群体中昆虫的集体行为的促进，我们研究了三维，和谐限制的维克斯克模型中的有限尺寸效应和关键性。我们发现了存在适当的噪声和较小限制强度的相变。在限制与噪声的临界线上，群体处于无尺度的混乱状态，其特征是相关时间最小，相关长度与群体大小和拓扑数据分析成正比。临界线将分散的单个簇与受限制的多簇群体分开。无尺度的混沌群占据了一个紧凑的空间区域，并包括一个可识别的“凝结”核和离开并进入它的颗粒。敏感性，相关长度，动态相关函数和最大的Lyapunov指数遵守功率定律。临界线和接近它的狭窄临界区域同时移动到无限多个颗粒的零限制强度。在第一个混乱窗口的结尾结束时，另一个相过渡到无限密度的有限大小的簇，可能称为黑洞植入蜂窝。
The Vicsek model encompasses the paradigm of active dry matter. Motivated by collective behavior of insects in swarms, we have studied finite size effects and criticality in the three dimensional, harmonically confined Vicsek model. We have discovered a phase transition that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Scale-free chaotic swarms occupy a compact region of space and comprise a recognizable `condensed' nucleus and particles leaving and entering it. Susceptibility, correlation length, dynamic correlation function and largest Lyapunov exponent obey power laws. The critical line and a narrow criticality region close to it move simultaneously to zero confinement strength for infinitely many particles. At the end of the first chaotic window of confinement, there is another phase transition to infinitely dense clusters of finite size that may be termed flocking black holes.
