Vicsek群的群居与个体行为及一级相变的开始
Gregarious vs Individualistic Behavior in Vicsek Swarms and the Onset of First-Order Phase Transitions
摘要：
标准Vicsek模型（SVM）是一个最小的自推进粒子的非平衡模型，似乎捕捉关键植绒现象的基本成分。在SVM中，粒子倾向于彼此对齐并形成有序的集体运动;然而，由噪声项控制的扰动导致噪声驱动的连续有序-无序相变。在这项工作中，我们通过引入一个参数$α$，允许粒子是个人主义的，而不是群居，即选择一个独立于他们的邻居的运动方向扩展SVM。通过专注于小噪声制度，我们表明，一个相对较小的概率的个人主义运动（约10%）是足以驱动系统从一个Vicsek有序相到无序相。尽管事实上，$α-$扩展模型保留了O（n）对称性，相互作用范围，以及底层SVM的维数，这种新的相变被发现是不连续的（一阶），一个有趣的表现丰富的非平衡群集/群集现象。
英文摘要：
The Standard Vicsek Model (SVM) is a minimal nonequilibrium model of self-propelled particles that appears to capture the essential ingredients of critical flocking phenomena. In the SVM, particles tend to align with each other and form ordered flocks of collective motion; however, perturbations controlled by a noise term lead to a noise-driven, continuous order-disorder phase transition. In this work, we extend the SVM by introducing a parameter $α$ that allows particles to be individualistic instead of gregarious, i.e. to choose a direction of motion independently of their neighbors. By focusing on the small-noise regime, we show that a relatively small probability of individualistic motion (around 10%) is sufficient to drive the system from a Vicsek-like ordered phase to a disordered phase. Despite the fact that the $α-$extended Model preserves the O(n) symmetry, the interaction range, as well as the dimensionality of the underlying SVM, this novel phase transition is found to be discontinuous (first-order), an intriguing manifestation of the richness of the nonequilibrium flocking/swarming phenomenon.
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