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arXiv · 1010.3155

Statistics of layered zigzags: a two-dimensional generalization of TASEP

Mikhail Tamm·Sergei Nechaev·Satya N. Majumdar
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Abstract

A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: i) directed motion of zigzags on a cylinder, ii) interacting interlaced TASEP layers, and iii) growing heap over 2D substrate with a restricted minimal local height gradient. We demonstrate that the coarse-grained behavior of this model is described by the two-dimensional Kardar-Parisi-Zhang equation. The coefficients of different terms in this hydrodynamic equation can be derived from the steady state flow-density curve, the so called `fundamental' diagram. A conjecture concerning the analytical form of this flow-density curve is presented and is verified numerically.

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Mikhail Tamm, Sergei Nechaev, Satya N. Majumdar. 2010-10-15. Statistics of layered zigzags: a two-dimensional generalization of TASEP. https://doi.org/10.1088/1751-8113/44/1/012002

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