J J Dong et al 2009 J. Phys. A: Math. Theor. 42 015002 doi:10.1088/1751-8113/42/1/015002
J J Dong1,2, R K P Zia2 and B Schmittmann2
Show affiliationsWe 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 TASEP's coupled through the defect, we study various methods to match a finite TASEP and an 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 α and q. For the case where the defect is located at the entry site, we obtain an analytical expression for J(α, 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 (1968 Biopolymers 6 1) 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.
87.15.H- Dynamics of biomolecules
92D20 Protein sequences, DNA sequences
82C80 Numerical methods (Monte Carlo, series resummation, etc.)
Issue 1 (9 January 2009)
Received 11 September 2008, in final form 17 October 2008
Published 19 November 2008
J J Dong et al 2009 J. Phys. A: Math. Theor. 42 015002
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