保持对齐运动的速度和距离
Keeping speed and distance for aligned motion
摘要：
自主智能体的凝聚集体运动（群集、群集）在自然和人为环境中被广泛观察和利用，因此，描述它的极小模型是必不可少的。在一个具有连续空间和时间的模型中，我们发现，如果两个粒子以大角度对称地到达一个平面，那么（i）径向排斥和（ii）朝向固定的优选速度的线性自推进足以使它们以较小的角度离开。对于这种局部动量增益，不需要明确的速度对齐，也不需要粘附/吸引，粒子的非弹性或各向异性，或非线性阻力。当许多粒子遵守这些微观运动规则时，我们发现它们在空间上被限制在一个具有周期性边界的正方形中（这是一种间接的吸引形式），从而导致了稳定的宏观有序。在恒定系统尺寸下改变颗粒密度和在恒定颗粒密度下改变系统尺寸后，我们预测在无限系统尺寸（或密度）极限下，磁滞回线消失，过渡变得连续。我们注意到，动物、人类、无人机等倾向于异步移动，并且通常对运动的反应比位置更敏感。因此，对于它们，基于速度的连续模型可以提供比基于坐标的模型更高的精度。该模型的一个额外的特点和现实的特点是，收敛到有序状态是最快的有限密度，这是在对比模型应用（不连续）明确的速度对齐和离散时间。总之，我们发现，所研究的模型可以提供一个最小的描述植绒。
英文摘要：
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space and time we find that if two particles arrive symmetrically in a plane at a large angle, then (i) radial repulsion and (ii) linear self-propelling toward a fixed preferred speed are sufficient for them to depart at a smaller angle. For this local gain of momentum explicit velocity alignment is not necessary, nor are adhesion/attraction, inelasticity or anisotropy of the particles, or nonlinear drag. With many particles obeying these microscopic rules of motion we find that their spatial confinement to a square with periodic boundaries (which is an indirect form of attraction) leads to stable macroscopic ordering. After varying the density of particles at constant system size and varying the size of the system with constant particle density we predict that in the infinite system size (or density) limit the hysteresis loop disappears and the transition becomes continuous. We note that animals, humans, drones, etc. tend to move asynchronously and are often more responsive to motion than positions. Thus, for them velocity-based continuous models can provide higher precision than coordinate-based models. An additional characteristic and realistic feature of the model is that convergence to the ordered state is fastest at a finite density, which is in contrast to models applying (discontinuous) explicit velocity alignments and discretized time. In summary, we find that the investigated model can provide a minimal description of flocking.
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。
