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We study a totally asymmetric simple exclusion process (TASEP) with one defect site, hopping rate $q<1$, near the system boundary. Regarding our system as a pair of uniform TASEPs coupled through the defect, we study various methods to match a emph{finite} TASEP and an emph{infinite} one across a common boundary. Several approximation schemes are investigated. Utilizing the finite segment mean-field (FSMF) method, we set up a framework for computing the 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 an analytical expression for $J(alpha, q) $ which is in good agreement with Monte Carlo simulation results. When the defect is located deeper in the bulk, we refined the scheme of MacDonald, et.al. [Biopolymers, textbf{6}, 1 (1968)] and find reasonably good fits to the density profiles before the defect site. We discuss the strengths and limitations of each method, as well as possible avenues for further studies.
The TASEP is a paradigmatic model of out-of-equilibrium statistical physics, for which many quantities have been computed, either exactly or by approximate methods. In this work we study two new kinds of observables that have some relevance in biolog
The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Examples are strongly interacting a
Basic properties of the nuclear tensor mean fields are reviewed, and their role in changing the shell structure and masses of nuclei is analyzed within the spherical Hartree-Fock-Bogolyubov approach.
It is explained how field-theoretic methods and the dynamic renormalisation group (RG) can be applied to study the universal scaling properties of systems that either undergo a continuous phase transition or display generic scale invariance, both nea
We propose a mean field theory for the localization of damage in a quasistatic fuse model on a cylinder. Depending on the quenched disorder distribution of the fuse thresholds, we show analytically that the system can either stay in a percolation reg