Jamming transition in a homogeneous one-dimensional system: The bus route model
Jamming transition in a homogeneous one-dimensional system: The bus route model
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DOI：
10.1103/physreve.58.1404
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发表时间：
1998-08-01
影响因子：
2.4
通讯作者：
Cates, ME
中科院分区：
文献类型：
--
作者：
O'Loan, OJ;Evans, MR;Cates, ME
我们提出了一个驱动扩散模型，我们称之为巴士路线模型。该模型被定义在一个一维晶格上，每个晶格点有两个二元变量，其中一个是保守的（“巴士”），另一个是非保守的（“乘客”）。公共汽车被驱动在一个首选的方向，并放慢了存在的乘客谁到达率λ。我们通过模拟、启发式论证和均值持有理论来研究该模型。所有这些方法都提供了强有力的证据，表明随着总线密度的增加，在非均匀“堵塞”阶段（总线聚在一起）和均匀阶段之间存在过渡。然而，我们认为，严格的相变只存在于极限λ-> 0。对于小λ，我们认为，过渡是由一个突然的交叉，是指数急剧1/λ。我们还研究了在拥挤的制度巴士之间的差距粗化。另一种解释的模型中，巴士和巴士本身之间的空间互换。这描述了一个颗粒系统，其流动性随着静止时间的延长而降低，并且可以为凝胶或粘性材料沿着管道的流动提供模型。
We present a driven diffusive model that we call the bus route model. The model is defined on a one dimensional lattice, with each lattice site having two binary variables, one of which is conserved (''buses'') and one of which is nonconserved ("passengers"). The buses are driven in a preferred direction and are slowed down by the presence-of passengers who arrive with rate lambda. We study the model by simulation, heuristic argument, and a mean-held theory. All these approaches provide strong evidence of a transition between an inhomogeneous "jammed" phase (where the buses bunch together) and a homogeneous phase as the bus density is increased. However, we argue that a strict phase transition is present only in the limit lambda --> 0. For small lambda, we argue that the transition is replaced by an abrupt crossover that is exponentially sharp in 1/lambda. We also study the coarsening of gaps between buses in the jammed regime. An alternative interpretation of the model is given in which the spaces between buses and the buses themselves are interchanged. This describes a system of particles whose mobility decreases the longer they have been stationary and could provide a model for, say, the flow of a gelling or sticky material along a pipe.