论文标题
压缩活性cosserat晶体的过度阻尼晶格动力学
Overdamped Lattice Dynamics of Sedimenting Active Cosserat Crystals
论文作者
论文摘要
微极性物质需要其运动学描述位置和定向自由度。活性在微极性被动物质中没有的这些运动学变量之间产生动态耦合，例如Cosserat兄弟首先研究的定向晶体。在这里，我们研究了单轴活性对最初结晶状态的球形胶体状态的动力学的影响，在远离限制边界的粘性流体中缓慢沉积。尽管液体摩擦过度阻尼，但晶格仍承认了位置和方向的行进浪潮。在长波长下，这些遵守由活性确定的Lamé常数的矢量波方程。我们发现，这些波的至少一种极化模式始终是不稳定的，导致晶体的融化。通过识别由哈密顿量和相关的Casimir不变性组成的奇数泊松结构来阐明这些结果，其中位置和方向的线性组合被鉴定为共轭变量。我们的结果表明，在缓慢的粘性流中有活性颗粒通常存在泊松结构，从而允许在存在这些耗散系统的情况下应用平衡参数。
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.
