Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates

@article{Lakatos2006HydrodynamicMS,
  title={Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates},
  author={Greg Lakatos and Jackson O'Brien and Tom Chou},
  journal={Journal of Physics A},
  year={2006},
  volume={39},
  pages={2253-2264}
}
We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of… 

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