Publication

Geomorphological Width Functions and the Random Cascade

1994
Journal Articles

Abstract

We examine the geomorphological width functions of several river basins through the formalism of conservative (microcanonical) random cascades and we compare the results with those of more conventional fractal and multifractal analyses. We suggest that the spatial patterns of aggregation described by the width functions analyzed show common recurrent characters and that the implications of the robust identification of the singularity spectra via Legendre transforms are supported also by random cascade rationale.

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1994
Journal Articles

Abstract

Official source

Related concepts (22)

Microcanonical ensemble

In statistical mechanics, the microcanonical ensemble is a statistical ensemble that represents the possible states of a mechanical system whose total energy is exactly specified. The system is assumed to be isolated in the sense that it cannot exchange energy or particles with its environment, so that (by conservation of energy) the energy of the system does not change with time. The primary macroscopic variables of the microcanonical ensemble are the total number of particles in the system (symbol: N), the system's volume (symbol: V), as well as the total energy in the system (symbol: E).

Statistical mechanics

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, chemistry, and neuroscience.

Legendre transformation

In mathematics, the Legendre transformation (or Legendre transform), named after Adrien-Marie Legendre, is an involutive transformation on real-valued convex functions of one real variable. In physical problems, it is used to convert functions of one quantity (such as velocity, pressure, or temperature) into functions of the conjugate quantity (momentum, volume, and entropy, respectively).