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Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces

A. Bahraminasab·M. Sadegh Movahed·S. D. Nassiri·A. A. Masoudi·Muhammad Sahimi
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Abstract

We carry out an exact analysis of the average frequency $ν_{αx_i}^+$ in the direction $x_i$ of positive-slope crossing of a given level $α$ such that, $h({\bf x},t)-\bar{h}=α$, of growing surfaces in spatial dimension $d$. Here, $h({\bf x},t)$ 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.

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A. Bahraminasab, M. Sadegh Movahed, S. D. Nassiri, A. A. Masoudi, Muhammad Sahimi. 2006-11-13. Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces. https://doi.org/10.1007/s10955-006-9179-7

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