Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Abstract: C1.00223 : Non-Equilibrium Statistical Dynamics of River Network Evolution
Author:
According to the erosion rule in a natural process, a Langevin
Equation
describing the prolongation of river channel is defined. The
determinate
prolongation is given by consideration of the characteristics of
the early
stage in the development of a river channel. The random growth
(diffusion)
is expressed by the fluctuations of the related stochastic
variables or
factors. A Fokker-Planck equation that describes the evolution of
the
distribution of the channel length is derived from this Langevin
Equation.
The solution presents the transition probability and exceedence
probability
with a Power-Exponent function which indicates that the channel
length
distributes in a complicated way. The details show that there
exists a
critical time, before which river network is developing and
marked by
exponent distribution., and beyond which river network is
developed and
marked by power distribution. On the basis of Hack's law, the
transition
probability of river's area and the corresponding exceedence
probability are
obtained. They are in excellent agreement with them obtained by
field
observations.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.MAR.C1.223
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