Title: Space and Time Scaling Exponents on Fractals and Compact Metric Spaces
Speaker: John Dever (Bowling Green State University)
Abstract: We discuss two scaling exponents that may be defined on any compact metric space: the local Hausdorff dimension and the local walk dimension. Intuitively, the local Hausdorff dimension determines how the volume of metric balls scales with the radius of the ball, and the local walk dimension determines how fast a diffusion process leaves a ball on average relative to its radius. Spaces that have walk dimension not equal to 2 exhibit what is called anomalous diffusion. We give examples of fractals that have continuously variable Hausdorff dimension and continuously variable walk dimension. Moreover, we explain how these dimensions may be useful in approximating diffusion on a compact metric space.
