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- Title
Exact Analysis of Level-Crossing Statistics for ( d+1)-Dimensional Fluctuating Surfaces.
- Authors
Bahraminasab, A.; Movahed, M. Sadegh; Nasiri, S. D.; Masoudi, A. A.; Sahimi, Muhammad
- Abstract
We carry out an exact analysis of the average frequency ν+α xi in the direction x i of positiveslope crossing of a given level α such that, h( x, t) − $$\bar{h}$$ = α, of growing surfaces in spatial dimension d. Here, h( x, t) is the surface height at time t, and $$\bar{h}$$ 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 t d/2 for both the KPZ equation and the RD model.
- Subjects
LEVEL-crossing spectroscopy; NUMERICAL solutions to integral equations; GAUSSIAN processes; FOKKER-Planck equation; SURFACES (Physics); CUSP forms (Mathematics)
- Publication
Journal of Statistical Physics, 2006, Vol 124, Issue 6, p1471
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-006-9179-7