Schramm–Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes

N. Posé (), K. J. Schrenk (), N. A. M. Araújo and H. J. Herrmann
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N. Posé: ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
K. J. Schrenk: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
N. A. M. Araújo: Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal4Centro de Física Teórica e Computacional, Universidade de Lisboa, 1749-016 Lisboa, Portugal
H. J. Herrmann: ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland5Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 01, 1-10

Abstract: Real landscapes exhibit long-range height–height correlations, which are quantified by the Hurst exponent H. We give evidence that for negative H, in spite of the long-range nature of correlations, the statistics of the accessible perimeter of isoheight lines is compatible with Schramm–Loewner evolution curves and therefore can be mapped to random walks, their fractal dimension determining the diffusion constant. Analytic results are recovered for H=−1 and H=0 and a conjecture is proposed for the values in between. By contrast, for positive H, we find that the random walk is not Markovian but strongly correlated in time. Theoretical and practical implications are discussed.

Keywords: Isoheight lines; accessible perimeter; Schramm–Loewner evolution (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183118500080

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