论文标题
弯曲生物膜中的涡流流和流线拓扑
Vortex Flows and Streamline Topology in Curved Biological Membranes
论文作者
论文摘要
当考虑生物膜中的流动时，通常将它们视为平坦，尽管通常通常是弯曲的表面，甚至是极度弯曲的，例如内质网。在这里，我们研究了曲率对膜流的拓扑作用。专注于许多点涡流缺陷的系统，我们能够根据几何哈密顿量来施放缺陷的粘性动力学。与平面状况相反，流量会产生额外的阳性指数缺陷。对于两个涡流的更简单情况，我们可以分析预测这些停滞点的位置。在低弯曲极限下，动力学类似于理想流体中涡旋的动力学，但在高曲率下发生了相当大的偏差。几何公式使我们能够构建由涡流之间流体动力相互作用引起的流动拓扑的时空演化。流线揭示了新的动力分叉，导致自发的缺陷对创建和融合。此外，我们发现膜曲率介导了缺陷结合，并将全局旋转旋转到多涡流系统，并且各个涡旋仍在局部相互作用。
When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological effects of curvature on flows in membranes. Focusing on a system of many point vortical defects, we are able to cast the viscous dynamics of the defects in terms of a geometric Hamiltonian. In contrast to the planar situation, the flows generate additional defects of positive index. For the simpler situation of two vortices, we analytically predict the location of these stagnation points. At the low curvature limit, the dynamics resemble that of vortices in an ideal fluid, but considerable deviations occur at high curvatures. The geometric formulation allows us to construct the spatio-temporal evolution of streamline topology of the flows resulting from hydrodynamic interactions between the vortices. The streamlines reveal novel dynamical bifurcations leading to spontaneous defect-pair creation and fusion. Further, we find that membrane curvature mediates defect binding and imparts a global rotation to the many-vortex system, with the individual vortices still interacting locally.
