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Exact analysis of level-crossing statistics for (d+1)-dimensional fluctuating surfaces
Bahraminasab, A ; Sharif University of Technology | 2006
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- Type of Document: Article
- DOI: 10.1007/s10955-006-9179-7
- Publisher: 2006
- Abstract:
- We carry out an exact analysis of the average frequency ν+ αxi in the direction x i of positiveslope crossing of a given level α 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 t d/2 for both the KPZ equation and the RD model. © 2006 Springer Science+Business Media, LLC
- Keywords:
- Level crossing analysis ; Surface growth
- Source: Journal of Statistical Physics ; Volume 124, Issue 6 , 2006 , Pages 1471-1490 ; 00224715 (ISSN)
- URL: https://link.springer.com/article/10.1007%2Fs10955-006-9179-7