6533b7d2fe1ef96bd125f50a

RESEARCH PRODUCT

Scaling properties of topologically random channel networks

Francesco D'asaroCarmelo AgneseGiovanna GrossiRenzo Rosso

subject

Discrete mathematicsDimension (vector space)YardstickLaw of large numbersStochastic processStructure (category theory)Magnitude (mathematics)Statistical physicsScalingWater Science and TechnologyMathematicsCommunication channel

description

Abstract The analysis deals with the scaling properties of infinite topologically random channel networks (ITRNs) fast introduced by Shreve (1967, J. Geol. , 75: 179–186) to model the branching structure of rivers as a random process. The expected configuration of ITRNs displays scaling behaviour only asymptotically, when the ruler (or ‘yardstick’) length is reduced to a very small extent. The random model can also reproduce scaling behaviour at larger ruler lengths if network magnitude and diameter are functionally related according to a reported deterministic rule. This indicates that subsets of rrRNs can be scaling and, although rrRNs are asymptotically plane-filling due to the law of large numbers, scaling ITRNs can also display fractional dimension.

yearjournalcountryeditionlanguage
1996-12-01Journal of Hydrology
https://doi.org/10.1016/s0022-1694(96)03095-8