Cluster dynamics in the open-boundary heterogeneous ASEPs coupled with interacting energies

Abstract

Cluster dynamics possess the promising studies in statistical physics and complexity science. While proposing physical models, applying analytical methods and exploring macroscopic properties and microscopic interactions are critical to investigate physical mechanisms of cluster dynamics. Among these physical models, totally asymmetric simple exclusion process is an important non-equilibrium statistical physics model, as it is essential enough to lattice models. Besides, it is also abbreviated as TASEP. Additionally, asymmetric simple exclusion processes, ASEPs, are derivatives, whose dynamics are based on TASEP with other nonlinear physical processes. Actually, heterogeneity of ASEPs is available to depict the real physical and engineering phenomena in a more reasonable manner. Different with previous researches, connected ASEPs are proposed here, which are constituted by two isolated ASEP coupled with a conjunction. As for each individual ASEP, its dynamics are dominated by interacting energies. Different with previous work, two completely different energies are introduced in system, which are used to describe the competition between subsystems. By analyzing complete transition processes among different particle configurations, mean-field dynamical equations are established. Phase diagrams under different energies are obtained, which yield to findings of coexistence phase of low densities, coexistence phase of high densities and coexistence phase of low and high densities. These local densities are qualitatively different. Hereafter, evolution regularities of phase diagrams obtained from local densities and currents are obtained to deeply understand physical mechanisms of complexity science. Expanded results and discussions about potential applications and fewer basic results are also presented. Expanded model with different Langmuir kinetics and internal interacting energies is established. Governing partially differential equations of the whole system are derived. Four steady stacking states of kinesin-II and OSM-3 on bovine brain tubulins affected by two different kinds of buffers are found. This work will help and promote the understanding of non-equilibrium statistical evolutions and nonlinear dynamic behaviors of such multibody system.