Empirical observations have established connections between river network geometry
and various hydrophysical quantities of interest. Since rivers can be decomposed into
basic components known as links, one would like to understand the physical processes at
work in link formation and maintenance. The author develops a natural stochastic
geometric model for this problem, for the particular type of link known as exterior links.
In the model, the distribution of distance from a uniformly distributed point to a fixed
graph is computed. This model yields an approximate expression for the distribution of
length of exterior links that incorporates junction angles and drainage density, and
compares favorably with observed length distributions. The author goes on to investigate
related mathematical questions of independent interest, such as the case where the
previously mentioned graph is itself a realization of a random process, and in so doing
derives a formula for the first contact distribution of a general random Voronoi tesselation
(also associated with the names of Dirichlet and Thiessen). Since this random tesselation
is a natural starting point for modelling spatial processes in a wide variety of fields, these
results should find immediate applications. It is also shown how these results can be
interpreted as a generalization of a classical problem considered by Buffon. / Graduation date: 1991
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/31922 |
| Date | 14 February 1990 |
| Creators | Peckham, Scott |
| Contributors | Waymire, Edward |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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