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Aggregation-Fragmentation of Clusters in the Framework of gTASEP with Attraction Interaction
Physics of Particles and Nuclei ( IF 0.4 ) Pub Date : 2021-04-12 , DOI: 10.1134/s1063779621020027
N. Zh. Bunzarova , N. C. Pesheva

Abstract

This article provides summary of some of our results, concerning a model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time discrete-space kinetics of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) with open boundaries. The model in essence is the ordinary TASEP with backward ordered sequential update with special kinematic interaction added, i.e., it has a second modified hopping probability \(~{{p}_{m}}\) for particles in a cluster in addition to the standard hopping probability \(p\). We consider separately the two cases of attraction interaction (\(p\) < \(~{{p}_{m}}\)): (1) the limiting case of irreversible aggregation (\({{p}_{m}}\) = 1); and (2) the generic case of attraction, when \(~p\) < \(~{{p}_{m}}\) < 1 (then aggregation and fragmentation of clusters is allowed). We put special emphasis on the use of random walk theory in the study of gTASEP. It is applied to study the inter-cluster gaps time evolution, which helps to assess the properties of the nonequilibrium stationary phases of the system and the phase transitions between them. Theoretical conclusions are in agreement with the Monte Carlo simulations.



中文翻译:

具有吸引力相互作用的gTASEP框架中簇的聚集-片段化

摘要

本文提供了一些我们的结果的总结,涉及遵循服从开放边界的广义完全不对称简单排除过程(gTASEP)的随机离散时间离散空间动力学的粒子簇的聚集和破碎模型。本质上,该模型是普通的TASEP,具有向后顺序更新并添加了特殊的运动学交互作用,即,除了具有集群中的粒子之外,它还具有第二个修改的跳跃概率\(〜{{p} _ {m}} \)标准跳变概率\(p \)。我们分别考虑两种吸引相互作用的情况(\(p \) < \(〜{{{p} _ {m}} \))):(1)不可逆聚集的极限情况(\({{p} _ { m}} \) =1); (2)当\(〜p \) < \(〜{{{p} _ {m}} \)\) <1(然后允许群集的聚集和碎片化时的吸引的一般情况。在gTASEP的研究中,我们特别强调了随机游走理论的使用。它被用于研究集群间间隙的时间演化,这有助于评估系统的非平衡固定相的性质以及它们之间的相变。理论结论与蒙特卡洛模拟相符。

更新日期:2021-04-12
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