EVENT DETAILS AND ABSTRACT

Title: Aquifers and Streams as Fractal Filters: Fractal Calculus in Your Backyard
Speaker: Dave Benson
Speaker Info: Desert Research Institute
Brief Description:
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Abstract:

Fractal calculus, which concerns derivatives of rational order (e.g.,the 1.65th) is a seemingly esoteric topic. Diffusion-like equations with fractional derivatives are the governing equations of particles that do not move in a smooth, Euclidean world. Instead, they move in a rough world that has randomness on all scales. For example, most of the dye molecules placed in a mountain stream will move away quickly, but a small amount will be caught for minutes to days in eddies, while another fraction may move into the relatively motionless water beneath the streambed. It may take months or years before the last molecules are washed away. The same is true for contaminants spilled into aquifers. Generalizations of the classical central limit theorem relegate this behavior to power-law random functions. The nonlinearity is off-putting until we realize that these random motions are described by linear, non-integer order governing equations. The equations are parsimonious and easy to solve, even though they model terrifically complex, multiscale behavior.