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Models of Fractal River Basins

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Abstract

Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following nontrivial power laws in experimentally relevant distributions. Previous numerical estimates on the critical exponents, when existing, are confirmed and superseded. A physical motivation for both models in the present framework is also discussed.

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REFERENCES

  1. D. G. Tarboton, R. L. Bras, and I. Rodriguez-Iturbe, Water Resour. Res. 24:1317 (1988); D. Lavallée, S. Lovejoy and D. Schertzer, Fractals in Geography, N. S. Lam and L. De Cola, eds. (Prentice Hall, Englewood Cliffs, 1993), 159; I. Rodriguez-Iturbe, M. Marani, R. Rigon, A. Rinaldo, Water Resour. Res. 30:3531 (1994); D. R. Montgomery and W. E. Dietrich, Nature 336:232 (1988); Science 255:826 (1992); S. P. Breyer and R. S. Snow, Geomorphology 5:143 (1992).

    Google Scholar 

  2. C. P. Stark, Nature 352:423 (1991).

    Google Scholar 

  3. S. S. Manna and B. Subramanian, Phys. Rev. Lett. 76:3460 (1996).

    Google Scholar 

  4. I. Rodriguez-Iturbe, A. Rinaldo, R. Rigon, R. L. Bras, E. Ijjasz-Vasquez, A. Marani, Water Resour. Res. 28:1095 (1992); R. Rigon, A. Rinaldo, I. Rodriguez-Iturbe, E. Ijjasz-Vasquez, R. L. Bras, Water Resour. Res. 29:1980 (1993); A. Rinaldo, I. Rodriguez-Iturbe. R. Rigon, E. Ijjasz-Vasquez and R. L. Bras, Phys. Rev. Lett. 70:822 (1993); for earlier studies linking optimization principles to drainage networks, see A. D. Howard, Water Res. Res. 7:863 (1971); 26:2107 (1990) and references therein.

    Google Scholar 

  5. A. Maritan, F. Colaiori, A. Flammini, M. Cieplak and J. R. Banavar, Science 272:984 (1996); F. Colaiori, A. Flammini, A. Maritan and J. R. Banavar, Phys. Rev. E 55:1298 (1997).

    Google Scholar 

  6. Lattice models of river basin evolution are discussed, eg., by S. Kramer and M. Marder, Phys. Rev. Lett. 68:205 (1992); R. L. Leheny and S. R. Nagel, Phys. Rev. Lett. 71:1470 (1993).

    Google Scholar 

  7. T. Sun, P. Meakin and T. Jøssang, Phys. Rev. E 49:4865 (1994); 51:5353 (1995); Water Res. Res. 30:2599 (1994); P. Meakin, J. Feder and T. Jøssang, Physica A 176:409 (1991).

    Google Scholar 

  8. A. Maritan, A. Rinaldo, R. Rigon, A. Giacometti and I. Rodriguez-Iturbe, Phys. Rev. E 53:1510 (1996).

    Google Scholar 

  9. J. R. Banavar, F. Colaiori, A. Flammini, A. Giacometti, A. Maritan and A. Rinaldo, Phys. Rev. Lett. 78:4522 (1997).

    Google Scholar 

  10. S. S. Manna, D. Dhar and S. N. Majumdar, Phys. Rev. B 46:4471 (1992).

    Google Scholar 

  11. R. Rigon, I. Rodriguez-Iturbe, A. Maritan, A. Giacometti, D. G. Tarboton and A. Rinaldo, Water Resour. Res. 32:3367 (1996).

    Google Scholar 

  12. J. T. Hack, U.S. Geol. Surv. Prof. Paper 294:1 (1957).

    Google Scholar 

  13. R. Chandler, J. Koplik, Lerman and J. Willemsen, J. Fluid Mech. 119:249 (1982); R. Lenormand, C. R. Seances, Acad. Sci. Ser. B 291:279 (1980).

    Google Scholar 

  14. See e.g., H. Takayasu, M. Takayasu, A. Provata and G. Huber, J. Stat. Phys. 65:725 (1991).

    Google Scholar 

  15. A.-L. Barabasi, Phys. Rev. Lett. 76:3750 (1996).

    Google Scholar 

  16. C. M. Newman and D. L. Stein, Phys. Rev. Lett. 72:2286 (1994).

    Google Scholar 

  17. M. Cieplak, A. Maritan and J. R. Banavar, Phys. Rev. Lett. 72:2320 (1994).

    Google Scholar 

  18. J. Feder, Fractals (Plenum, New York, 1988).

    Google Scholar 

  19. P. Meakin, Phys. Scr. 45:69 (1992); P. Meakin, J. Phys. A 20:L1113 (1987).

    Google Scholar 

  20. J. Krug and P. Meakin, Phys. Rev. A 40:2064 (1989).

    Google Scholar 

  21. M. Cieplak, A. Maritan, and J. R. Banavar, Phys. Rev. Lett. 76:3754 (1996).

    Google Scholar 

  22. G. Caldarelli, A. Giacometti, A. Maritan, I. Rodrigues-Iturbe and A. Rinaldo, Phys. Rev. E 55:R4865 (1997); A. Rinaldo, I. Rodrigues-Iturbe, R. Rigon, E. Ijjazs-Vasques and R. L. Bras, Phys. Rev. Lett. 70:822 (1993).

    Google Scholar 

  23. B. Tadic, Phys. Rev. Lett. (in press) (1997).

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Cieplak, M., Giacometti, A., Maritan, A. et al. Models of Fractal River Basins. Journal of Statistical Physics 91, 1–15 (1998). https://doi.org/10.1023/A:1023069201470

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  • DOI: https://doi.org/10.1023/A:1023069201470

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