Contributor info: Prof. Arvind Kumar Gupta

Ashish Kumar Pandey, Arvind Kumar Gupta

SciPost Phys. Core 8, 089 (2025) · published 3 December 2025 | Toggle abstract · pdf

Motivated by the role of limited particle resources in multi-species bidirectional transport processes observed in various biological and physical systems, we investigate a one-dimensional closed system consisting of two parallel lanes with narrow entrances, where each lane accommodates two oppositely directed particle species. Each particle species is linked to a separate finite reservoir, which is coupled to both lanes and regulates the entry rates of particle into the lanes. To analyze the effect of finite particle reservoirs on the stationary properties of the system, we employ a mean-field theoretical framework to characterize the density profiles, particle currents, and phase behavior, complemented by a boundary layer analysis based on fixed point methods to capture spatial variations near the boundaries. The impact of individual species population, quantified by species-specific filling factors, is systematically examined under both equal and unequal conditions. For equal filling factors, system undergoes spontaneous symmetry breaking and supports both symmetric and asymmetric phases. In contrast, for unequal filling factors, only asymmetric phases are realized, with the phase diagram exhibiting up to five distinct phases. A striking feature observed in both scenarios is the emergence of a back-and-forth transition, along with a non-monotonic dependence of the number of phases on the filling factors. All theoretical findings are extensively validated through stochastic simulations based on the Gillespie algorithm, confirming the robustness of the analytical results.

Nikhil Bhatia, Arvind Kumar Gupta

SciPost Phys. Core 8, 009 (2025) · published 27 January 2025 | Toggle abstract · pdf

Motivated by the significant influence of the defects in the dynamics of the natural or man-made transportation systems, we propose an open, dynamically disordered, totally asymmetric simple exclusion process featuring bulk particle attachment and detachment. The site-wise dynamic defects might randomly emerge or vanish at any lattice location, and their presence slows down the motion of the particles. Using a mean-field approach, we obtain an analytical expression for both particle and defect density and validate them using Monte Carlo simulation. The study investigates the steady-state characteristics of the system, including phase transitions, analysis of boundary layers, and phase diagrams. Our approach streamlines the defect dynamics by integrating two parameters into one called the obstruction factor, which helps in determining an effective binding constant. The impact of the obstruction factor on the phase diagram is explored across various combinations of binding constants and detachment rates. A critical value of the obstruction factor is obtained, about which an infinitesimal change results in a substantial qualitative change in the structure of the phase diagrams. Further, the effect of the detachment rate is studied, and critical values along which the system observes a quantitative transition of the stationary phases are obtained as a function of the obstruction factor. Overall, the system shows stationary phases ranging from three to seven depending upon the value of the obstruction factor, the binding constant, and the detachment rate. Moreover, we scrutinized the impact of the obstruction factor on the shock dynamics and found no finite-size effect.