Equivalence of finite dimensional input-output models of solute   transport and diffusion in geosciences
  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 quite popular in geo-sciences. Moreover, we provide explicit methods to construct these equivalent representations. The proofs show that controllability property is playing a crucial role for obtaining equivalence. These results contribute to our fundamental understanding on the effect of fine-scale geological structures on the transfer and dispersion of solute, and, eventually, on their interaction with soil microbes and minerals. 
Alain Rapaport (MISTEA), Alejandro Rojas-Palma (MISTEA, DIM, CMM),   Jean-Raynald De Dreuzy (GR), Hector Ramirez (DIM, CMM)
math.OC