粘细菌菌落的动力学模拟
Kinetic Modelling of Colonies of Myxobacteria
摘要：
一个新的动力学模型的粘细菌菌落在平坦的表面上的动力学推导正式，并提出了第一个分析和数值结果。该模型是基于两种不同类型的硬二进制碰撞的假设：对齐和反转。我们研究了两个不同的版本：a）现实的杆状细菌和b）人工圆形细菌称为麦克斯韦粘细菌参考麦克斯韦分子的气体动力学玻尔兹曼方程的类似简化。相应的碰撞算子的总和产生朝向向列对齐平衡的松弛，即在相反方向上极化的两组细菌。对于空间齐次模型，证明了全局解的存在唯一性，以及在特殊的初始条件和Maxwell粘滞系统下指数衰减到平衡点的结果。对于杆形情况，只有部分结果可用。这些结果说明了数值模拟，并提出了一个正式的讨论的宏观极限。
英文摘要：
A new kinetic model for the dynamics of myxobacteria colonies on flat surfaces is derived formally, and first analytical and numerical results are presented. The model is based on the assumption of hard binary collisions of two different types: alignment and reversal. We investigate two different versions: a) realistic rod-shaped bacteria and b) artificial circular shaped bacteria called Maxwellian myxos in reference to the similar simplification of the gas dynamics Boltzmann equation for Maxwellian molecules. The sum of the corresponding collision operators produces relaxation towards nematically aligned equilibria, i.e. two groups of bacteria polarized in opposite directions. For the spatially homogeneous model a global existence and uniqueness result is proved as well as exponential decay to equilibrium for special initial conditions and for Maxwellian myxos. Only partial results are available for the rod-shaped case. These results are illustrated by numerical simulations, and a formal discussion of the macroscopic limit is presented.
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