Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801-3080, USA.
Phys Rev E. 2019 Oct;100(4-1):040602. doi: 10.1103/PhysRevE.100.040602.
A large class of mesoscopic or macroscopic flocking theories are coarse-grained from microscopic models that feature binary interactions as the chief aligning mechanism. However, while such theories seemingly predict the existence of polar order with just binary interactions, actomyosin motility assay experiments show that binary interactions are insufficient to obtain polar order, especially at high densities. To resolve this paradox, here we introduce a solvable one-dimensional flocking model and derive its stochastic hydrodynamics. We show that two-body interactions are insufficient to generate polar order unless the noise is non-Gaussian. We show that noisy three-body interactions in the microscopic theory allow us to capture all essential dynamical features of the flocking transition, in systems that achieve orientational order above a critical density.
一大类介观或宏观 flock 理论是从小尺度模型粗粒化得到的，这些模型的主要对齐机制是二元相互作用。然而，尽管这些理论似乎仅通过二元相互作用就预测了极序的存在，但肌球蛋白运动检测实验表明，二元相互作用不足以获得极序，尤其是在高密度下。为了解决这一矛盾，我们引入了一个可解的一维 flock 模型，并推导出其随机流体动力学。我们表明，除非噪声是非高斯的，否则二体相互作用不足以产生极序。我们表明，微观理论中的噪声三体相互作用使我们能够捕捉到 flock 转变的所有基本动力学特征，在这些系统中，在临界密度以上实现了方向有序。
