一类广义Vicsek类集体运动模型的相变
Phase transitions on a class of generalized Vicsek-like models of collective motion
摘要：
由相互作用的自推进粒子（SPP）组成的系统表现出与集体运动相关的不同形式的有序-无序相变。在本文中，我们提出了一个推广的Vicsek模型，其特征在于一个角噪声项以下的任意概率密度函数，这可能取决于系统的状态，从而具有乘法字符。我们表明，建立良好的矢量Vicsek模型可以表示在这个一般的形式主义，推导出相应的角概率密度函数，以及我们提出了两个新的乘法模型组成的双变量高斯分布和包裹高斯分布。与建议的形式主义，平均场系统可以解决使用的角度随机项的平均合成长度。因此，当SPP全局相互作用时，相变的特征取决于噪声分布的选择，对于矢量和包裹高斯分布是具有混合缩放的一阶，而对于双变量高斯分布是二阶。数值模拟表明，当SPP之间的相互作用由静态复杂网络给出时，这种情况也成立。另一方面，使用空间短程相互作用显示，在所有考虑的情况下，一个不连续的过渡与共存区域，符合Vicsek模型的原始配方。
英文摘要：
Systems composed of interacting self-propelled particles (SPPs) display different forms of order-disorder phase transitions relevant to collective motion. In this paper we propose a generalization of the Vicsek model characterized by an angular noise term following an arbitrary probability density function, which might depend on the state of the system and thus have a multiplicative character. We show that the well established vectorial Vicsek model can be expressed in this general formalism by deriving the corresponding angular probability density function, as well as we propose two new multiplicative models consisting on a bivariate Gaussian and a wrapped Gaussian distributions. With the proposed formalism, the mean-field system can be solved using the mean resultant length of the angular stochastic term. Accordingly, when the SPPs interact globally, the character of the phase transition depends on the choice of the noise distribution, being first-order with an hybrid scaling for the vectorial and wrapped Gaussian distributions, and second order for the bivariate Gaussian distribution. Numerical simulations reveal that this scenario also holds when the interactions among SPPs are given by a static complex network. On the other hand, using spatial short-range interactions displays, in all the considered instances, a discontinuous transition with a coexistence region, consistent with the original formulation of the Vicsek model.
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