Coupling driven exclusion and diffusion processes on parallel lanes: boundary induced phase transitions and boundary layers

We study a driven many particle system comprising of two identical lanes of finite lengths. On one lane, particles hop diffusively with a bias in a specific direction. On the other lane, particles hop in a specific direction obeying mutual exclusion rule. In addition, the two lanes are connected with each other through exchange of particles with certain rules. The system, at its two ends, is in contact with particle reservoirs which maintain specific particle densities at the two ends. In this paper, we study boundary-induced phase transitions exhibited by this system and predict the phase diagram using the technique of fixed point based boundary layer analysis. An interesting manifestation of the interplay of two density variables associated with two lanes is found in the shock phase in which the particle density profile across the lane with unidirectional hopping shows a jump discontinuity (shock) from a low- to a high-density region. The density profile on the diffusion-lane never exhibits a shock. However, the shock in the other lane gives rise to a discontinuity in the slope of the diffusion-lane density profile. We show how an approximate solution for the slope can be obtained in the boundary layer analysis framework.