{"paper":{"title":"Crossing Statistics of Anisotropic Stochastic Surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM","cond-mat.mtrl-sci","cond-mat.stat-mech"],"primary_cat":"physics.comp-ph","authors_text":"M. Ghasemi Nezhadhaghighi, S. M. S. Movahed, S. M. Vaez Allaei, T. Yasseri","submitted_at":"2015-08-06T14:06:58Z","abstract_excerpt":"In this paper, we propose crossing statistics and its generalization, as a new framework to characterize the anisotropy in a 2D field, e.g. height on a surface, extendable to higher dimensions. By measuring $\\nu^+$, the number of up-crossing (crossing points with positive slope at a given threshold of height ($\\alpha$)), and $N_{tot}$ (the generalized roughness function), it is possible to distinguish the nature of anisotropy, rotational invariance and Gaussianity of any given surface. For the case of anisotropic correlated self- or multi-affine surfaces (even with different correlation length"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01409","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}