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Watersheds are schramm-loewner evolution curves

Daryaei, E ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevLett.109.218701
  3. Publisher: 2012
  4. Abstract:
  5. We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner evolution (SLE) curves, being described by one single parameter κ. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLEκ, with κ=1.734±0.005, being the only known physical example of an SLE with κ<2. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore, it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic conformal field theory with a central charge c-7/2
  6. Keywords:
  7. Conformal invariance ; Continuum limits ; Dual model ; Evolution curve ; Logarithmic conformal field theories ; Numerical evaluations ; Single parameter ; Landforms ; Watersheds
  8. Source: Physical Review Letters ; Volume 109, Issue 21 , 2012 ; 00319007 (ISSN)
  9. URL: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.218701