A hierarchical cluster system based on Horton-Strahler rules for river networks

Studies in Applied Mathematics

Volumn 109, Issue 3, 2002, Pages 163-204

  Da Costa, F P ^a   Grinfeld, M ^b   Wattis, J A D ^c  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^c UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTER ANALYSIS;

ADDITIVE RULE; APPROXIMATE EQUATION; BEHAVIOR OF SOLUTIONS; CLUSTERS SYSTEM; DIFFERENTIAL SYSTEMS; FIXED-ORDER; HIERARCHICAL CLUSTERS; RIVER NETWORK; TIME DYNAMIC; TWO PARAMETER;

HIERARCHICAL SYSTEMS;

EID: 0036810011     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9590.00221     Document Type: Article

References (23)

1. P.B. Dubovskii, Mathematical Theory of Coagulation, Research Institute of Mathematics/ Global Analysis Research Center, Lecture Notes Series No. 23, Seoul National University, Seoul, 1994.
2. P. Coveney and J.A.D. Wattis, Becker-Döring model of self-reproduction vesicles, J. Chem. Soc., Faraday Trans. 94:233-246 (1998).
3. J.A.D. Wattis, A Becker-Döring model of competitive nucleation, J. Phys. A: Math. Gen. 32:8755-8784 (1999).
4. R. Dunwell, The Becker-Döring cluster equations, Ph.D. Thesis, Heriot-Watt University, Edinburgh, 1997.
5. R. Horton, Erosional development of streams and their drainage basins: Hydrophysical approach to quantitative morphology, Bull. Geol. Soc. Amer. 56:275-370 (1945).
6. A.N. Strahler, Hypsometric (area-altitude) analysis of erosional topography, Bul. Geol. Soc. Amer. 63:1117-1142 (1952).
7. L.B. Leopold, M.G. Wolman, and J.P. Miller, Fluvial Processes in Geomorphology, W.H. Freeman, San Francisco, 1970.
8. A.E. Scheidegger, Theoretical Geomorphology, 2nd revised ed., Allen & Unwin/Springer-Verlag, London/Berlin, 1970.
9. A.P. Ershov, On programming of arithmetic operations, Commum. ACM 1:3-6 (1958).
10. X.G. Viennot, Trees everywhere, in CAAP'90: 15th Colloquium on Trees in Algebra and Programming, Copenhagen, Denmark May 1990 (A. Arnold, Ed.), pp. 18-41, Lecture Notes in Computer Science 431, Springer-Verlag, Heidelberg, 1990.
11. A. Gabrielov, W.I. Newman, and D.L. Turcotte, Exactly soluble hierarchical clustering model: Inverse cascades, self-similarity, and scaling, Phys. Rev. E 60:5293-5300 (1999).
12. J. Carr, F.P. Da Costa, and J.A.D. Wattis (work in progress).
13. P. Coveney and J.A.D. Wattis, Cluster renormalization in the Becker-Döring equations, J. Phys. A: Math. Gen. 32:7145-7152 (1999).
14. F.P. Da Costa, A finite dimensional dynamical model for gelation in coagulation processes, J. Nonlinear Sci. 8:619-653 (1998).
15. Ph. Laurençot, Global solutions to the discrete coagulation equations, Mathematika 46:433-442 (1999).
16. J.M. Ball and J. Carr, The discrete coagulation-fragmentation equations: Existence, uniqueness, and density conservation, J. Stat. Phys. 61:203-234 (1990).
17. F.P. Da Costa, Existence and uniqueness of density conserving solutions to the coagulation-fragmentation equations with strong fragmentation, J. Math. Anal. Appl. 192:892-914 (1995).
18. J. Carr and F.P. Da Costa, Asymptotic behavior of solutions to the coagulation-fragmentation equations: II. Weak fragmentation, J. Stat. Phys. 77:89-123 (1994).
19. J.M. Ball, J. Carr and O. Penrose, The Becker-Döring cluster equations: Basic properties and asymptotic behavior of solutions, Commun. Math. Phys. 104:657-692 (1986).
20. W.H. White, A global existence theorem for Smoluchowski's coagulation equations, Proc. Amer. Math. Soc. 80:273-276 (1980).
21. F. Leyvraz and H.R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys. A: Math. Gen. 14:3389-3405 (1981).
22. M. Grinfeld, Notes on fracture (unpublished notes).
23. A.N. Strahler, Quantitative analysis of watershed geomorphology, Trans. Amer. Geophys. Union 38:913-920 (1957).