论文标题
在通道上有效扩散的坐标免费公式
A Coordinate Free Formulation of Effective Diffusion on Channels
论文作者
论文摘要
我们研究通过通过在任意维度弯曲空间上的向量的相流来滑动横截面来产生的区域的扩散过程。我们通过研究试图通过投影方法将N维扩散方程减少为1维扩散方程时产生的有效扩散系数D。我们使用外部微积分的数学语言在无限和有限的横向扩散率案例中得出该系数的自由公式。这些技术的使用导致了D的公式，该公式比使用依赖性方法更深入地了解有效扩散。
We study diffusion processes in regions generated by sliding a cross section by the phase flow of vector filed on curved spaces of arbitrary dimension. We do this by studying the effective diffusion coefficient D that arises when trying to reduce the n-dimensional diffusion equation to a 1-dimensional diffusion equation by means of a projection method. We use the mathematical language of exterior calculus to derive a coordinate free formula for this coefficient in both infinite and finite transversal diffusion rate cases. The use of these techniques leads to a formula for D which provides a deeper understanding of effective diffusion than when using a coordinate dependent approach.
