Emergence of self-similar tree network organization

Complexity

Volumn 13, Issue 4, 2008, Pages 30-37

  Paik, Kyungrock ^a,b   Kumar, Praveen ^a  

^a University of Illinois at Urbana Champaign   (United States)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Complex networks; Landscape evolution; Pattern formation; Self organization

Indexed keywords

EID: 51549104114     PISSN: 10762787     EISSN: 10990526     Source Type: Journal    
DOI: 10.1002/cplx.20214     Document Type: Article

References (69)

1. Prigogine, I. From Being to Becoming: Time and Complexity in the Physical Sciences; Freeman: San Francisco, 1980, 272 p.
2. Smyth, D.; Hübler, A. A conductivity-dependent phase transition from closed-loop to open-loop dendritic networks. Complexity 2003, 9, 56-60.
3. Peckham, S.D. New results for self-similar trees with applications to river networks. Water Resour Res 1995, 31, 1023-1029.
4. Banavar, J.R.; Maritan, A.; Rinaldo, A. Size and form in efficient transportation networks. Nature (London), 1999, 399, 130-132.
5. Zamir, M. On fractal properties of arterial trees. J Theor Biol 1999, 197, 517-526.
6. Turcotte, D.L.; Pelletier, J.D.; Newman, W.I. Networks with side branching in biology. J Theor Biol 1998, 193, 577-592.
7. West, G.B.; Brown, J.H.; Enquist, B.J. A general model for the structure and allometry of plant vascular systems. Nature (London), 1999, 400, 664-667.
8. Merté, B.; Gaitzsch, P.; Fritzenwanger, M.; Kropf, W.; Hübler, A.; Lüscher, E. Stable stationary dendritic patterns with minimal dissipation. Helvetica Phys Acta 1988, 61, 76-79.
9. Jun, J.K.; Hübler, A.H. Formation and structure of ramified charge transportation networks in an electromechanical system. Proc Natl Acad Sci USA 2005, 102, 536-540.
10. Niemeyer, L.; Pietronero, L.; Wiesmann, H.J. Fractal dimension of dielectric breakdown. Phys Rev Lett 1984, 52, 1033-1036.
11. Jain, S.K.; Singh, V.P. Lightning paths in sky share similarities with channel networks on Earth. Eos Trans AGU 2004, 85, 249, 253, 254.
12. Banavar, J.R.; Colaiori, F.; Flammini, A.; Maritan, A.; Rinaldo, A. Scaling, optimality, and landscape evolution. J Stat Phys 2001, 104, 1-48.
13. Buchanan, M. A game of chance. Nature (London), 2002, 419, 787.
14. Rodríguez-Iturbe, I.; Rinaldo, A.; Rigon, R.; Bras, R.L.; Marani, A.; Ijjász-Vásquez, E.J. Energy dissipation, runoff production, and the three-dimensional structure of river basins. Water Resour Res 1992, 28, 1095-1103.
15. Rinaldo, A.; Rodríguez-Iturbe, I.; Rigon, R.; Bras, R.L.; Ijjász-Vásquez, E.J.; Marani, A. Minimum energy and fractal structures of drainage networks. Water Resour Res 1992, 28, 2183-2195.
16. Rodríguez-Iturbe, I.; Rinaldo, A.; Rigon, R.; Bras, R.L.; Ijjász-Vásquez, E.J.; Marani, A. Fractal structures as least energy patterns: The case of river networks. Geophys Res Lett 1992, 19, 889-892.
17. Rinaldo, A.; Rodríguez-Iturbe, I.; Rigon, R.; Ijjász- Vásquez, E.J.; Bras, R.L. Self-organized fractal river networks. Phys Rev Lett 1993, 70, 822-825.
18. Sun, T.; Meakin, P.; Jøssang, T. The topography of optimal drainage basins. Water Resour Res 1994, 30, 2599-2610.
19. Sun, T.; Meakin, P.; Jøssang, T. Minimum energy dissipation model for river basin geometry. Phys Rev E 1994, 49, 4865-4872.
20. Maritan, A.; Colaiori, F.; Flammini, A.; Cieplak, M.; Banavar, J.R. Universality classes of optimal channel networks. Science 1996, 272, 984-986.
21. Colaiori, F.; Flammini, A.; Maritan, A.; Banavar, J.R. Analytical and numerical study of optimal channel networks. Phys Rev E 1997, 55, 1298-1310.
22. Caldarelli, G.; Marchetti, R.; Pietronero, L. The fractal properties of Internet. Europhys Lett 2000, 52, 386-391.
23. Hergarten, S.; Neugebauer, H.J. Self-organized critical drainage networks. Phys Rev Lett 2001, 86, 2689-2692.
24. Huggett, R.J. Dissipative systems: Implications for geomorphology. Earth Surface Processes and Landforms 1988, 13, 45-49.
25. Rodríguez-Iturbe, I.; Rinaldo, A. Fractal River Basins: Chance and Self-Organization; Cambridge University Press: New York, 1997; 547 p.
26. O'Callaghan, J.F.; Mark, D.M. The extraction of drainage networks from digital elevation data. Comput Vis Graph Image Process 1984, 28, 323-344.
27. Schoklitsch, A. Der geschiebetrieb und die geschiebefraeht. Wasserkraft und Wasserwirtschaft 1934, 39, 1-7.
28. Willgoose, G.; Bras, R.L; Rodríguez-Iturbe, I. A coupled channel network growth and hillslope evolution model: I. Theory. Water Resour Res 1991, 27, 1671-1684.
29. Chow, V.T.; Maidment, D.R.; Mays, L.W. Applied Hydrology; McGraw Hill: New York, 1988; 572 p.
30. Willgoose, G.; Bras, R.L.; Rodríguez-Iturbe, I. A physical explanation of an observed link area-slope relationship. Water Resour Res 1991, 27, 1697-1702.
31. Li, Y.-H. Denudation of Taiwan island since the Pliocene epoch. Geology 1976, 4, 105-107.
32. Carllng, P.A.; Reader, N.A. Structure, composition and bulk properties of upland stream gravels. Earth Surface Processes and Landforms 1982, 7, 349-365.
33. Parker, R.S. Experimental study of drainage basin evolution and its hydrologic implications. Hydrology Papers 90, Colorado State University: Fort Colins, Colorado, 1977.
34. Hack, J.T.. Studies of longitudinal stream profiles in Virginia and Maryland. U.S. Geological Survey Professional Paper, 294B, 1957.
35. Rigon, R.; Rodríguez-Iturbe, I.; Maritan, A.; Giacometti, A.; Tarboton, D.G.; Rinaldo, A. On Hack's law. Water Resour Res 1996, 32, 3367-3374.
36. Crave, A.; Davy, P. Scaling relationships of channel networks at large scales: Examples from two large-magnitude watersheds in Brittany, France. Tectonophysics 1997, 269, 91-111.
37. Rodríguez-Iturbe, I.; Ijjász-Vásquez, E.J.; Bras, R.L.; Tarboton, D.G. Power law distributions of discharge mass and energy in river basins. Water Resour Res 1992, 28, 1089-1093.
38. Paik, K.; Kumar, P. River networks as emergent characteristics of open dissipative systems. In: 4th IAHR Symposium on River, Coastal, and Estuarine Morphodynamics, Urbana, Illinois, A. A. Balkema Publishers, October 4-7, 2005, pp 1107-1116.
39. Kramer, S.; Marder, M. Evolution of river networks. Phys Rev Lett 1992, 68, 205-208.
40. Takayasu, H.; Inaoka, H. New type of serf-organized criticality in a model of erosion. Phys Rev Lett 1992, 68, 966-969.
41. Leheny, R.L.; Nagel, S.R. Model for the evolution of river networks. Phys Rev Lett 1993, 71, 1470-1473.
42. Howard, A.D. A detachment-limited model of drainage basin evolution. Water Resour Res 1994, 30, 2261-2285.
43. Prigozhin, L. Sandpiles and river networks: Extended systems with nonlocal interactions. Phys Rev E 1994, 49, 1161-1167.
44. Giacometti, A.; Maritan, A.; Banavar, J.R. Continuum model for river networks. Phys Rev Lett 1995, 75, 577-580.
45. Sinclair, K.; Ball, R.C. Mechanism for global optimization of river networks from local erosion rules. Phys Rev Lett 1996, 76, 3360-3363.
46. Banavar, J.R.; Colaiori, F.; Flammini, A.; Giacometti, A.; Maritan, A.; Rinaldo, A. Sculpting of a fractal river basin. Phys Rev Lett 1997, 78, 4522-4525.
47. Caldarelli, G.; Giacometti, A.; Maritan, A.; Rodríguez-Iturbe, I.; Rinaldo, A. Randomly pinned landscape evolution. Phys Rev E 1997, 55, R4865-R4868.
48. Somfai, E.; Sander, L.M. Scaling and river networks: A Landau theory for erosion. Phys Rev E 1997, 56, R5-R8.
49. Errera, M.R.; Bejan, A. Deterministic tree networks for river drainage basins. Fractals 1998, 6, 245-261.
50. Giacometti, A. Local minimal energy landscapes in river networks. Phys Rev E 2000, 62, 6042-6051.
51. Kim, H.-J.; Kim, I.-M.; Kim, J.M. River networks on the slope-correlated landscape. Phys Rev E 2000, 62, 3121-3124.
52. Caldarelli, G. Cellular models for river networks. Phys Rev E 2001, 63, 021118.
53. Stølum, H.-H. River meandering as a self-organization process. Science 1996, 271, 1710-1713.
54. Milgram, S. The small-world problem. Psychol Today 1967, 1, 60-67.
55. Watts, D.J.; Strogatz, S.H. Collective dynamics of 'small-world' networks. Nature (London), 1998, 393, 440-442.
56. Girvan, M.; Newman, M.E.J. Community structure in social and biological networks. Proc Natl Acad Sci USA 2002, 99(12), 7821-7826.
57. Guimerä, R.; Danon, L.; Díaz-Guilera, A.; Giralt, F.; Arenas, A. Self-similar community structure in a network of human interactions. Phys Rev E 2003, 68, 065103(R).
58. Barabási, A.-L.; Albert, R. Emergence of scaling in random networks. Science 1999, 286, 509-512.
59. Goh, K.-I.; Kahng, B.; Kim, D. Universal behavior of load distribution in scale-free networks. Phys Rev Lett 2001, 87, 278701.
60. De Los Rios, P. Power law size distribution of supercritical random trees. Europhys Lett 2001, 56, 898-903.
61. Caldarelli, G.; Cartazo, C.C.; De Los Rios, P.; Servedio, V.D.P. Widespread occurrence of the inverse square distribution in social sciences and taxonomy. Phys Rev E 2004, 69, 035101(R).
62. Paik, K.; Kumar, P. Inevitable self-similar topology of binary tress and their diverse hierarchial density. Eur Phys J B 2007, 60, 247-258.
63. Leopold, L.B.; Langbein, W.B. The concept of entropy in landscape evolution. U. S. Geological Survey Professional Paper, 500A, 1962.
64. Scheidegger, A.E. A stochastic model for drainage patterns into an intramontane treinch. Bull Int Assoc Sci Hydrol 1967, 12, 15-20.
65. Witten, T.A. Jr.; Sander, L.M. Diffusion-limited aggregation, a kinetic critical phenomenon. Phys Rev Lett 1981, 47, 1400-1403.
66. Takayasu, H.; Nishikawa, I.; Tasaki, H. Power-law mass distribution of aggregation systems with injection. Phys Rev A 1988, 37, 3110-3117.
67. Lewandowska, M.; Mathur, H.; Yu, Y.-K. Dynamics and critical behavior of the q model. Phys Rev E 2001, 64, 026107.
68. Wang, S.; Zhang, C. Weighted competition scale-free network. Phys Rev E 2004, 70, 066127.
69. Albert, R.; Barabási, A.-L. Statistical mechanics of complex networks. Rev Modern Phys 2002, 74, 47-97.