Local minimal energy landscapes in river networks

Details Local minimal energy landscapes in river networks Local minimal energy landscapes in river networks

2000-08-29

arxiv.org/abs/cond-mat/0008424v1

Physics

Condensed Matter

Statistical Mechanics

12 pages, 13 figures, revtex+epsfig style, to appear in Phys. Rev. E (Nov. 2000)

Scientific paper

10.1103/PhysRevE.62.6042

The existence and stability of the universality class associated to local minimal energy landscapes is investigated. Using extensive numerical simulations, we first study the dependence on a parameter $\gamma$ of a partial differential equation which was proposed to describe the evolution of a rugged landscape toward a local minimum of the dissipated energy. We then compare the results with those obtained by an evolution scheme based on a variational principle (the optimal channel networks). It is found that both models yield qualitatively similar river patterns and similar dependence on $\gamma$. The aggregation mechanism is however strongly dependent on the value of $\gamma$. A careful analysis suggests that scaling behaviors may weakly depend both on $\gamma$ and on initial condition, but in all cases it is within observational data predictions. Consequences of our results

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