THE FRACTIONAL LAPLACIAN AS A LIMITING CASE OF A SELF-SIMILAR SPRING MODEL AND APPLICATIONS TO n-DIMENSIONAL ANOMALOUS DIFFUSION
Résumé
We analyze the "fractional continuum limit" and its generalization to n dimensions of a self-similar discrete spring model which we introduced recently (PRE 80, 011135 (2009)). In the fractional continuum limit the discrete self-similar Laplacian takes the form of the fractional Laplacian. We analyze the fundamental link of fractal vibrational features of the discrete self-similar spring model and the smooth regular ones of the corresponding fractional continuum limit model in n dimensions.Furthermore, we study in this setting anomalous diffusion generated by this Laplacian which is the source of Levi flights in n-dimensions.
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