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Paper   IPM / Physic / 8390
School of Physics
Title:   Exact Analysis of Level-Crossing Statistics for (d + 1)-Dimensional Fluctuating Surfaces
Author(s):
 1 A. Bahraminasab 2 M. S. Movahed 3 S. D. Nasiri 4 A. A . Masoudi 5 M . Sahimi
Status:   Published
Journal: J. Stat. Phys.
No.:  6
Vol.:  124
Year:  2006
Pages:   1471-1490
Supported by:  IPM
Abstract:
We carry out an exact analysis of the average frequency ν+axi in the direction xi of positiveslope crossing of a given level xi such that, h(x,t)−h = α, of growing surfaces in spatial dimension d. Here, h(x, t) is the surface height at time t, and h is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface tension, in the time regime prior to appearance of cusp singularities (sharp valleys), as well as in the random deposition (RD) model. The total number N+ of such level-crossings with positive slope in all the directions is then shown to scale with time as td/2 for both the KPZ equation and the RD model.

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