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Equivalence of finite dimensional input-output models of solute transport and diffusion in geoscience

Abstract : We show that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in geological media, there exist equivalent "multi-rate mass transfer" and "multiple interacting continua" representations, which are quitepopular in geosciences. Moreover, we provide explicit methods to construct these equivalent representations. The proofs show that controllability property is playing a crucial role. These results contribute to our fundamental understanding on the effect of fine-scale geological structures on the transfer and dispersion of solute.
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Alain Rapaport, Alejandro Rojas-Palma, Jean-Raynald de Dreuzy, Hector Ramirez. Equivalence of finite dimensional input-output models of solute transport and diffusion in geoscience. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2017, 62 (10), pp.5470-5477. ⟨10.1109/TAC.2017.2701150⟩. ⟨hal-01334540v3⟩

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