准一维反趋化流的鞍结分岔到阻塞态
Saddle-Node Bifurcation to Jammed State for Quasi-One-Dimensional Counter Chemotactic Flow
摘要：
本文研究了在准一维路径中反趋化颗粒流从自由流动状态到堵塞状态的转变。这种流动的特征之一是组成颗粒自发地形成阻塞路径的团簇，称为路径阻塞团簇（PBC），并且当颗粒密度大于阈值时导致堵塞状态。在阈值附近，PBC偶尔会自行解溶以恢复自由流动。换句话说，PBC大小的时间演变决定了反趋化流的通量。在本文中，随机元胞自动机（SCA）模型的数值结果的基础上，我们介绍了一个Langevin方程模型的PBC的尺寸演化再现SCA模型的定性特征。结果表明，准一维逆流中堵塞状态的出现是由鞍结分岔引起的。
英文摘要：
The transition of a counter chemotactic particle flow from a free-flow state to a jammed state in a quasi-one-dimensional path is investigated. One of the characteristic features of such a flow is that the constituent particles spontaneously form a cluster that blocks the path, called a path-blocking cluster (PBC), and causes a jammed state when the particle density is greater than a threshold value. Near the threshold value, the PBC occasionally desolve itself to recover the free flow. In other words, the time evolution of the size of the PBC governs the flux of a counter chemotactic flow. In this paper, on the basis of numerical results of a stochastic cellular automata (SCA) model, we introduce a Langevin equation model for the size evolution of the PBC that reproduces the qualitative characteristics of the SCA model. The results suggest that the emergence of the jammed state in a quasi-one-dimensional counter flow is caused by a saddle-node bifurcation.
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