论文标题
主动悬浮液中模式形成的弱非线性分析
Weakly nonlinear analysis of pattern formation in active suspensions
论文作者
论文摘要
我们考虑了Stokes流动中活性棒状颗粒的Saintillan--shelley动力学模型（Saintillan＆Shelley 2008a，b），在某些情况下，已知均匀的，应悬浮液的均匀，各向同性悬浮液在某些情况下是不稳定的。通过弱非线性分析以及数值模拟，我们准确地确定了各向同性稳态如何在不同参数方面失去稳定性。我们研究了系统所接受的每种类型的分叉，包括亚临界和超临界霍夫夫和干草叉分叉。在这些分叉附近阐明该系统的行为提供了一种理论手段，将该模型与过渡到湍流的其他物理系统进行了比较，并对可以在实验中探索的主动悬架中分叉性质进行了预测。
We consider the Saintillan--Shelley kinetic model of active rodlike particles in Stokes flow (Saintillan & Shelley 2008a,b), for which the uniform, isotropic suspension of pusher particles is known to be unstable in certain settings. Through weakly nonlinear analysis accompanied by numerical simulations, we determine exactly how the isotropic steady state loses stability in different parameter regimes. We study each of the various types of bifurcations admitted by the system, including both subcritical and supercritical Hopf and pitchfork bifurcations. Elucidating this system's behavior near these bifurcations provides a theoretical means of comparing this model with other physical systems which transition to turbulence, and makes predictions about the nature of bifurcations in active suspensions that can be explored experimentally.
