自推进粒子排列的连续介质模型
A continuum model for nematic alignment of self-propelled particles
摘要：
从基于个体的粒子群模型出发，建立了一个连续介质模型，描述了自推进粒子群通过平行排列相互作用的过程。该方法包括引入相应的平均场动力学方程的流体动力学标度。由于广义碰撞不变量的概念，由此产生的扰动问题得到解决。它产生了一个双曲线，但非保守的方程组的平均方向的流动和粒子的密度平行或反平行于这个平均方向。在弱非局部相互作用假设下引入扩散项，证明扩散系数为正。应用粘细菌的建模概述。
英文摘要：
A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean-field kinetic equation. The resulting perturbation problem is solved thanks to the concept of generalized collision invariants. It yields a hyperbolic but non-conservative system of equations for the nematic mean direction of the flow and the densities of particles flowing parallel or anti-parallel to this mean direction. Diffusive terms are introduced under a weakly non-local interaction assumption and the diffusion coefficient is proven to be positive. An application to the modeling of myxobacteria is outlined.
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