The fractional Fick's law for anomalous transport in turbulent plasmas with boundaries.
Zimbardo G., Perri S.
II - Fisica della materia
Aula 32B-2 - Venerdì 21 h 15:30 - 18:30
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Non-diffusive, anomalous transport is related to non-locality, so that the standard Fick's law cannot represent the flux-gradient relation. Here we revisit the fractional Fick's law for turbulent plasmas. We propose to use the Caputo fractional derivative of order $\beta < 1$ to express the particle flux in a bounded system. Simple steady-state solutions are given: in the case of a plasma at rest, we show that the solutions are power laws of order $\beta$; then we consider an advection-diffusion equation, and we show that the solutions are given by the Mittag-Leffler functions.