极端波纹管中的偏置布朗运动
Biased Brownian motion in extreme corrugated tubes
摘要：
研究了点尺寸颗粒在三维光滑变截面管道中的偏置布朗运动。在我们最近的工作中[Martens等人，PRE 83，051135]我们对管几何形状的几何参数中的稳态概率密度进行了渐进分析。我们证明了首阶项等价于Fick-Jacobs近似。导出了概率密度高阶修正的表达式。使用此展开阶数，我们得到，在扩散主导的制度的平均粒子流等于零阶Fick-Jacobs结果校正的一个因素，包括管的几何形状的λ。特别是，我们证明，这种估计是更准确的极端波纹几何形状相比，常用的方法，使用空间依赖的扩散系数D（x，f）。分析结果证实了与正弦形管的有限元计算。
英文摘要：
Biased Brownian motion of point-size particles in a three-dimensional tube with smoothly varying cross-section is investigated. In the fashion of our recent work [Martens et al., PRE 83,051135] we employ an asymptotic analysis to the stationary probability density in a geometric parameter of the tube geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. Expression for the higher order corrections to the probability density are derived. Using this expansion orders we obtain that in the diffusion dominated regime the average particle current equals the zeroth-order Fick-Jacobs result corrected by a factor including the corrugation of the tube geometry. In particular we demonstrate that this estimate is more accurate for extreme corrugated geometries compared to the common applied method using the spatially dependent diffusion coefficient D(x,f). The analytic findings are corroborated with the finite element calculation of a sinusoidal-shaped tube.
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