National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China.
College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, China.
Sci Rep. 2023 May 20;13(1):8169. doi: 10.1038/s41598-023-35238-w.
The motional consensus of self-propelled particles is studied in both noise-free cases and cases with noise by the standard Vicsek model. In the absence of noise, we propose a simple method, using grid-based technique and defining the normalized variance of the ratio of the number of particles locally to globally, to quantitatively study the movement pattern of the system by the spatial distribution of the particles and the degree of aggregation of particles. It is found that the weaker correlation of velocity leads to larger degree of aggregation of the particles. In the cases with noise, we quantify the competition between velocity alignment and noise by considering the difference of the variety of order parameter result from the velocity alignment and noise. The variation of the effect of noise on motional consensus is non-monotonic for the change of the probability distribution of noise from uniform to non-uniform. Our results may be useful and encourage further efforts in exploring the basic principles of collective motion.
利用标准的 Vicsek 模型研究了无噪声和噪声情况下自主运动粒子的协同运动。在无噪声情况下，我们提出了一种简单的方法，使用基于网格的技术并定义粒子局部数量与全局数量之比的归一化方差，通过粒子的空间分布和粒子的聚集程度定量研究系统的运动模式。结果表明，速度相关性越弱，粒子的聚集程度越大。在有噪声的情况下，我们通过考虑速度对准和噪声引起的序参量变化的差异，量化了速度对准和噪声之间的竞争。噪声对协同运动的影响随噪声概率分布从均匀变为非均匀而呈非单调变化。我们的研究结果可能有助于进一步探索集体运动的基本原理。
