  In this paper, we proposed a stochastic model which describes two species of
particles moving in counterflow. The model generalizes the theoretical
framework describing the transport in random systems since particles can work
as mobile obstacles, whereas particles of one species move in opposite
direction to the particles of the other species, or they can work as fixed
obstacles remaining in their places during the time evolution. We conducted a
detailed study about the statistics concerning the crossing time of particles,
as well as the effects of the lateral transitions on the time required to the
system reaches a state of complete geographic separation of species. The
spatial effects of jamming were also studied by looking into the deformation of
the concentration of particles in the two-dimensional corridor. Finally, we
observed in our study the formation of patterns of lanes which reach the steady
state regardless the initial conditions used for the evolution. A similar
result is also observed in real experiments involving charged colloids motion
and simulations of pedestrian dynamics based on Langevin equations, when
periodic boundary conditions are considered (particles counterflow in a ring
symmetry). The results obtained through Monte Carlo numerical simulations and
numerical integrations are in good agreement with each other. However,
differently from previous studies, the dynamics considered in this work is not
Newton-based, and therefore, even artificial situations of self-propelled
objects should be studied in this first-principle modeling.
