沉积活性Cosserat晶体的过阻尼晶格动力学
Overdamped Lattice Dynamics of Sedimenting Active Cosserat Crystals
摘要：
微极活性物质的运动学描述需要位置自由度和取向自由度。活动在这些运动学变量之间产生动力学耦合，而这些动力学变量在微极被动物质中是不存在的，例如由Cosserat兄弟首先研究的定向晶体。在这里，我们研究单轴活动的动态的初始结晶状态的球状胶体缓慢沉积在远离封闭边界的粘性流体的影响。尽管有流体的摩擦过阻尼，晶格允许位置和方向的行波。在长波长下，它们服从一个矢量波方程，其拉梅常数由活度决定。我们发现，这些波的至少一个偏振模式总是不稳定的，导致熔化的晶体。这些结果阐明了通过确定一个奇数维泊松结构组成的哈密顿量和相关的Casimir不变量，其中的位置和方向的线性组合被确定为共轭变量。我们的研究结果表明，泊松结构一般可能存在于缓慢的粘性流中的活性粒子，从而允许平衡的参数应用在这些耗散系统的存在下。
英文摘要：
Micropolar active matter requires for its kinematic description both positional and orientational degrees of freedom. Activity generates dynamic coupling between these kinematic variables that are absent in micropolar passive matter, such as the oriented crystals first studied by the Cosserat brothers. Here we study the effect of uniaxial activity on the dynamics of an initially crystalline state of spheroidal colloids sedimenting slowly in a viscous fluid remote from confining boundaries. Despite frictional overdamping by the fluid, the crystalline lattice admits traveling waves of position and orientation. At long wavelengths these obey a vector wave equation with Lamé constants determined by the activity. We find that at least one polarization mode of these waves is always unstable, leading to the melting of the crystal. These results are elucidated by identifying an odd-dimensional Poisson structure consisting of a Hamiltonian and an associated Casimir invariant, where linear combinations of position and orientation are identified as conjugate variables. Our results suggest that Poisson structures may exist generally for active particles in slow viscous flow and thereby allow equilibrium arguments to be applied in the presence of these dissipative systems.
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