Probing Non-Integer Dimensions

Abstract

We show that two-dimensional convection-diffusion problems with a radial sink or source at the origin may be recast as a pure diffusion problem in a fictitious space in which the spatial dimension is continuously-tunable with the Peclet number. This formulation allows us to probe various diffusion-controlled processes in non-integer dimensions.Comment: 6 pages, 2 column-revtex4 format. Submitted to special issue of Journal of Physics: Condensed Matter, on "Chemical Kinetics Beyond the Textbook: Fluctuations, Many-Particle Effects and Anomalous Dynamics", eds. K. Lindenberg, G. Oshanin, & M. Tachiy