非完整集体流：具有微结构的连续介质中的速度-取向锁定
Nonholonomic collective flows: velocity--orientation locking in a continuum with microstructure
AI总结：
该研究建立含矢量微结构的连续介质理论，将无侧滑约束应用于细长粒子流体，推导运动方程，揭示约束对集体效应的塑造作用，为主动流体动力学提供力学基础并恢复相关经典模型。
AI中文摘要：
我们为沿自身轴线运动的细长粒子流体建立了连续介质理论，绵羊群、自驱动杆、车辆交通及转弯鸟群等体系均理想地遵循相同的运动学规律。在带有矢量微结构的连续介质框架中，每一点还携带取向信息，我们将无侧滑（打滑）条件 $\boldsymbol{v}=u\boldsymbol{n}$ 作为理想的、不可积分的内约束施加。我们通过虚功率原理推导得到纯运动方程及约束反力的控制方程。利用向列液晶的Ericksen-Leslie理论提供的本构封闭关系，我们展示该约束如何塑造集体效应：它将抛物型取向扩散转变为双曲型取向密度波，并禁止任何定常简单剪切；它将经验的Toner-Tu对流系数固定为胶体滚轮中测得的流动-取向对齐比率，从而为微极主动流体动力学中的角声提供力学基础；它还恢复了鸟群的惯性自旋模型，同时增加了倾斜力和转弯-密度耦合；最后，它恢复了一维车辆交通流的经典宏观模型，同时在二维框架中描述转向、侧向轮胎力及道路几何。
英文摘要：
We develop a continuum theory for a fluid of elongated particles that advance along their own axes. The same kinematics is ideally shared by flocks of sheep, self-propelled rods, vehicular traffic, and turning flocks of birds. Within the framework of continua with vectorial microstructure, in which each point also carries an orientation, we impose the no-side-slip (skate) condition $\vv=u\,\nn$ as an ideal, non-integrable internal constraint. We derive the pure equations of motion and the equation governing the constraint reaction from the principle of virtual power. Using a constitutive closure provided by the Ericksen-Leslie theory of nematic liquid crystals, we show how the constraint also shapes collective effects. It turns parabolic orientational diffusion into hyperbolic orientation-density waves and forbids any steady simple shear. It fixes the empirical Toner-Tu convective coefficient to the flow-alignment ratio measured in colloidal rollers, thereby providing a mechanical foundation for angular sound in micropolar active hydrodynamics. It also recovers the inertial spin model of bird flocks, with the addition of a banking force and a turn-density coupling. Finally, it recovers the classical macroscopic models of one-dimensional traffic flow, while describing steering, lateral tyre forces, and road geometry in two dimensions.
