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- W15560238 abstract "Field data, obtained in heterogeneous aquifers, show behaviors not compatible with Fick's law, which holds for homogeneous media, and states that the flux of a passive tracer is proportional to the gradient of the concentration. Depending on the medium, deviations may be due to trapping sites or to preferential paths. Here, we focus on the second possibility, which corresponds to concentration profiles showing heavy tails and skewness. For those situations, small scale models are random walks with Levy laws for the jump-length distribution. On the large scale, they correspond to partial differential equations involving fractional derivatives for the evolution of the concentration. The solutions to those equations were shown to satisfy fractional variants of Fick's law, with flux proportional to a fractional derivative of the concentration, in infinite domains. Here, we use a natural and physical definition of fractional derivatives, which allows us to extend the result to domains limited by boundary-conditions, more especially when the jump-length distribution is non-symmetric." @default.
- W15560238 created "2016-06-24" @default.
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- W15560238 date "2007-01-01" @default.
- W15560238 modified "2023-09-27" @default.
- W15560238 title "Seminar N° 81 Fractional non-symmetric Fick's law in heterogeneous media" @default.
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