T Antal et al 2008 J. Phys. A: Math. Theor. 41 465002 doi:10.1088/1751-8113/41/46/465002
Front propagation in flipping processes
T Antal1, D ben-Avraham2, E Ben-Naim3 and P L Krapivsky3,4
Show affiliationsWe study a directed flipping process that underlies the performance of the random edge simplex algorithm. In this stochastic process, which takes place on a one-dimensional lattice whose sites may be either occupied or vacant, occupied sites become vacant at a constant rate and simultaneously cause all sites to the right to change their state. This random process exhibits rich phenomenology. First, there is a front, defined by the position of the leftmost occupied site, that propagates at a nontrivial velocity. Second, the front involves a depletion zone with an excess of vacant sites. The total excess Δk increases logarithmically, Δk 
ln k, with the distance k from the front. Third, the front exhibits ageing—young fronts are vigorous but old fronts are sluggish. We investigate these phenomena using a quasi-static approximation, direct solutions of small systems and numerical simulations.
- PACS
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05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
- MSC
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82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
60G50 Sums of independent random variables; random walks
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. (See also 60G50)
82C80 Numerical methods (Monte Carlo, series resummation, etc.)
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
- Subjects
- Dates
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Issue 46 (21 November 2008)
Received 1 August 2008, in final form 3 September 2008
Published 16 October 2008
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Front propagation in flipping processes
T Antal et al 2008 J. Phys. A: Math. Theor. 41 465002
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