Phys. Rev. E 48, 3545–3555 (1993)Diffusion on deterministic and quasirandom models of diffusion-limited aggregates. I. Isotropic diffusionReceived 17 February 1993; published in the issue dated November 1993 We discuss the diffusion of a particle on deterministic and quasirandom fractal structures designed to mimic the properties of diffusion-limited aggregates. In this paper we deal with unbiased transport, while the following paper deals with transport in the presence of an external field. Our method is based on a renormalization procedure that allows us to calculate the scaling properties relating distance and time. We calculate the random-walk dimension dw for a variety of structures and show how this dimension depends on the branching properties of the model. We find that random walks on these structures become slower as the branching intricacies of the model increase. © 1993 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.48.3545
DOI:
10.1103/PhysRevE.48.3545
PACS:
05.40.+j, 02.50.-r
See AlsoSee Also: Hernan L. Martinez, Juan M. Parrondo, and Katja Lindenberg, Diffusion on deterministic and quasirandom models of diffusion-limited aggregates. II. Anisotropic diffusion, Phys. Rev. E 48, 3556 (1993). |
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