Mathematics & Computer Science Department, Western Colorado University, 1 Western Way, Gunnison, Colorado 81231, USA.
Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois St., Golden, Colorado 80401, USA.
Phys Rev E. 2020 Sep;102(3-1):033114. doi: 10.1103/PhysRevE.102.033114.
Flagella are hairlike appendages attached to microorganisms that allow the organisms to traverse their fluid environment. The algae Volvox are spherical swimmers with thousands of individual flagella on their surface, and their coordination is not fully understood. In this work, a previously developed minimal model of flagella synchronization is extended to the outer surface of a sphere submerged in a fluid. Each beating flagellum tip is modeled as a small sphere, elastically bound to a circular orbit just above the spherical surface and a regularized image system for Stokes flow outside of a sphere is used to enforce the no-slip condition. Biologically relevant distributions of rotors results in a rapidly developing and robust symplectic metachronal wave traveling from the anterior to the posterior of the spherical Volvox body.
鞭毛是附着在微生物上的毛发状附属物，使生物体能够在其流体环境中穿行。藻类团藻是具有数千条鞭毛的球形游泳者，但其协调机制尚不完全清楚。在这项工作中，之前开发的鞭毛同步最小模型被扩展到浸没在流体中的球体的外表面。每个拍打鞭毛的尖端被建模为一个小球体，弹性地固定在一个圆形轨道上，该轨道刚好在球体表面上方，并且使用球体外部的斯托克斯流正则化图像系统来强制实施无滑移条件。生物相关的转子分布导致快速发展和稳健的准同步波从球形团藻身体的前部传播到后部。
