Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Avenida Universidad s/n, Colonia Chamilpa, Código Postal, 62210, Cuernavaca, Morelos, Mexico.
Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Ciudad de México, Mexico.
Sci Rep. 2018 Oct 26;8(1):15872. doi: 10.1038/s41598-018-34208-x.
Since the pioneering work by Vicsek and his collaborators on the motion of self-propelled particles, most of the subsequent studies have focused on the onset of ordered states through a phase transition driven by particle density and noise. Usually, the particles in these systems are placed within periodic boundary conditions and interact via short-range velocity alignment forces. However, when the periodic boundaries are eliminated, letting the particles move in open space, the system is not able to organize into a coherently moving group since even small amounts of noise cause the flock to break apart. While the phase transition has been thoroughly studied, the conditions to keep the flock cohesive in open space are still poorly understood. Here we extend the Vicsek model of collective motion by introducing long-range alignment interactions between the particles. We show that just a small number of these interactions is enough for the system to build up long lasting ordered states of collective motion in open space and in the presence of noise. This finding was verified for other models in addition to the Vicsek one, suggesting its generality and revealing the importance that long-range interactions can have for the cohesion of the flock.
自 Vicsek 及其合作者对自推进粒子的运动进行开创性研究以来，大多数后续研究都集中在通过粒子密度和噪声驱动的相变来研究有序状态的出现。通常，这些系统中的粒子被放置在周期性边界条件下，并通过短程速度对准力相互作用。然而，当消除周期性边界条件，让粒子在开放空间中移动时，由于即使少量的噪声也会导致鸟群解体，系统无法组织成一个协调一致的移动群体。虽然已经对相变进行了彻底的研究，但在开放空间中保持鸟群凝聚力的条件仍知之甚少。在这里，我们通过在粒子之间引入远程对齐相互作用来扩展 Vicsek 集体运动模型。我们表明，只需少量这些相互作用就足以使系统在开放空间中并在噪声存在的情况下建立持久的集体运动有序状态。这一发现除了 Vicsek 模型之外，还在其他模型中得到了验证，表明其普遍性，并揭示了远程相互作用对鸟群凝聚力的重要性。
