One-dimensional discrete aggregation-fragmentation model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Non-equilibrium Systems

Background:

• The ordinary totally asymmetric simple exclusion process (TASEP) models particle systems with hard-core exclusion.
• The generalized TASEP (gTASEP) introduces modified hopping probabilities to model cluster interactions.
• Understanding non-equilibrium stationary properties is crucial for complex particle systems.

Purpose of the Study:

• To analyze the aggregation and fragmentation dynamics of particle clusters in a one-dimensional gTASEP model.
• To investigate the impact of modified hopping probabilities on system throughput and phase diagrams.
• To characterize the phase transitions between different stationary states.

Main Methods:

• Utilizing stochastic discrete-time kinetics for the gTASEP on open chains.
• Employing backward-ordered sequential update (BSU) with two hopping probabilities (p and p_m).
• Conducting extensive computer simulations (Monte Carlo) and applying random walk theory.

Main Results:

• The gTASEP with attractive cluster interactions enhances system throughput.
• The phase diagram topology shifts significantly when the modified probability (p_m) drops below unity, introducing aggregation-fragmentation.
• Critical values for injection and ejection were determined, and properties of phase transitions were assessed.

Conclusions:

• The modified kinematic interaction in gTASEP fundamentally alters system behavior compared to ordinary TASEP.
• The study provides insights into the non-equilibrium phase transitions driven by cluster dynamics.
• The findings are supported by both theoretical analysis and extensive simulations.