One-dimensional discrete aggregation-fragmentation model.

We study here one-dimensional model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time kinetics of the generalized totally asymmetric simple exclusion process (gTASEP) on open chains. The gTASEP is essentially the ordinary TASEP with backward-ordered sequential update (BSU), however, equipped with two hopping probabilities: p and p_{m}. The second modified probability p_{m} models a special kinematic interaction between the particles of a cluster in addition to the simple hard-core exclusion interaction, existing in the ordinary TASEP. We focus on the nonequilibrium stationary properties of the gTASEP in the generic case of attraction between the particles of a cluster. In this case the particles of a cluster have higher chance to stay together than to split, thus producing higher throughput in the system. We explain how the topology of the phase diagram in the case of irreversible aggregation, occurring when the modified probability equals unity, changes sharply to the one, corresponding to the ordinary TASEP with BSU, as soon as the modified probability becomes less than unity and aggregation-fragmentation of clusters appears. We estimate various physical quantities in the system and determine the parameter-dependent injection and ejection critical values by extensive computer simulations. With the aid of random walk theory, supported by the Monte Carlo simulations, the properties of the phase transitions between the three stationary phases are assessed.