Propagation processes through fractal media with applications to biology

Transport properties of fractal structures have been widely studied during the lastdecades. However, most works have been focused on diffusion and random-walksprocesses. The study of propagation dynamics on fractals has been usually restrictedto specific works and applications, which makes difficult to find references where theessentials of such processes are presented. The current contribution is thus aimed to bean introductory work for those researchers who want to get a general overview of thekey concepts involved in propagation on fractals. For simplicity, we restrict ourselvesjust to propagation dynamics resulting fromreaction-diffusion and advection-diffusionprocesses. In the first part of the work we review some known concepts of differentanalytical theories proposed to describe diffusion on fractals, from which reactiondiffusionand advection-diffusion processes will be derived. We apply different theoreticalcriteria to determine the validity and the robustness of such approaches, whichis supported by an exhaustive numerical analysis. Finally, to illustrate the importanceof propagation through fractals on real systems, three selected examples from the biologicalrealm are studied: i) the propagation of substances through water streams (forapplication to transport of contaminants in rivers), ii) the propagation of forest firesthrough heterogeneous landscapes, and iii) the spreading of tumor growth, which isknown to be a consequence of cell migration. According to the pedagogic aim of thepresent work, these three examples are intended to present minimal approaches to suchcomplicated processes, which may serve as a guide for researchers to develop furtherand more exhaustive models. © 2012 Nova Science Publishers, Inc. All rights reserved.