How winding is the coast of Britain? Conformal invariance of rocky shorelines

Geophysical Research Letters

Volumn 35, Issue 3, 2008, Pages

  Boffetta, G ^a,b,c   Celani, A ^c,d   Dezzani, D ^a   Seminara, A ^d,e  

^a UNIVERSITY OF TURIN   (Italy)

^b CENTER FOR NONLINEAR STUDIES   (United States)

^c CNR   (Italy)

^d INSTITUT NON LINÉAIRE DE NICE   (France)

^e UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COASTAL ZONES; EROSION; FRACTAL DIMENSION; MARINE POLLUTION; MATHEMATICAL MODELS;

CONFORMAL INVARIANCE; ROCKY SHORELINES;

SHORE PROTECTION;

COASTAL EROSION; SHORELINE; SPATIAL DISTRIBUTION;

EID: 41949126576     PISSN: 00948276     EISSN: None     Source Type: Journal    
DOI: 10.1029/2007GL033093     Document Type: Article

References (25)

1. Bauer, M., and D. Bernard (2006), 2D growth processes: SLE and Loewner chains, Phys. Rep., 432, 115.
2. Belavin, A. A., A. M. Polyakov, and A. A. Zamolodchikov (1985), Conformal field theory, Nucl. Phys. B, 241, 333.
3. Bernard, D., G. Boffetta, A. Celani, and G. Falkovich (2006), Conformal invariance in two-dimensional turbulence, Nature Phys., 2, 124.
4. Bernard, D., G. Boffetta, A. Celani, and G. Falkovich (2007), Inverse turbulent cascades and conformally invariant curves, Phys. Rev. Lett., 98, 024501, doi:10.1103/PhysRevLett.98.024501.
5. Bettelheim, E., I. Rushkin, I. A. Gruzberg, and P. Wiegmann (2005), Harmonic measure of critical curves, Phys. Rev Lett., 95, 170602, doi:10.1131/PhysRevLett.95.170602.
6. Cardy, J. (2005), SLE for theoretical physicists, Ann. Phys., 318, 81.
7. Carter, R. W. G., and C. D. Woodroffe (1994), Coastal Evolution: Late Quaternaty Shoreline Morphodynamics, Cambridge Univ. Press, Cambridge, U. K.
8. Duplantier, B. (2000), Conformally invariant fractals and potential theory, Phys. Rev. Lett, 84, 1363.
9. Duplantier, B., and I. A. Binder (2002), Harmonic measure and winding of conformally invariant curves, Phys. Rev. Lett., 89, 264101, doi:10.1093/imrn/rnm060.
10. Duplantier, B., and H. Saleur (1988), Winding-angle distributions of two-dimensional self-avoiding walks from conformal invariance, Phys. Rev. Lett., 60, 2343.
11. Goodchild, M. F., and D. M. Mark (1987), The fractal nature of geographic phenomena, Ann. Assoc. Am. Geogr., 77, 265.
12. Grassberger, P., and I. Procaccia (1983), Measuring the strangeness of strange attractors, Physica D, 9, 189.
13. Grossman, T., and A. Aharony (1986), Structure and perimeters of percolation clusters, J. Phys. A, 19, L745, doi:10.1088/0305-4470/ 19/12/009.
14. Lawler, G. F., O. Schramm, and W. Werner (2004), On the scaling limit of planar self-avoiding walk, Proc. Symp. Pure Math., 72, 339.
15. Mandelbrot, B. (1967), How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science, 156, 636.
16. Marshall, J., E. Shuckburgh, H. Jones, and C. Hill (2006), Estimates and implications of surface eddy diffusivity in the Southern Ocean derived from tracer transport, J. Phys. Oceanogr., 36, 1806.
17. Ottino, J. M. (1989), The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge Univ. Press, Cambridge, U. K.
18. Peterson, C. H., et al. (2003), Long-term ecosystem response to the Exxon Valdez oil spill, Science, 302, 2082.
19. Polyakov, A. M. (1970), Conformal symmetry of critical fluctuations, JETP Lett., 12, 381.
20. Saleur, H., and B. Duplantier (1987), Exact determination of the percolation hull exponent in two dimensions, Phys. Rev. Lett., 58, 2325.
21. Sapoval, B., A. Baldassarri, and A. Gabrielli (2004), Self-stabilized fractality of seacoasts through damped erosion Phys, Rev. Lett., 93, 098501.
22. Schramm, O. (2006), Conformally invariant scaling limits (an overview and a collection of problems), in Proceedings of the International Congress of Mathematicians, Madrid, August 22-30, 2006, edited by M. Sans-Sole et al, Eur. Math. Soc., Zurich, Switzerland. (Available at http://arxiv.org/abs/math/0602151.)
23. Stauffer, D., and A. Aharony (1991), Introduction to Percolation Theory, Taylor and Francis, London.
24. Wessel, P., and W. H. F. Smith (1996), A global, self-consistent, hierarchical, high-resolution shoreline database, J. Geophys. Res., 101, 8741-8743.
25. Wieland, B., and D. B. Wilson (2003), Winding angle variance of Fortuin-Kasteleyn contours, Phys. Rev. E, 68, 056101, doi:10.1103/ PhysRevE.68. 056101.