Abstract
ABSTRACT In hydrology, branching-type phenomena occur in several instances, for example in ground-water flow (splitting flow channels in a porous medium) and in the formation of a natural river network (combining, i.e., inverse branching, of small rivers to form large rivers). Such phenomena can be treated by the statistics of topological bifurcating arborescences. It is shown how ensembles of arborescences can be generated on a computer and expectation values for observables can be calculated. In this fashion, the laws of dispersion processes in flow through porous media and Horton's law of stream numbers in drainage basins are shown to be the outcome of very simple statistical assumptions.
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