论文标题
流体流动诱导边界头发的变形
Fluid Flow Induced Deformation of a Boundary Hair
论文作者
论文摘要
通道中的stokes流动引起的一片浓密地毯的变形可以通过非线性插差方程来描述单头发的形状，该方程具有几种用于给定参数选择的解决方案。虽然在先前的研究中摆姿势并与力学中的摆问题相似，但直到现在尚未分析求解该方程。尽管存在非线性功能依赖性对因变量的积分，但该系统是可集成的。我们将分析获得的溶液与有限差分数值方法进行比较，确定物理上可实现的溶液分支，并通过保守的能量样数量简要研究溶液结构。时间依赖性的流体结构相互作用是一个丰富而复杂的研究主题，我们认为本文讨论的解决方案可以用作理解这些系统的基础。
The deformation of a dense carpet of hair due to Stokes flow in a channel can be described by a nonlinear integro-differential equation for the shape of a single hair, which possesses several solutions for a given choice of parameters. While being posed in a previous study and bearing resemblance to the pendulum problem from mechanics, this equation has not been analytically solved until now. Despite the presence on an integral with a nonlinear functional dependence on the dependent variable, the system is integrable. We compare the analytically obtained solution to a finite-difference numerical approach, identify the physically realizable solution branch, and briefly study the solution structure through a conserved energy-like quantity. Time-dependent fluid-structure interactions are a rich and complex subject to investigate and we argue that the solution discussed herein can be used as a basis for understanding these systems.
