Kalinay P, Percus J K
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Dec;72(6 Pt 1):061203. doi: 10.1103/PhysRevE.72.061203. Epub 2005 Dec 14.
We derive an extended Fick-Jacobs equation for the diffusion of noninteracting particles in a two- and symmetric three-dimensional channels of varying cross section A(x), using a variational approach. The result is a diffusion differential equation of second order in only one space (longitudinal) coordinate. This equation is tested on the task of calculating the stationary flux through a hyperboloidal tube, and its solution is compared with that of other methods.
我们使用变分法推导了一个扩展的菲克 - 雅各布斯方程，用于描述非相互作用粒子在具有可变横截面(A(x))的二维和对称三维通道中的扩散。结果得到一个仅在一个空间（纵向）坐标上的二阶扩散微分方程。该方程在计算通过双曲面管的稳态通量的任务中进行了测试，并将其解与其他方法的解进行了比较。
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