Abstract
Campos, Mendez, and Fort (CMF) derived an approximate formula for the speed of reaction-diffusion fronts in fractal media. By way of a continuation of their earlier studies, we perform numerical simulations of reaction- diffusion equations with au(1 u)(1 u) for 0 ¶ ¶ 1 as the reaction term on various generalized Sierpicarpets (including infinitely ramified and random ones). The CMF formula agrees well with the mean front speed as a function of a obtained from our simulations for the classic Sierpi´ nski carpet, a randomized version of the carpet, and some finitely ramified carpets containing loops. In these cases the mean front speed also shows no significant dependence on , as predicted by the CMF formula. However, the agreement is not so good in the case of the other carpets tested and this is probably a result of the mean distance of the front from the starting point against time behaving erratically in such cases. We also propose some nomenclature for generalized Sierpi´ nski carpets and introduce a compact formulation of
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