ALGEBRAIC MICROSCOPIC APPROACH TO DRIFT-DIFFUSION

A recently proposed approach [1] to describe rigorously diffusion and diffusion-related reactions on arbitrary networks in terms of elementa ry jumps has been extended to include drift-diffusion capability. The method is based on a combined density function approach to diffusion a nd on an adjacency matrix concept used in graph theory. The new method allows flexible and selective mixing of drift and diffusion on any tw o-dimensional domain of arbitrary outer and inner geometry. In particu lar, identity rank four tensors operating on subdomains are introduced to allow preservation of results of previous operations not affected by the subsequent mechanisms. As an application, it is shown that swit ching-off behavior of currents depends sensitively on the geometry of the domain. At present, numeric implementation and computational limit ations restrict the use of the method to rather small macroscopic doma ins.