Active particles under confinement: Aggregation at the wall and gradient formation inside a channel

I study the confinement-induced aggregation phenomenon in a minimal model of self-propelled particles inside a channel. Starting from first principles, I derive a set of equations that govern the density profile of such a system at the steady-state, and calculate analytically how the aggregation at the walls varies with the physical parameters of the system. I also investigate how the gradient of the particle density varies if the inside of the channel is partitioned into two regions within which the active particles exhibit distinct levels of fluctuations in their directions of travel.