Motivated by the significant effect of particle–particle interactions on the driven stochastic transport system, we examine how interacting particles control the lattice polymerization and depolymerization dynamics under the restricted supply of involved resources. We carried out a theoretical analysis based on the simple mean-field and cluster mean-field theory to predict the fundamental role of interactions on the steady-state length dynamics. It has been detected that there is a strong correlation between the lattice length dynamics and the concentration of the total number of lattice sites in the reservoir. For lower and higher values of available resources, depolymerization and polymerization process dominates the lattice dynamics, respectively, while for intermediate values of resources we observe a competition between polymerization and depolymerization kinetics. Further, it is examined that for a specific range of interaction energy E , the system remains in low density phase, on the contrary, for its significantly higher value, the system transits to high-density phase. In contrast to the high density phase, it is observed that in low density phase, lattice length decreases with an increase in interaction strength. Finally, the theoretical outcomes are validated with extensive Monte Carlo simulations.

中文翻译：

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相互作用粒子和有限资源在晶格长度动力学调节中的作用

受粒子 - 粒子相互作用对驱动随机传输系统的显着影响的启发，我们研究了相互作用的粒子如何在所涉及资源供应受限的情况下控制晶格聚合和解聚动力学。我们基于简单平均场和聚类平均场理论进行了理论分析，以预测相互作用对稳态长度动力学的基本作用。已经检测到，晶格长度动力学与储层中晶格位点总数的浓度之间存在很强的相关性。对于较低和较高的可用资源值，解聚和聚合过程分别支配着晶格动力学，而对于资源的中间值，我们观察到聚合和解聚动力学之间的竞争。此外，检查了对于特定范围的相互作用能 E ，系统保持在低密度阶段，相反，对于其显着更高的值，系统过渡到高密度阶段。与高密度相相反，观察到在低密度相中，晶格长度随着相互作用强度的增加而减小。最后，理论结果通过广泛的蒙特卡罗模拟得到验证。观察到在低密度相中，晶格长度随着相互作用强度的增加而减小。最后，理论结果通过广泛的蒙特卡罗模拟得到验证。观察到在低密度相中，晶格长度随着相互作用强度的增加而减小。最后，理论结果通过广泛的蒙特卡罗模拟得到验证。