We continue the study of a particle (atom, molecule) undergoing an unbiased random walk on the Sierpinski gasket, and obtain for the gasket and tower the eigenvalue spectrum of the associated stochastic master equation. Analytic expressions for recurrence relations among the eigenvalues are derived. The recurrence relations obtained are compared with those determined for two Euclidean lattices, the closed chain with an absorbing site and a finite chain with an absorbing site at one end. We check and confirm the internal consistency between the smallest eigenvalue and the mean walklength in each of the cases studied. Attention is drawn to the relevance of the results obtained to a problem of electron transfer in proteins.
The theory of vegetation patterns presented rests on two hypotheses: (i) the selforganization hypothesis that attributes their cause to interactions intrinsic to vegetation dynamics; (ii) the complementary self-assembly hypothesis that attributes their large spatial scale to the proximity of their dynamical conditions with a critical point. A non-local version of the F-KPP equation allows us to formulate these hypotheses in terms of individual plant properties. Both general and parsimonious, this formulation is strictly quantitative. It only relies on structural parameters that can be measured with precision in the field. Quantitative interpretation of observations and of the predictions provided by the theory is illustrated by an analysis of the periodic patterns found in some Sub-Sahelian regions.
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