Peano basin

Find the waiting time PDF for the Peano basin with Q = 3. Calculate (x )(t) when t 00. 

Fig. 7.11 Plot of the results for the front velocity vs the parameter rr. The points tire obttiined from simulations of the stochastic process on the OCNs (fiill circles) tmd the Peano basin open circles). The lines correspond to theoretical values from the Fisher equation (solid) and for the Peano basin (dotted and dotted-dashed). Reprinted from [64]. Copyright 2006, with permission from Elsevier...

Figure 7.11 summarizes the results obtained from (7.42) (lines) and compares it with random walk simulations on the Peano basin up to order Q = 10 (open circles) and OCNs (full circles). In the simulations, all the walkers were initially on the left side of the lattice and the front advanced to the right. A logistic growth rp(l — p) was introduced at every site at every time step to simulate the reaction process. For the OCNs, we averaged over 10 different 200 x 200 networks. 

Table 7.3 includes results for different values of Q, because the settlers moved mainly following the major river valleys according to historical reports. One might conclude therefore that small details in the sfructure of the Peano basin, namely tertiary, quaternary, and higher-order channels, do not affect the dynamics of the migration process, and a low order in Q should be chosen. 

Pig. 6.4 The first three construction levels of the Peano fractal basin... 

Great efforts have been undertaken to describe the intricate geometry of river networks [363]. In Chap. 6 we illustrated some models, such as the Peano network, which resembles fractal river basins. Another well-known structure that was proposed to describe better the evolution and formation of river basins and that agrees with most of the observations is the Optimal Channels Network (OCN) model, based on some optimization principles that minimize the energy expenditure by the net-... 

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