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.

中文翻译：

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粘菌菌落的动力学模型

正式推导了平面上粘菌菌落动力学的新动力学模型，并给出了第一批分析和数值结果。该模型基于两种不同类型的硬二进制冲突的假设：对齐和反转。我们研究了两种不同的版本：a）现实的杆状细菌和b）称为麦克斯韦粘菌的人造圆形细菌参照麦克斯韦分子的气体动力学玻尔兹曼方程的相似简化。相应的碰撞算子的总和使向着向列对齐的平衡（即两组细菌在相反的方向极化）产生弛豫。对于空间均匀模型，证明了整体存在和唯一性结果，以及对于特殊初始条件和条件，指数衰减到平衡。麦克斯韦的黏液。对于棒形外壳，只有部分结果可用。通过数值模拟说明了这些结果，并对宏观极限进行了正式讨论。