Abstract:
We investigate a geometric adaptation of a totally asymmetric simple exclusion process with open boundary conditions,
where each site of a one-dimensional channel is connected to a lateral space (pocket). The number of particles that may be
accommodated in each pocket is determined by its capacity q. The continuum mean-field approximation is deployed for the case
q 1 where both lattice and pocket strictly follow the hard-core exclusion principle. In contrast, a probability mass function is
utilized along with the mean-field theory to investigate the multiple-capacity case, where the pocket violates the hard-core exclusion
principle. The effect of both finite and infinite reservoirs has been studied in the model. The explicit expression for particle density
has been calculated, and the evolution of the phase diagram in α −β parameter space obtained with respect to q and the attachmentdetachment rates. In particular, the topology of the phase diagram is found to be unchanged in the neighborhood of q 1. Moreover,
the competition between lattice and pocket for finite resources and the unequal Langmuir kinetics captures a phenomenon in the
form of a back-and-forth transition. We have also investigated the limiting case q → ∞. The theoretically obtained phase boundaries
and density profiles are validated through extensive Monte Carlo simulations.
