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

  • Posé, N. ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
  • Schrenk, K. J. Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
  • Araújo, N. A. M. Centro de Física Teórica e Computacional, Universidade de Lisboa, 1749-016 Lisboa, Portugal
  • Herrmann, H. J. Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil
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  • 2018-2-28
Published in:
  • International Journal of Modern Physics C. - World Scientific Pub Co Pte Lt. - 2018, vol. 29, no. 01, p. 1850008
Mathematical Physics
Computational Theory and Mathematics
General Physics and Astronomy
Statistical and Nonlinear Physics
Computer Science Applications
English Real landscapes exhibit long-range height–height correlations, which are quantified by the Hurst exponent [Formula: see text]. We give evidence that for negative [Formula: see text], 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 [Formula: see text] and [Formula: see text] and a conjecture is proposed for the values in between. By contrast, for positive [Formula: see text], we find that the random walk is not Markovian but strongly correlated in time. Theoretical and practical implications are discussed.
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  • English
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green
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https://folia.unifr.ch/global/documents/283919
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