-
1
-
-
0000687019
-
-
R. L. Leheny and S. R. Nagel, Phys. Rev. Lett. 71, 1470 (1993); S. Kramer and M. Marder, ibid. 68, 205 (1992); T. Sun, P. Meakin, and T. Jossang, Phys. Rev. E 51, 5353 (1995).
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 1470
-
-
Leheny, R.L.1
Nagel, S.R.2
-
2
-
-
0002112394
-
-
R. L. Leheny and S. R. Nagel, Phys. Rev. Lett. 71, 1470 (1993); S. Kramer and M. Marder, ibid. 68, 205 (1992); T. Sun, P. Meakin, and T. Jossang, Phys. Rev. E 51, 5353 (1995).
-
(1992)
Phys. Rev. Lett.
, vol.68
, pp. 205
-
-
Kramer, S.1
Marder, M.2
-
3
-
-
9344236391
-
-
R. L. Leheny and S. R. Nagel, Phys. Rev. Lett. 71, 1470 (1993); S. Kramer and M. Marder, ibid. 68, 205 (1992); T. Sun, P. Meakin, and T. Jossang, Phys. Rev. E 51, 5353 (1995).
-
(1995)
Phys. Rev. E
, vol.51
, pp. 5353
-
-
Sun, T.1
Meakin, P.2
Jossang, T.3
-
10
-
-
0000705163
-
-
I. Rodriguez-Iturbe, R. L. Bras, E. Ijjasz-Vasquez, and D. G. Tarboton, Water Resour. Res. 28, 988 (1992).
-
(1992)
Water Resour. Res.
, vol.28
, pp. 988
-
-
Rodriguez-Iturbe, I.1
Bras, R.L.2
Ijjasz-Vasquez, E.3
Tarboton, D.G.4
-
11
-
-
20344399959
-
-
R. E. Horton, Geol. Soc. Am. Bull. 65, 275 (1945); A. E. Scheidegger, Water Resour. Res. 4. 167 (1968); 4, 1015 (1968); D. G. Tarboton, R. L. Bras, and I. Rodriguez-Iturbe, ibid. 24, 1317 (1988).
-
(1945)
Geol. Soc. Am. Bull.
, vol.65
, pp. 275
-
-
Horton, R.E.1
-
12
-
-
84927989819
-
-
R. E. Horton, Geol. Soc. Am. Bull. 65, 275 (1945); A. E. Scheidegger, Water Resour. Res. 4. 167 (1968); 4, 1015 (1968); D. G. Tarboton, R. L. Bras, and I. Rodriguez-Iturbe, ibid. 24, 1317 (1988).
-
(1968)
Water Resour. Res.
, vol.4
, pp. 167
-
-
Scheidegger, A.E.1
-
13
-
-
18344388257
-
-
R. E. Horton, Geol. Soc. Am. Bull. 65, 275 (1945); A. E. Scheidegger, Water Resour. Res. 4. 167 (1968); 4, 1015 (1968); D. G. Tarboton, R. L. Bras, and I. Rodriguez-Iturbe, ibid. 24, 1317 (1988).
-
(1968)
Water Resour. Res.
, vol.4
, pp. 1015
-
-
-
14
-
-
0024164717
-
-
R. E. Horton, Geol. Soc. Am. Bull. 65, 275 (1945); A. E. Scheidegger, Water Resour. Res. 4. 167 (1968); 4, 1015 (1968); D. G. Tarboton, R. L. Bras, and I. Rodriguez-Iturbe, ibid. 24, 1317 (1988).
-
(1988)
Water Resour. Res.
, vol.24
, pp. 1317
-
-
Tarboton, D.G.1
Bras, R.L.2
Rodriguez-Iturbe, I.3
-
16
-
-
18344362934
-
-
D. G, Tarboton, R. L. Bras, and I. Rodriguez-Iturbe, Water Resour. Res. 26, 2243 (1990).
-
(1990)
Water Resour. Res.
, vol.26
, pp. 2243
-
-
Tarboton, D.G.1
Bras, R.L.2
Rodriguez-Iturbe, I.3
-
18
-
-
0004263139
-
-
Freeman, San Francisco
-
B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982); A. Czirok, E. Somfai, and T. Vicsek, Phys. Rev. Lett. 71, 2154 (1993).
-
(1982)
The Fractal Geometry of Nature
-
-
Mandelbrot, B.B.1
-
19
-
-
0007257017
-
-
B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982); A. Czirok, E. Somfai, and T. Vicsek, Phys. Rev. Lett. 71, 2154 (1993).
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 2154
-
-
Czirok, A.1
Somfai, E.2
Vicsek, T.3
-
22
-
-
5244250054
-
-
note
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This is the weakest part of our argument. For near-equilibrium dynamics F is related to the Landau free energy and is necessarily analytic. For our case the rigorous justification of the method is less evident. We do get interesting results, as we will see.
-
-
-
-
24
-
-
0007937085
-
-
J. C. Luke, J. Geophys. Res. 77, 2460 (1972); 79, 4035 (1974).
-
(1974)
J. Geophys. Res.
, vol.79
, pp. 4035
-
-
-
25
-
-
0001663090
-
-
W. E. H. Culling, J. Geol. 68, 336 (1960); 71, 127 (1963).
-
(1960)
J. Geol.
, vol.68
, pp. 336
-
-
Culling, W.E.H.1
-
26
-
-
0000792025
-
-
W. E. H. Culling, J. Geol. 68, 336 (1960); 71, 127 (1963).
-
(1963)
J. Geol.
, vol.71
, pp. 127
-
-
-
30
-
-
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We are not considering the meandering instability, which causes large rivers to change course
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We are not considering the meandering instability, which causes large rivers to change course.
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31
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In contrast, Sinclair and Ball consider another kind of state in which the height at each point decreases as a power law. This may be appropriate for the late stages of erosion (the formation of a penneplain) where the boundary conditions dominate the behavior throughout the river basin. We give a more local approach. The resulting slope-area law is different in the two cases,
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