Model of overdamped motion of interacting magnetic vortices through narrow superconducting channels

The microscopic description of several physical systems can be successfully accomplished in terms of the overdamped flow approximation. It is under this broad framework that we investigate the flow of interacting particles in overdamped motion through narrow and irregular channels. By direct comparison with results from molecular dynamics simulations, we show that the behavior of the overdamped system is fully compatible with a continuum coarse-grained model, described in terms of a nonlinear diffusion equation. Remarkably, our results reveal that even in such cases where only a few layers of particles move through the channel, it is possible to obtain a consistent description for the density profiles from the continuum model. Moreover, we demonstrate the general validity of our theoretical approach with results from extensive numerical simulations of different model systems, including the propagation of vortices in superconducting substrates, the movement of pedestrians through corridors, and the flow of colloidal particles in pores.