Physics Department, American University of Beirut, Beirut, Lebanon.
Phys Rev E. 2016 Mar;93(3):032602. doi: 10.1103/PhysRevE.93.032602. Epub 2016 Mar 3.
We investigate a class of agent-based models of self-propelled particles (SPP) that interact according to a Morse potential in the presence of friction, a class which was able to reproduce many of the intriguing patterns of collective motion observed in nature. Specifically, we compare two closely related SPP models in the literature that differ by their prescription of particle drag and self-propulsion. Writing both models in terms of nondimensional parameters allows us to show that the dynamics in the highly viscous regime is independent of the precise forms of drag and propulsion. In contrast to what is indicated in the literature both models yield the same low-energy self-organized states: the coherent flock and the rigid rotation states which are highly ordered in both the coordinate and the velocity spaces and a velocity-disordered droplet state where particles are confined to rings which pass through the lattice points of the underlying Lagrange configuration. In contrast to the first two states which are stable, the third state is found to be a long-lived transient. In the regime studied, relaxing to one of the ordered steady states is inevitable, but how and when the transition occurs and what is the probability of ending in one state rather than the other are functions of the model parameters. Two types of transitions are characterized and first passage times are computed. Eventually, the evolution of the order parameter is explored in the framework of a Langevin-type equation, and the possible metastability of the random droplet state is discussed.
我们研究了一类基于主体的自推进粒子 (SPP) 模型，这些模型在存在摩擦的情况下根据 Morse 势相互作用，这类模型能够再现自然界中观察到的许多有趣的集体运动模式。具体来说，我们比较了文献中两种密切相关的 SPP 模型，它们在粒子阻力和自推进的规定上有所不同。将两个模型都用无量纲参数表示，可以证明在高粘性 regime 中动力学与阻力和推进的精确形式无关。与文献中所指出的相反，这两个模型都产生了相同的低能量自组织状态：相干 flock 和刚性旋转状态，在坐标和速度空间中都高度有序，以及速度无序的液滴状态，其中粒子被限制在通过基础 Lagrange 配置的晶格点的环中。与前两种稳定状态不同，第三种状态是一种长寿命的瞬态。在所研究的范围内，不可避免地会回到一个有序的稳定状态，但如何以及何时发生转变，以及以何种概率结束于一种状态而不是另一种状态，这些都是模型参数的函数。两种类型的转变被描述，并计算了首次通过时间。最终，在 Langevin 型方程的框架内探索了有序参数的演化，并讨论了随机液滴状态的可能亚稳定性。
