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Abstract
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 meanfield 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.
Original language  English 

Article number  P11013 
Pages (fromto)   
Number of pages  19 
Journal  Journal of Statistical Mechanics: Theory and Experiment 
DOIs  
Publication status  Published  Nov 2007 
Keywords
 driven diffusive systems (theory)
 stochastic particle dynamics (theory)
 molecular motors (theory)
 MOLECULAR MOTORS
 STEADYSTATES
 GROWTH
 MODEL
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 1 Finished

Edinburgh Soft Matter and Statistical Physics Group: Programme Grant
Cates, M., Ackland, G., Egelhaaf, S., Evans, M., Poon, W. & Pusey, P.
1/10/03 → 31/03/08
Project: Research