Natalie Kleinfelter

Scaling Laws and Fokker--Planck Equations for 3-Dimensional Porous Media with Fractal Mesoscale

Transport is studied in three-scale porous media with fractal mesoscale. On the microscale the dispersive mixing is governed by a stochastic ordinary differential equation with stationary, ergodic, Markovian drift velocity and an

Analysis of dispersion in porous media via matched-index particle tracking velocimetry experiments

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Application of the finite-size Lyapunov exponent to particle tracking velocimetry in fluid mechanics experiments.

-stable Levy diffusion. The inclusion of Levy diffusion allows one to study self-motile particles such as flagellated microbes. On the mesoscale it is assumed that a fractal Eulerian flow field with spatially homogeneous increments gives rise to a fractal drift velocity with temporally stationary increments. The drift velocity is assumed to be Levy. These processes have stationary increments and fractal graphs. The diffusive structure on the mesoscale is determined by the asymptotic microscale process. On the macroscale there is no additional drift; i.e., the physics is controlled solely by the asymptotic behavior of the mesoscale process. Scaling laws from the micro- to meso- and meso- to macroscales are obtained as well as the Fokker--Planck equations for the transition...