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Abstract：
Studies of collective motion have heretofore been dominated by a thermodynamic perspective in which the emergent \"flocked\" phases are analyzed in terms of their time-averaged orientational and spatial properties. Studies that attempt to scrutinize the dynamical processes that spontaneously drive the formation of these flocks from initially random configurations are far more rare, perhaps owing to the fact that said processes occur far from the eventual long-time steady state of the system and thus lie outside the scope of traditional statistical mechanics. For systems whose dynamics are simulated numerically, the nonstationary distribution of system configurations can be sampled at different time points, and the time evolution of the average structural properties of the system can be quantified. In this paper, we employ this strategy to characterize the spatial dynamics of the standard Vicsek flocking model using two correlation functions common to condensed matter physics. We demonstrate, for modest system sizes with 800 to 2000 agents, that the self-assembly dynamics can be characterized by three distinct and disparate time scales that we associate with the corresponding physical processes of clustering (compaction), relaxing (expansion), and mixing (rearrangement). We further show that the behavior of these correlation functions can be used to reliably distinguish between phenomenologically similar models with different underlying interactions and, in some cases, even provide a direct measurement of key model parameters.
摘要：
迄今为止，对集体运动的研究一直由热力学观点主导，在热力学观点中，根据其时间平均的方向和空间特性分析了新兴的“成群”阶段。试图仔细检查从最初的随机配置自发驱动这些羊群形成的动态过程的研究更为罕见，也许是由于上述过程的发生远离系统的最终长期稳定状态，因此超出了传统统计力学的范围。对于动力学是数值模拟的系统，系统配置的非平稳分布可以在不同的时间点进行采样，系统的平均结构特性的时间演变可以量化。在本文中,我们使用这种策略来描述标准Vicsek植绒模型的空间动力学，使用凝聚态物理学常见的两个相关函数。我们证明,对于800到2000个代理的适度系统大小，自组装动力学可以通过三个不同和不同的时间尺度来表征，我们将它们与相应的聚类物理过程（压实）相关联，放松（扩张），和混合（重排）。我们进一步表明，这些相关函数的行为可用于可靠地区分具有不同潜在相互作用的现象学相似模型，在某些情况下,甚至提供关键模型参数的直接测量。
