Onehyphen;dimensional Brownian motion near an absorbing boundary: Solution to the steady state Fokkerndash;Planck equation

摘要

The problem of steady, onehyphen;dimensional Brownian motion under prescribed flux in the presence of an infinite plane absorbing boundary is discussed from the point of view of the eigenfunction expansion solution to the relevant Fokkerndash;Planck equation. The expansion coefficients are determined by reducing it to a problem of the initial value type, using a parametrized Maxwellian for the velocity distribution of incoming particles only at the boundary. The number density function expressed in the form of an infinite series of exponentials is cast into a rapidly convergent form at the boundary layer. While some of the physical quantities obtained by this method are in essential agreement with those obtained by certain previous investigators, the following new results are to be noted: (i) the fractional power law variation of the number density in the vicinity of the boundary; and (ii) the complete vanishing of the space dependent diffusion coefficient at the boundary. The results are further discussed.