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Paper   IPM / P / 8390
School of Physics
  Title:   Exact Analysis of Level-Crossing Statistics for (d + 1)-Dimensional Fluctuating Surfaces
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
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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