论文标题
集体运动快速放松
Quick Relaxation in Collective Motion
论文作者
论文摘要
我们建立了足够的条件，可以在经典的Vicsek-Cucker-Smale鸟类植物模型中快速放松到动力学平衡。只要羊群的数量保持界限，鸟类的收敛时间是多项式的。这个新结果依赖于两种关键成分：利用嵌入式平均系统的凸几何形状；并在断开协议系统的S能量上得出新的界限。我们还应用技术来约束Sugihara和Suzuki研究的某些模式形成机器人系统的放松时间。
We establish sufficient conditions for the quick relaxation to kinetic equilibrium in the classic Vicsek-Cucker-Smale model of bird flocking. The convergence time is polynomial in the number of birds as long as the number of flocks remains bounded. This new result relies on two key ingredients: exploiting the convex geometry of embedded averaging systems; and deriving new bounds on the s-energy of disconnected agreement systems. We also apply our techniques to bound the relaxation time of certain pattern-formation robotic systems investigated by Sugihara and Suzuki.
