论文标题
粒细菌菌落的动力学建模
Kinetic Modelling of Colonies of Myxobacteria
论文作者
论文摘要
一种新的动力学模型，用于正式得出平坦表面上的粘菌群菌落的动力学模型，并提出了首先分析和数值结果。该模型基于两种不同类型的硬性二进制碰撞的假设：对齐和逆转。我们研究了两个不同的版本：a）逼真的棒状细菌和b）人造圆形细菌，称为麦克斯韦菌Myxos，参考了Maxwellian分子的气体动力学Boltzmann方程的类似简化。相应的碰撞算子的总和会使朝着对准平衡的平衡产生松弛，即两组细菌在相反的方向上极化。 对于在空间均匀模型的情况下，全球存在和独特性结果被证明，以及针对特殊初始条件和Maxwellian myxos的指数衰减。仅适用于杆状外壳的部分结果。这些结果通过数值模拟说明，并对宏观极限进行了正式讨论。
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.
