The transverse correlation length for randomly rough surfaces |
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Authors: | A A Maradudin T Michel |
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Institution: | (1) Department of Physics and Institute for Surface and Interface Science, University of California, 92717 Irvine, California |
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Abstract: | It is shown by numerical simulations for a random, one-dimensional surface defined by the equationx
3=(x
1), where the surface profile function (x
1) is a stationary, stochastic, Gaussian process, that the transverse correlation lengtha of the surface roughness is a good measure of the mean distance d between consecutive peaks and valleys on the surface. In the case that the surface height correlation function (x
1)(x
1)/2(x
1)=W (|x
1–x
1|) has the Lorentzian formW(|x
1|)=a
2/(x
1
2
+a
2) we find that d=0.9080a; when it has the Gaussian formW(|x
1|)=exp(–x
1
2
/a
2), we find that d=1.2837a; and when it has the nonmonotonic formW(|x
1|)=sin(x
1/a)/(x
1/a), we find that d=1.2883a. These results suggest that d is larger, the faster the surface structure factorg(|Q|) the Fourier transform ofW(|x
1|)] decays to zero with increasing |Q|. We also obtain the functionP(itx
1), which is defined in such a way that, ifx
1=0 is a zero of (x
1),P(x
1)dx
1 is the probability that the nearest zero of (x
1) for positivex
1 lies betweenx
1 andx
1+dx
1. |
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Keywords: | Transverse correlation length rough surfaces |
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