Statistical topography. I. Fractal dimension of coastlines and number-area rule for Islands

M. B. Isichenko; J. Kalda

doi:10.1007/bf01238814

journal article Sep 01, 1991

Statistical topography. I. Fractal dimension of coastlines and number-area rule for Islands

M. B. Isichenko J. Kalda

Journal of Nonlinear Science Vol. 1 No. 3 pp. 255-277 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf01238814

Topics

No keywords indexed for this article. Browse by subject →

References

29

[1]

M. B. Isichenko, J. Kalda, E. B. Tatarinova, O. V. Tel'kovskaya, and V. V. Yankov, ?Diffusion in a medium with vortex flow,? Zh. Eksp. Teor. Fiz.96, 913 (1989) [Sov. Phys. JETP69, 517 (1989)].

[2]

A. V. Gruzinov, M. B. Isichenko, and J. Kalda, ?Two-dimensional turbulent diffusion,? Zh. Eksp. Teor. Fiz.97, 476 (1990) [Sov. Phys. JETP70, 263 (1990)].

[3]

How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension

Benoit Mandelbrot

Science 1967 10.1126/science.156.3775.636

[4]

B. B. Mandelbrot, ?Stochastic models for the Earth's relief, the shape and fractal dimensions of the coastlines, and the number-area rule for islands,? Proc. Natnl. Acad. Sci. (USA)72, 3825 (1975). 10.1073/pnas.72.10.3825

[5]

B. B. Mandelbrot,The Fractal Geometry of Nature (W. H. Freeman, San Francisco, 1983).

[6]

Special Issue: Essays in Honor of Benoit B. Mandelbrot, Physica D38 (1989).

[7]

R. Zallen and H. Scher, ?Percolation on a continuum and the localization-delocalization transition in amorphous semiconductors,? Phys. Rev.B4, 4471 (1971). 10.1103/physrevb.4.4471

[8]

J. M. Ziman,Models of Disorder (Cambridge University Press, New York, 1979).

[9]

S. A. Trugman, ?Percolation, localization, and quantum Hall effect,? Phys. Rev.B27, 7539 (1983). 10.1103/physrevb.27.7539

[10]

A. S. Kingsep, K. V. Chukbar, and V. V. Yankov, ?Electron magnetohydrodynamics,? inReviews of Plasma Physics, B. B. Kadomtsev, ed. (Consultants Bureau, New York, 1990), vol. 16, p. 243.

[11]

M. B. Isichenko and J. Kalda, ?Anomalous resistance of randomly inhomogeneous Hall media,? Zh. Eksp. Teor. Fiz.99, 224 (1991).

[12]

M. S. Longuet-Higgins, ?Reflection and refraction at a random moving surface,? J. Opt. Soc. Am.50, 838 (1960). 10.1364/josa.50.000838

[13]

Scaling theory of percolation clusters

D. Stauffer

Physics Reports 1979 10.1016/0370-1573(79)90060-7

[14]

S. Havlin and D. Ben-Avraham, ?Diffusion in disordered media,? Adv. Phys.36, 695 (1987). 10.1080/00018738700101072

[15]

B. I. Shklovskii and A. L. Efros,Electronic Properties of Doped Semiconductors (Springer-Verlag, New York, 1984). 10.1007/978-3-662-02403-4

[16]

A. Weinrib, ?Percolation threshold of a two-dimensional continuum system,? Phys. Rev.B26, 1352 (1982). 10.1103/physrevb.26.1352

[17]

P. Pfeuty and G. Toulouse,Introduction to the Renormalization Group and to Critical Phenomena (Wiley, New York, 1977).

[18]

Ya. B. Zeldovich, ?Percolation properties of a random two-dimensional stationary magnetic field,? Pis'ma v Zh. Eksp. Teor. Fiz.38, 51 (1983) [JETP Lett.38, 57 (1983)].

[19]

M. B. Isichenko and J. Kalda, ?Statistical topography. II. Two-dimensional transport of a passive scalar,? J. Nonlinear Sci.1(4), (1991), to appear. 10.1007/bf02429846

[20]

M. P. M. den Nijs, ?A relation between the temperature exponents of the eight-vertex and 9-state Potts model,? J. Phys.A12, 1857 (1979).

[21]

H. Saleur and B. Duplantier, ?Exact determination of the percolation hull exponent in two dimensions,? Phys. Rev. Lett.58, 2325 (1987). 10.1103/physrevlett.58.2325

[22]

B. Sapoval, M. Rosso, and J. F. Gouyet, ?The fractal nature of a diffusion front and the relation to percolation,? J. Physique Lett.51, 2048 (1985).

[23]

A. Weinrib, ?Long-range correlated percolation,? Phys. Rev.B29, 387 (1984). 10.1103/physrevb.29.387

[24]

I. M. Sokolov, ?Dimensionalities and other geometric critical exponents in percolation theory,? Usp. Fiz. Nauk150, 221 (1986) [Sov. Phys. Usp.29, 924 (1986)]. 10.3367/ufnr.0150.198610b.0221

[25]

The Map of Estonia 1:300 000 (Teede Ministeerium, Tallinn, 1931).

[26]

Noukogude Eesti [Soviet Estonia] (Valgus, Tallinn, 1978).

[27]

V. E. Zakharov, ?Kolmogorov spectra of weak turbulence,? inBasic Plasma Physics, A. A. Galeev and R. N. Sudan, eds. (North-Holland, New York, 1984), Vol. II, p. 3.

[28]

The Quantum Hall Effect, R. E. Prange and S. M. Girvin, eds. (Springer-Verlag, New York, 1990).

[29]

A. Weinrib and B. I. Halperin, ?Critical phenomena in systems with long-range correlated quenched disorder,? Phys. Rev.B27, 413 (1983). 10.1103/physrevb.27.413

Metrics

39

Citations

29

References

Details

Published: Sep 01, 1991
Vol/Issue: 1(3)
Pages: 255-277
License: View

Authors

Cite This Article

M. B. Isichenko, J. Kalda (1991). Statistical topography. I. Fractal dimension of coastlines and number-area rule for Islands. Journal of Nonlinear Science, 1(3), 255-277. https://doi.org/10.1007/bf01238814

Statistical topography. I. Fractal dimension of coastlines and number-area rule for Islands

You May Also Like