title: Random walk in chemical space of Cantor dust as a paradigm of superdiffusion.
abstract: We point out that the chemical space of a totally disconnected Cantor dust K(n) [Symbol: see text E(n) is a compact metric space C(n) with the spectral dimension d(s) = d(ℓ) = n > D, where D and d(ℓ) = n are the fractal and chemical dimensions of K(n), respectively. Hence, we can define a random walk in the chemical space as a Markovian Gaussian process. The mapping of a random walk in C(n) into K(n) [Symbol: see text] E(n) defines the quenched Lévy flight on the Cantor dust with a single step duration independent of the step length. The equations, describing the superdiffusion and diffusion-reaction front propagation ruled by the local quenched Lévy flight on K(n) [Symbol: see text] E(n), are derived. The use of these equations to model superdiffusive phenomena, observed in some physical systems in which propagators decay faster than algebraically, is discussed.
authors.affiliation: Grupo Mecánica Fractal, Instituto Politécnico Nacional, México Distrito Federal 07738, Mexico.
authors.forename: Alexander S
authors.initials: AS
authors.lastname: Balankin
authors.forename: Baltasar
authors.initials: B
authors.lastname: Mena
authors.forename: C L
authors.initials: CL
authors.lastname: Martínez-González
authors.forename: Daniel Morales
authors.initials: DM
authors.lastname: Matamoros
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D015233:Models, Statistical