Far from equilibrium transport on TASEP with pockets
Department of Mathematics, IIT Ropar, 140001, Rupnagar, Punjab, India
Accepted: 26 July 2022
Published online: 5 August 2022
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 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 parameter space obtained with respect to q and the attachment-detachment rates. In particular, the topology of the phase diagram is found to be unchanged in the neighborhood of . 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 . The theoretically obtained phase boundaries and density profiles are validated through extensive Monte Carlo simulations.
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