Asymmetric exclusion processes with fixed resources: Reservoir crowding and steady states,Physical Review E

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Asymmetric exclusion processes with fixed resources: Reservoir crowding and steady states
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-07 , DOI: 10.1103/physreve.104.034106
Astik Haldar ₁ , Parna Roy ₂ , Abhik Basu ₁

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We study the reservoir crowding effect by considering the nonequilibrium steady states of an asymmetric exclusion process (TASEP) coupled to a reservoir with fixed available resources and dynamically coupled entry and exit rate. We elucidate how the steady states are controlled by the interplay between the coupled entry and exit rates, both being dynamically controlled by the reservoir population, and the fixed total particle number in the system. The TASEP can be in the low-density, high-density, maximal current, and shock phases. We show that such a TASEP is different from an open TASEP for all values of available resources: here the TASEP can support only localized domain walls for any (finite) amount of resources that do not tend to delocalize even for large resources, a feature attributed to the form of the dynamic coupling between the entry and exit rates. Furthermore, in the limit of infinite resources, in contrast to an open TASEP, the TASEP can be found in its high-density phase only for any finite values of the control parameters, again as a consequence of the coupling between the entry and exit rates.

中文翻译：

具有固定资源的不对称排斥过程：水库拥挤和稳态

我们通过考虑与具有固定可用资源和动态耦合进入和退出率的储层耦合的非对称排斥过程 (TASEP) 的非平衡稳态来研究储层拥挤效应。我们阐明了如何通过耦合进入和退出速率之间的相互作用来控制稳态，两者都由储层数量和系统中固定的总粒子数动态控制。TASEP 可以处于低密度、高密度、最大电流和冲击阶段。我们证明了这样的 TASEP 不同于对所有人开放的 TASEP可用资源的价值：在这里，TASEP 只能支持任何（有限）数量的资源的局部畴壁，即使对于大资源也不会去局部化，这一特征归因于进入率和退出率之间的动态耦合形式。此外，在无限资源的限制下，与开放的 TASEP 相比，TASEP 只能在控制参数的任何有限值的高密度阶段中找到，这也是进入和退出率之间耦合的结果.

更新日期：2021-09-07

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