Chapter 2


The process of nondimensionalisation is illustrated, first on the damped pendulum equation, then in viscous fluid flow, heat transport and thermal convection; finally on a phenomenological model of Meinhardt for the formation of branched network structures such as leaf veins and blood vessels. This model, involving the nonlinear interaction of an activator, an inhibitor, a substrate and an indicator variable which is switched on by the activator, formed the inspiration for Willgoose et al's 1989 model for the formation of drainage networks in river basins. Further discussion of this is in chapter 15, pages 265 and 270.

The exercises discuss scaling of models for earthquakes, respiratory ventilation, snow melt runoff and oscillatory populations (the Lotka Volterra model). Exercise 2.3 has some omissions (see the corrections page for these). The stick-slip rheology used in it is a simplified version of a more accurate `rate and state dependent' law which is nicely reviewed by C.H. Scholz (Nature 391, 37-42 (1998). Actually, this exercise is a good entry point into the perplexing question, how do you model/predict self-similar/fractal behaviour of continuous systems obeying deterministic laws? I've no idea what the answer to this is, yet.

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