References
- [1] G. Taylor, Diffusion and mass transport in tubes, Proc. Phys. Soc. B 67(857), 1954.
- [2] R. Aris, On the dispersion of a solute in a fluid owing through a tube, Proc. Roy Soc. London A 235:67, 1956.
- [3] J. Glimm, W.B. Lindquist, F. Pereira, Q. Zhang, A theory of macrodispersion for the scale up problem, Transp. Porous Med. 13: 97, 1993.
- [4] N. Suciu, Diffusion in random velocity fields with applications to contaminant transport in groundwater, Adv. Water Resour., 69: 114-133, 2014.
- [5] N. Suciu, S. Attinger, F. A. Radu, C. Vamos, J. Vanderborght, H. Vereecken and P. Knabner, Solute transport in aquifers with evolving scale heterogeneity, An. St. Univ. Ovidius Constanta, 23(3): 167-186, 2015.
- [6] N. Suciu, F.A. Radu, S. Attinger, L. Schueler and P. Knabner, A Fokker- Planck approach for probability distributions of species concentrations transported in heterogeneous media, J. Comput. and Appl. Math., 289 (1): 114-133, 2015.
- [7] J.P. Gwo, P.M. Jardine, G.V. Wilson, G.T. Yeh: Using a multiregion model to study the effects of advective and diffusive mass transfer on local physical nonequilibrium and solute mobility in a structured soil, Wat. Resour. Res., 32: 561, 1996.
- [8] B. Berkowitz, A. Cortis, M. Dentz, H. Scher, Modeling non-Fickian trans- port in geological formations as a continuous time random walk, Rev. Geophys., 44: RG2003, 2006.
- [9] L. Vasilyev, A. Raoof, J.M. Nordbotten, Effect of Mean Network Coordination Number on Dispersivity Characteristics, Transp. Porous Med. 95: 447-463, 2012.
- [10] L. Vasilyev, J.M. Nordbotten, F.A. Radu and K. Kumar, On the proper- ties of the parameter space of generalized continuum transport model for description of fluid ow in porous networks, submitted, 2017.
- [11] J.S. Aronofsky, J.P. Heller: A diffusion model to explain mixing of owing miscible fluids in porous media, Trans. Am. Inst. Min. Metall. Pet. Eng., 210: 345{349, 1957.
- [12] A.E. Scheidegger: An evaluation of the accuracy of the diffusivity equation for describing miscible displacement in porous media, Proc. Theory Fluid Flow Porous Media Conf. 2nd: 101-116, 1959.
- [13] C. Kennedy, W. Lennox: A stochastic interpretation of the tailing effect in solute transport, Stochastic Environmental Research and Risk Assesment, 15: 325{340, 2001.
- [14] D.K. Jaiswal, A. Kumar, R.R. Yadav, Analytical Solution to the One- Dimensional Advection-Diffusion Equation with Temporally Dependent Coeffcients, Journal of Water Resource and Protection, 3: 76{84, 2011.
- [15] N. Suciu, C. Vamos, F.A. Radu, H. Vereecken, P. Knabner, Persistent memory of diffusing particles, Phys. Rev. E 80:061134, 2014.
- [16] C. Vamos, N. Suciu, H. Vereecken, Generalized random walk algorithm for the numerical modeling of complex diffusion process, J. Comput. Phys. 186(2): 527{44, 2003.
- [17] N. Suciu, C. Vamos, H. Vereecken, P. Knabner, Global random walk simulations for sensitivity and uncertainty analysis of passive transport models, Annals of the Academy of Romanian Scientists, Series on Mathematics and its Applications 3 (1), 2011.
- [18] B. Berkowitz, J. Klafter, R. Metzler, H. Scher, Physical pictures of transport in heterogeneous media: Advection dispersion, random-walk, and fractional derivative formulations, Water Resour. Res., 38(10): 1191, 2002.
- [19] T. Vogel, H.H. Gerke, R. Zhang, M.Th. van Genuchten, Modeling ow and transport in a two-dimensional dual-permeability system with spatially variable hydraulic properties, Journal of Hydrology, 238: 78-89, 2000.
- [20] J.M. Nordbotten, L. Vasilyev, On the relationship between multiple porosity models and continuous time random walk, XVIII International Conference on Water Resources CMWR2010, 2010.
- [21] M.Th. van Genuchten, W.J. Alves, Analyitical slutions of the one- dimensional convective-dispersive solute transport equation. U.S. Department of Agriculture, Technical Bulletin, No. 1661, 1982.
- [22] V.M Kenkre, E.W. Montroll, M.F. Shlesinger, Generalized master equations for continuous-time random walks, J. Stat. Phys., 9(1): 45-50, 1973.
- [23] J.A. Nelder, R. Mead, A simplex method for function optimization. Com- put. J. 7: 308{313, 1965.
- [24] M.F. Shlesinger, Asymptotic solutions of continuous-time random walks, J. Stat. Phys., 10(5): 421-434, 1974.
- [25] M. Dentz, A. Cortis, H. Scher, B. Berkowitz, Time behavior of solute transport in heterogeneous media: Transition from anomalous to normal transport, Adv. Water Resour., 27: 155-173, 2004.
- [26] M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, Dover, Mineola, N.Y., 1970.
- [27] F.A. Radu, N. Suciu, J. Hoffmann, A. Vogel, O. Kolditz, C-H. Park and S. Attinger, Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: a comparative study. Adv. Water Resour., 34 (1): 47-61, 2011.