Power series solution of the inhomogeneous exclusion process.
Power series solution of the inhomogeneous exclusion process.
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DOI：
10.1103/physreve.97.052139
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发表时间：
2018-03
期刊：
影响因子：
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通讯作者：
J. Szavits-Nossan;M. Romano;L. Ciandrini
中科院分区：
文献类型：
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作者：
J. Szavits-Nossan;M. Romano;L. Ciandrini
我们开发了一个幂级数方法的非均匀的一维完全不对称的简单排斥过程（TASEP）的非平衡定态的接触与两个粒子水库和网站依赖的跳跃率在散装。幂级数是在入口或出口率与水库的颗粒交换，相应的粒子流的分析计算的立方项的入口或出口率，分别。我们还展示了如何计算高阶项使用组合对象称为杨tableaux。我们的研究结果解决了长期悬而未决的问题，找到确切的非平衡稳态的非均匀TASEP。这些发现特别与mRNA翻译的建模相关，其中翻译起始速率（对应于TASEP中的进入速率）通常很小。
We develop a power series method for the nonequilibrium steady state of the inhomogeneous one-dimensional totally asymmetric simple exclusion process (TASEP) in contact with two particle reservoirs and with site-dependent hopping rates in the bulk. The power series is performed in the entrance or exit rates governing particle exchange with the reservoirs, and the corresponding particle current is computed analytically up to the cubic term in the entry or exit rate, respectively. We also show how to compute higher-order terms using combinatorial objects known as Young tableaux. Our results address the long outstanding problem of finding the exact nonequilibrium steady state of the inhomogeneous TASEP. The findings are particularly relevant to the modeling of mRNA translation in which the rate of translation initiation, corresponding to the entrance rate in the TASEP, is typically small.