Non-equilibrium processes in an unconserved network model with limited resources
Department of Mathematics, Indian Institute of Technology Ropar, 140001, Rupnagar, Punjab, India
Accepted: 19 January 2023
Published online: 1 February 2023
We present a study of a peculiar form of network topology comprising of lanes connected via a junction, competing for particles in a reservoir of limited capacity with non-conserving dynamics. We exploit mean-field approximation to thoroughly analyze stationary dynamic properties such density profiles, phase boundaries, and phase diagrams. The steady-state properties have been studied by taking into account the time evolution of particle density. It is found that the ratio of the number of incoming and outgoing lanes from the network junction as well as that of the kinetic rates substantially influences the number of stationary phases and the complexity of the phase diagram concerning the increasing number of particles in the system. The maximal current phase can persist in a fragment or the complete lanes, when the number of incoming and outgoing lanes is equal, as opposed to unequal counterparts. For lower values of the total number of particles, only low density phase is achieved in the left subsystem. All the theoretical findings are supported by extensive Monte Carlo simulations and explained using simple physical arguments.
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