Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces |
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| Authors: | A Bahraminasab M Sadegh Movahed S D Nasiri A A Masoudi Muhammad Sahimi |
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| Institution: | (1) International Center for Theoretical Physics, Strada Costiera 11, I-34100 Trieste, Italy;(2) Deptartment of Physics, Sharif University of Technology, Tehran, 11365-9161, Iran;(3) Institute for Studies in Theoretical Physics and Mathematics, Tehran, 19395-5531, Iran;(4) Shahid Beheshti University, Tehran, 19395-4716, Iran;(5) Department of Physics, Alzahra University, Tehran, 19834, Iran;(6) Mork Family Department of Chemical Engineering & Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA |
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| 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) − = α, of growing surfaces in spatial dimension d. Here, h(x, t) is the surface height at time t, and  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.
PACS number(s): 52.75.Rx, 68.35.Ct |
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| Keywords: | level crossing analysis surface growth |
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