严格度量自由群的密度调节
Density regulation in strictly metric-free swarms
摘要：
现在有实验证据表明，最近邻相互作用的鸟群是度量自由，即它们没有特征的相互作用长度尺度。然而，涉及拓扑分配的邻居之间的相互作用的模型在空间扩展下自然不变，支持密度连续降低至零，除非引入额外的内聚相互作用或人为控制密度，例如通过有限的系统大小。我们提出了一个解决方案，涉及到一个度量的自由运动的偏见，这些个人的拓扑确定为边缘的群体。该模型只有两个主要的控制参数，一个控制随机噪声的相对强度的程度的共同对齐和另一个控制的程度的运动偏置的边缘上，相对于共同对齐的趋势。我们发现一个新的幂律缩放的真实空间密度与个人的数量N以及一个熟悉的有序到无序的过渡。
英文摘要：
There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are assigned topologically are naturally invariant under spatial expansion, supporting a continuous reduction in density towards zero, unless additional cohesive interactions are introduced or the density is artificially controlled, e.g. via a finite system size. We propose a solution that involves a metric-free motional bias on those individuals that are topologically identified to be on an edge of the swarm. This model has only two primary control parameters, one controlling the relative strength of stochastic noise to the degree of co-alignment and another controlling the degree of the motional bias for those on the edge, relative to the tendency to co-align. We find a novel power-law scaling of the real-space density with the number of individuals N as well as a familiar order-to-disorder transition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
