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

Author

Listed:
  • 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)

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.

Suggested Citation

  • N. Posé & K. J. Schrenk & N. A. M. Araújo & H. J. Herrmann, 2018. "Schramm–Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-10, January.
    • Handle: RePEc:wsi:ijmpcx:v:29:y:2018:i:01:n:s0129183118500080
    DOI: 10.1142/S0129183118500080
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