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Asymmetric simple exclusion process with position-dependent hopping rates: Phase diagram from boundary-layer analysis.
Sutapa, Mukherji (2018) Asymmetric simple exclusion process with position-dependent hopping rates: Phase diagram from boundary-layer analysis. Physical Review E, 97. pp. 321-330.
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Physical Review E Volume 97 issue 3 2018 [doi 10.1103%2FPhysRevE.97.032130] Mukherji, Sutapa -- Asymmetric simple exclusion process with position-dependent hopping rates- Phase diagram from boundary-l.pdf - Published Version Restricted to Registered users only Download (429kB) | Request a copy |
Abstract
In this paper, we study a one-dimensional totally asymmetric simple exclusion process with position-dependent hopping rates. Under open boundary conditions, this system exhibits boundary-induced phase transitions in the steady state. Similarly to totally asymmetric simple exclusion processes with uniform hopping, the phase diagram consists of low-density, high-density, and maximal-current phases. In various phases, the shape of the average particle density profile across the lattice including its boundary-layer parts changes significantly. Using the tools of boundary-layer analysis, we obtain explicit solutions for the density profile in different phases. A detailed analysis of these solutions under different boundary conditions helps us obtain the equations for various phase boundaries.Next, we showhowthe shape of the entire density profile including the location of the boundary layers can be predicted from the fixed points of the differential equation describing the boundary layers.We discuss this in detail through several examples of density profiles in various phases. The maximal-current phase appears to be an especially interesting phase where the boundary layer flows to a bifurcation point on the fixed-point diagram.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | asymmetric simple exclusion, hopping rates |
| Subjects: | 500 Natural Sciences and Mathematics > 04 Chemistry and Allied Sciences > 08 Physical Chemistry |
| Divisions: | Protein Chemistry and Technology |
| Depositing User: | Food Sci. & Technol. Information Services |
| Date Deposited: | 07 Feb 2019 04:14 |
| Last Modified: | 07 Feb 2019 04:14 |
| URI: | http://ir.cftri.res.in/id/eprint/13935 |
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