Analytical representation of the relations of inertial diffusion transport

A generalized approach has been proposed to describe the diffusive transport of inertial particles at which the known inertialess relations (in particular, between the concentration of particles and the corresponding flux) are supplemented by a factor allowing the calculation of inertial effects in terms of the matrix continued fraction method. The advantage of this approach, which is in the analytical representation of the results, is illustrated by solving the problem of the determination of the effective diffusion coefficient of an inertial particle in a sawtooth potential and the average velocity of the adiabatic inertial ratchet. The character of the nonanalytic behavior of these quantities in the presence of large gradients of the potential has been established.