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

ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland

E-mail Address: [email protected]

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K. J. Schrenk

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK

E-mail Address: [email protected]

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N. A. M. Araújo

Corresponding author.

Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal

Centro de Física Teórica e Computacional, Universidade de Lisboa, 1749-016 Lisboa, Portugal

E-mail Address: [email protected]

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and

H. J. Herrmann

ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland

Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil

E-mail Address: [email protected]

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https://doi.org/10.1142/S0129183118500080Cited by:1

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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:

PACS: 89.75.Da, 64.60.al, 91.10.Jf

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Published: 1 February 2018

- Cited By 1
  - Schramm-Loewner evolution and perimeter of percolation clusters of correlated random landscapes
    C. P. de Castro, M. Luković, G. Pompanin, R. F. S. Andrade and H. J. Herrmann
    27 March 2018 | Scientific Reports, Vol. 8, No. 1
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Vol. 29, No. 01
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Received 10 November 2017

Accepted 20 January 2018
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Schramm–Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes

Abstract

References

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