自推进粒子简单模型中的四重缺陷线涡
Vortex with four-fold defect lines in a simple model of self-propelled particles
摘要：
本文用计算机模拟和理论分析相结合的方法，研究了自推进粒子极小模型中四重对称涡旋的形成。除了涡旋模式，我们还观察到系统中的其他五个相：均匀气相，能带结构，移动团块，移动集群和振动环。所有六个阶段都是通过控制噪音的强度以及排斥和排列相互作用的贡献而出现的。我们详细研究了涡旋的形状及其对称性。该图案显示了指数缺陷线，其中传入和传出的粒子流发生碰撞。我们表明，粒子之间的排列和排斥相互作用是必要的，以形成这样的图案。最后，我们推导出我们的模型的流体动力学方程，并将它们与计算机模拟和Quincke转子的结果进行比较。观察到三者之间的良好一致性。
英文摘要：
We studied formation of vortex with four-fold symmetry in a minimal model of self-propelled particles, confined inside a squared box, using computer simulations and also theoretical analysis. In addition to the vortex pattern, we observed five other phases in the system: homogeneous gaseous phase, band structures, moving clumps, moving clusters and vibrating rings. All six phases emerge from controlling strength of noise and contribution of repulsion and alignment interactions. We studied shape of the vortex and its symmetry in detail. The pattern shows exponential defect lines where incoming and outgoing flows of particles collide. We show that alignment and repulsion interactions between particles are necessary to form such patterns. Finally, we derived hydro-dynamical equations for our model and compared them with the results of both computer simulations and Quincke rotors. A good agreement between the three is observed.
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