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We exclude those situations in which the boundary conditions are such that the steady state profile has macroscopic regions of different slopes, e.g., as in a heap of sand with open boundary conditions at both ends in which the present discussions apply to each half of the pile separately. Also are excluded systems with quenched disorder, e.g., as in G. Tripathy and M. Barma, Phys. Rev. Lett. 78, 3039 (1997).
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85069020293
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note
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xJ (z,x,t) = 0, with the diffusion constant diverging as at z = 3/2 for the LLS. However, for different models the critcal slope would be different from 3/2, and hence it is more natural to write the equation for ρ with the singularity always at ρ = 0.
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note
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n(x,t) as for the spatially averaged ones.
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23
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note
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1ρ+⋯.
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24
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85069010220
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J. G. Oliveira, J.F.F. Mendes, and G. Tripathy (unpublished)
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J. G. Oliveira, J.F.F. Mendes, and G. Tripathy (unpublished).
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25
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85069016093
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note
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2 in the range of system sizes we study.
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