http://arxiv.org/abs/1508.01409

We use crossing statistics and its generalization to determine the anisotropic direction imposed on a stochastic fields in $(2+1)$Dimension. This approach enables us to examine not only the rotational invariance of morphology but also we can determine the Gaussianity of underlying stochastic field in various dimensions. Theoretical prediction of up-crossing statistics (crossing with positive slope at a given threshold $\alpha$ of height fluctuation), $\nu^+_{\diamond}(\alpha)$, and generalized roughness function, $N^{\diamond}_{tot}(q)$, for correlation length ($\xi_{\diamond}$) and/with scaling exponent ($\gamma_{\diamond}$) anisotropies are calculated. The strategy to examine the anisotropy nature and to determine its direction is as follows: we consider a set of normal axes, and sign them $||$ (parallel) and $ \bot$ (normal) with respect to unknown anisotropic direction. Then we determine $\nu_{\diamond}^+ (\alpha)$ and $N^{\diamond}_{tot}(q)$ in both directions. The directional dependency of difference between computed results in mentioned directions are clarify. Finally we systematically recognize the anisotropy direction at $3\sigma$ confidence interval using P-value approach. In order to distinguish between nature of anisotropies, after applying a typical method in determining the scaling exponents in both mentioned directions with respect to the recognized anisotropy direction using up-crossing statistics, the kind and the ratio of correlation length anisotropy are specified. Our algorithm can be mounted with a simple software on various instruments for surface analysis, such as AFM, STM and etc.

M. Nezhadhaghighi, S. Movahed, T. Yasseri, et. al.

Fri, 7 Aug 15

35/51

Comments: 14 pages and 11 figures