Diffusion's induced transport in periodic channels and an inverse problem

TL;DR

This paper investigates diffusion-induced transport in periodic channels modeled by a Fokker-Planck equation, proposing an inverse problem to determine the driving force from flow response data, with partial solutions under simplifying assumptions.

Contribution

It introduces an inverse problem framework for identifying the deriving force in diffusion transport models, offering partial solutions and analysis.

Findings

Flow generated by diffusion and periodic force in 1D channels

Formulation of an inverse problem to recover the deriving force

Partial solution of the inverse problem under simplifying assumptions

Abstract

A diffusion's induced transport is defined for a linear model of a Fokker-Plank equation under periodic boundary conditions in one-dimensional geometry. The flow is generated by a diffusion and a periodic deriving force induced by a velocity potential. An inverse problem is suggested for evaluating the deriving force in terms of the response function associated with the flow. It is also shown that the inverse problem can be partially solved under some simplifying assumption.