Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
复制标题
DOI：
10.1088/1751-8113/42/44/445001
复制
发表时间：
2009-11-06
影响因子：
2.1
通讯作者：
Gregoire, Guillaume
中科院分区：
文献类型：
--
作者：
Bertin, Eric;Droz, Michel;Gregoire, Guillaume
考虑气体的自推进粒子与二元相互作用，我们推导出流体动力学方程的密度和速度场的微观动力学，在相关的玻尔兹曼方程的框架。给出了输运系数的显式表达式，作为模型的微观参数的函数。我们表明，流体动力学速度为零的均匀状态是不稳定的临界密度以上（这取决于微观参数），信号的集体运动的开始。与自推进粒子的标准模型上的数值模拟的比较表明，我们得到的相图是强大的，在这个意义上说，它只稍微依赖于模型的精确定义。虽然均匀流被发现是稳定的远离过渡线，它变得不稳定，相对于有限波长的扰动接近过渡，这意味着一个非平凡的时空结构所产生的流。我们发现孤立波的流体动力学方程的解决方案，非常类似的条纹报告中的直接数值模拟的自推进粒子。
Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation. Explicit expressions for the transport coefficients are given, as a function of the microscopic parameters of the model. We show that the homogeneous state with zero hydrodynamic velocity is unstable above a critical density (which depends on the microscopic parameters), signalling the onset of a collective motion. Comparison with numerical simulations on a standard model of self-propelled particles shows that the phase diagram we obtain is robust, in the sense that it depends only slightly on the precise definition of the model. While the homogeneous flow is found to be stable far from the transition line, it becomes unstable with respect to finite-wavelength perturbations close to the transition, implying a non-trivial spatio-temporal structure for the resulting flow. We find solitary wave solutions of the hydrodynamic equations, quite similar to the stripes reported in direct numerical simulations of self-propelled particles.