Kalinay Pavol
Institute of Physics, Slovak Academy of Sciences, Dúbravska Cesta 9, 84511 Bratislava, Slovakia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031106. doi: 10.1103/PhysRevE.80.031106. Epub 2009 Sep 4.
Diffusion in an external potential in a two-dimensional channel of varying cross section is considered. We show that a rigorous mapping procedure applied on the corresponding Smoluchowski equation yields a one-dimensional evolution equation of the Fick-Jacobs type corrected by an effective coefficient D(x). The procedure enables us to derive this function within a recurrence scheme. We test this result on a model of stationary diffusion in a linear cone in a homogeneous potential, which is exactly solvable. Extension of the approximate formulas for D(x) derived for the diffusion alone is discussed.
考虑在具有可变横截面的二维通道中的外部势场中的扩散。我们表明，应用于相应的斯莫卢霍夫斯基方程的严格映射过程会产生一个一维Fick-Jacobs型演化方程，该方程由有效系数D(x)修正。该过程使我们能够在递推方案中导出此函数。我们在均匀势场中线性圆锥内的稳态扩散模型上测试了这一结果，该模型是可精确求解的。讨论了仅针对扩散导出的D(x)近似公式的扩展。
