Universality classes of optimal channel networks

Science

Volumn 272, Issue 5264, 1996, Pages 984-986

  Maritan, Amos ^a,b   Colaiori, Francesca ^a,b   Flammini, Alessandro ^a,b   Cieplak, Marek ^c   Banavar, Jayanth R ^d  

^a SISSA   (Italy)

^b SEZIONE DI TRIESTE   (Italy)

^c INSTITUTE OF PHYSICS   (Poland)

^d PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COMPUTER SIMULATION; GEOLOGY; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; RIVER; WATER FLOW;

CHANNEL NETWORK; ENERGY MINIMIZATION; RIVER NETWORK; UNIVERSALITY CLASS;

EID: 0029667945     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.272.5264.984     Document Type: Article

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27. j does not change the universality class.
28. A. E. Scheidegger, Bull. Int. Assoc. Sci. Hydrol. 12, 15 (1967).
29. H. Takayasu, M. Takayasu, A. Provata, G. Huber, J. Stat. Phys. 65, 725 (1991).
30. A. Maritan, A. Rinaldo, R. Rigon, I. Rodriguez-Iturbe, A. Giacometti, Phys. Rev. E 53, 1501 (1996).
31. Our finite-size scaling arguments and the notion of universality are similar to those in critical phenomena. See, for example, M. E. Fisher, Rev. Mod. Phys. 46, 597 (1974).
32. 1 = 1 and H ≤ 1. All of our results hold for arbitrary networks without any restriction on their directedness.
33. J. T. Hack, U.S. Geol. Surv. Prof. Paper 294-B (1957). The principal cause of the anomalous exponent of Hack is a matter of debate. Basin elongation occurs in the Scheidegger model (9, 10), but this model is yet untested with large sets of data. Alternately, computer simulations (7) suggest that basin shapes have a similarity across scales.
34. This substitution is a generalization of the observation that the mean area is equal to the average distance to the outlet [B. M. Troutman and M. R. Karlinger, Water Resour. Res. 28, 563 (1992), and references therein].
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38. We are indebted to A. Giacometti and I. Rodriguez-Iturbe and especially to A. Rinaldo for numerous stimulating discussions. This work was supported by grants from the Komitet Badan Naukowych, the National Aeronautics and Space Administration, the North Atlantic Treaty Organization, the National Science Foundation, and the Petroleum Research Fund administered by the American Chemical Society.