Abstract
| Language | English |
|---|---|
| Pages | 163-204 |
| Number of pages | 41 |
| Journal | Studies in Applied Mathematics |
| Volume | 109 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2002 |
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Keywords
- Horton-Strahler
- river networks
- cluster system
- time dynamics
- applied mathematics
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A hierarchical cluster system based on Horton-Strahler rules for river networks. / Da Costa, F.P.; Wattis, J.A.D.; Grinfeld, M.
In: Studies in Applied Mathematics, Vol. 109, No. 3, 2002, p. 163-204.Research output: Contribution to journal › Article
TY - JOUR
T1 - A hierarchical cluster system based on Horton-Strahler rules for river networks
AU - Da Costa, F.P.
AU - Wattis, J.A.D.
AU - Grinfeld, M.
PY - 2002
Y1 - 2002
N2 - We consider a cluster system in which each cluster is characterized by two parameters: an "order"i, following Horton-Strahler rules, and a "mass"j following the usual additive rule. Denoting by ci,j(t) the concentration of clusters of order i and mass j at time t, we derive a coagulation-like ordinary differential system for the time dynamics of these clusters. Results about the existence and the behavior of solutions as t→∞ are obtained; in particular, we prove that ci,j(t) → 0 and Ni(c(t)) → 0 as t→∞, where the functional Ni(·) measures the total amount of clusters of a given fixed order i. Exact and approximate equations for the time evolution of these functionals are derived. We also present numerical results that suggest the existence of self-similar solutions to these approximate equations and discuss their possible relevance for an interpretation of Horton's law of river numbers.
AB - We consider a cluster system in which each cluster is characterized by two parameters: an "order"i, following Horton-Strahler rules, and a "mass"j following the usual additive rule. Denoting by ci,j(t) the concentration of clusters of order i and mass j at time t, we derive a coagulation-like ordinary differential system for the time dynamics of these clusters. Results about the existence and the behavior of solutions as t→∞ are obtained; in particular, we prove that ci,j(t) → 0 and Ni(c(t)) → 0 as t→∞, where the functional Ni(·) measures the total amount of clusters of a given fixed order i. Exact and approximate equations for the time evolution of these functionals are derived. We also present numerical results that suggest the existence of self-similar solutions to these approximate equations and discuss their possible relevance for an interpretation of Horton's law of river numbers.
KW - Horton-Strahler
KW - river networks
KW - cluster system
KW - time dynamics
KW - applied mathematics
UR - http://dx.doi.org/10.1111/1467-9590.00221
U2 - 10.1111/1467-9590.00221
DO - 10.1111/1467-9590.00221
M3 - Article
VL - 109
SP - 163
EP - 204
JO - Studies in Applied Mathematics
T2 - Studies in Applied Mathematics
JF - Studies in Applied Mathematics
SN - 0022-2526
IS - 3
ER -