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Abstract: We study a totally asymmetric simple exclusion process TASEP with onedefect site, hopping rate $q<1$, near the system boundary. Regarding our systemas a pair of uniform TASEP-s coupled through the defect, we study variousmethods to match a \emph{finite} TASEP and an \emph{infinite} one across acommon boundary. Several approximation schemes are investigated. Utilizing thefinite segment mean-field FSMF method, we set up a framework for computingthe steady state current $J$ as a function of the entry rate $% \alpha $ and$q$. For the case where the defect is located at the entry site, we obtain ananalytical expression for $J\alpha, q $ which is in good agreement with MonteCarlo simulation results. When the defect is located deeper in the bulk, werefined the scheme of MacDonald, et.al. Biopolymers, \textbf{6}, 1 1968 andfind reasonably good fits to the density profiles before the defect site. Wediscuss the strengths and limitations of each method, as well as possibleavenues for further studies.



Autor: J.J. Dong, R. K. P. Zia, B. Schmittmann

Fuente: https://arxiv.org/



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