Houston Alexander J H, Alexander Gareth P
Department of Physics, Gibbet Hill Road, University of Warwick, Coventry CV4 7AL, United Kingdom.
Centre for Complexity Science, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom.
Phys Rev E. 2022 Jun;105(6):L062601. doi: 10.1103/PhysRevE.105.L062601.
We develop a description of defect loops in three-dimensional active nematics based on a multipole expansion of the far-field director and show how this leads to a self-dynamics dependent on the loop's geometric type. The dipole term leads to active stresses that generate a global self-propulsion for splay and bend loops. The quadrupole moment is nonzero only for nonplanar loops and generates a net "active torque," such that defect loops are both self-motile and self-orienting. Our analysis identifies right- and left-handed twist loops as the only force- and torque-free geometries, suggesting a mechanism for generating an excess of twist loops. Finally, we determine the Stokesian flows created by defect loops and describe qualitatively their hydrodynamics.
我们基于远场指向矢的多极展开，对三维活性向列相中的缺陷环进行了描述，并展示了这如何导致依赖于环的几何类型的自动力学。偶极项导致活性应力，该应力为展曲和弯曲环产生全局自推进力。四极矩仅对于非平面环是非零的，并产生净“活性扭矩”，使得缺陷环既是自运动的又是自定向的。我们的分析确定右手和左手扭曲环是唯一无外力和无扭矩的几何形状，这暗示了一种产生过量扭曲环的机制。最后，我们确定了由缺陷环产生的斯托克斯流，并定性地描述了它们的流体动力学。
