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Abstract
We introduce a model of a totally asymmetric simple exclusion process (TASEP) on a tree network where the aggregate hopping rate is constant from level to level. With this choice for hopping rates the model shows the same phase diagram as the onedimensional case. The potential applications of our model are in the area of distribution networks; where a single large source supplies material to a large number of small sinks via a hierarchical network. We show that mean field theory (MFT) for our model is identical to that of the onedimensional TASEP and that this mean field theory is exact for the TASEP on a tree in the limit of large branching ratio, $b$(or equivalently large coordination number). We then present an exact solution for the two level tree (or star network) that allows the computation of any correlation function and confirm how mean field results are recovered as $b\rightarrow\infty$. As an example we compute the steadystate current as a function of branching ratio. We present simulation results that confirm these results and indicate that the convergence to MFT with large branching ratio is quite rapid.
Original language  English 

Article number  405003 
Journal  Journal of Physics A: Mathematical and Theoretical 
Volume  46 
Issue number  40 
DOIs  
Publication status  Published  3 Jun 2013 
Keywords
 condmat.statmech
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Dive into the research topics of 'An exclusion process on a tree with constant aggregate hopping rate'. Together they form a unique fingerprint.Projects
 2 Finished


Design Principles for New Soft Materials
Cates, M., Allen, R., Clegg, P., Evans, M., MacPhee, C., Marenduzzo, D. & Poon, W.
7/12/11 → 6/06/17
Project: Research