Solon Alexandre P, Caussin Jean-Baptiste, Bartolo Denis, Chaté Hugues, Tailleur Julien
Université Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, 75205 Paris, France.
Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, Université de Lyon, CNRS, 46, allée d'Italie, 69007 Lyon, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062111. doi: 10.1103/PhysRevE.92.062111. Epub 2015 Dec 4.
We study in detail the hydrodynamic theories describing the transition to collective motion in polar active matter, exemplified by the Vicsek and active Ising models. Using a simple phenomenological theory, we show the existence of an infinity of propagative solutions, describing both phase and microphase separation, that we fully characterize. We also show that the same results hold specifically in the hydrodynamic equations derived in the literature for the active Ising model and for a simplified version of the Vicsek model. We then study numerically the linear stability of these solutions. We show that stable ones constitute only a small fraction of them, which, however, includes all existing types. We further argue that, in practice, a coarsening mechanism leads towards phase-separated solutions. Finally, we construct the phase diagrams of the hydrodynamic equations proposed to qualitatively describe the Vicsek and active Ising models and connect our results to the phenomenology of the corresponding microscopic models.
我们详细研究了描述极性活性物质向集体运动转变的流体动力学理论，以Vicsek模型和活性伊辛模型为例。通过一个简单的唯象理论，我们证明了存在无穷多个传播解，这些解描述了相分离和微相分离，我们对其进行了全面的刻画。我们还表明，相同的结果特别适用于文献中为活性伊辛模型和Vicsek模型的简化版本推导的流体动力学方程。然后，我们对这些解的线性稳定性进行了数值研究。我们表明，稳定的解只占其中的一小部分，然而，这包括了所有现有的类型。我们进一步认为，在实际中，一种粗化机制会导致相分离解。最后，我们构建了为定性描述Vicsek模型和活性伊辛模型而提出的流体动力学方程的相图，并将我们的结果与相应微观模型的现象学联系起来。
