A dynamically extending exclusion process

Details A dynamically extending exclusion process A dynamically extending exclusion process

2007-07-31

arxiv.org/abs/0707.4504v3

J. Stat. Mech. (2007) P11013

Physics

Condensed Matter

Statistical Mechanics

20 pages, 12 figures

Scientific paper

10.1088/1742-5468/2007/11/P11013

An extension of the totally asymmetric exclusion process, which incorporates a dynamically extending lattice is explored. Although originally inspired as a model for filamentous fungal growth, here the dynamically extending exclusion process (DEEP) is studied in its own right, as a nontrivial addition to the class of nonequilibrium exclusion process models. Here we discuss various mean-field approximation schemes and elucidate the steady state behaviour of the model and its associated phase diagram. Of particular note is that the dynamics of the extending lattice leads to a new region in the phase diagram in which a shock discontinuity in the density travels forward with a velocity that is lower than the velocity of the tip of the lattice. Thus in this region the shock recedes from both boundaries.

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