Confined run-and-tumble swimmers in one dimension

The persistent character of the motion of active particles gives rise to accumulation at boundaries. I investigate the problem of run-and-tumble swimmers confined in a 1D box with hard walls, reporting expressions for the particle's probability distribution and wall pressure. A crossover box length value is found below which the initial value of the pressure turns out to be higher than the asymptotic one, indicating a bounce effect of the active 'wave' of swimmers. The case of attracting and repelling boundaries are also investigated using two different tumble rates for particles in the bulk and at the walls. Escape problems are finally analyzed by considering partially permeable walls through which particles can leave the box. (paper)