An Introduction to Mathematical Modeling by Edward A. Bender

Author:Edward A. Bender
Language: eng
Format: epub
ISBN: 9780486137124
Publisher: Dover Publications
Published: 2012-07-17T16:00:00+00:00

We consider another way to approach randomness in stream networks. The idea is that the topography is random. Imagine a portion of a plane covered with squares. We think of the edge of each square as a possible stream link. Water might flow from or through any given vertex to an adjacent vertex. See Figure 3. This idea was suggested by a discussion in L. B. Leopold et al. ( 1964, p. 419). (a) Given a vertex v, choose an adjacent vertex at random and allow the water to flow from v to w. Be careful. We can’t do this if we’ve previously decided to let water flow from w to v. Bifurcating sources and “lost” rivers must be avoided. See A and B in Figure 3. How could you implement this on a computer? What about the possibility of water flowing in a closed loop such as C in Figure 3? Can you handle this by allowing lakes or by somehow stopping it by clever programing?

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