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 Previous numerical estimates on the critical exponents, when existing, are confirmed and superseded.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.
Similar content being viewed by others
REFERENCES
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).
C. P. Stark, Nature 352:423 (1991).
S. S. Manna and B. Subramanian, Phys. Rev. Lett. 76:3460 (1996).
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.
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).
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).
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).
A. Maritan, A. Rinaldo, R. Rigon, A. Giacometti and I. Rodriguez-Iturbe, Phys. Rev. E 53:1510 (1996).
J. R. Banavar, F. Colaiori, A. Flammini, A. Giacometti, A. Maritan and A. Rinaldo, Phys. Rev. Lett. 78:4522 (1997).
S. S. Manna, D. Dhar and S. N. Majumdar, Phys. Rev. B 46:4471 (1992).
R. Rigon, I. Rodriguez-Iturbe, A. Maritan, A. Giacometti, D. G. Tarboton and A. Rinaldo, Water Resour. Res. 32:3367 (1996).
J. T. Hack, U.S. Geol. Surv. Prof. Paper 294:1 (1957).
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).
See e.g., H. Takayasu, M. Takayasu, A. Provata and G. Huber, J. Stat. Phys. 65:725 (1991).
A.-L. Barabasi, Phys. Rev. Lett. 76:3750 (1996).
C. M. Newman and D. L. Stein, Phys. Rev. Lett. 72:2286 (1994).
M. Cieplak, A. Maritan and J. R. Banavar, Phys. Rev. Lett. 72:2320 (1994).
J. Feder, Fractals (Plenum, New York, 1988).
P. Meakin, Phys. Scr. 45:69 (1992); P. Meakin, J. Phys. A 20:L1113 (1987).
J. Krug and P. Meakin, Phys. Rev. A 40:2064 (1989).
M. Cieplak, A. Maritan, and J. R. Banavar, Phys. Rev. Lett. 76:3754 (1996).
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).
B. Tadic, Phys. Rev. Lett. (in press) (1997).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1023/A:1023069201470