메뉴 건너뛰기




Volumn 45, Issue 10, 2009, Pages

Monte Carlo simulation of superdiffusion and subdiffusion in macroscopically heterogeneous media

Author keywords

[No Author keywords available]

Indexed keywords

ANOMALOUS DIFFUSION; CONTINUOUS TIME RANDOM WALKS; DERIVATIVE MODELS; DISPERSION COEFFICIENT; EFFECTIVE POROSITY; EULERIAN; FRACTIONAL DERIVATIVE MODEL; HETEROGENEOUS MEDIA; HITTING TIME; LAGRANGIAN; LANGEVIN; MONTE CARLO APPROACH; MONTE CARLO SIMULATION; MOTION COMPONENTS; PARTICLE DYNAMICS; PARTICLE TRAJECTORIES; REFLECTION PROBABILITY; SUBDIFFUSION; SUPERDIFFUSION; TRANSPORT PARAMETERS;

EID: 72149104317     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2008WR007448     Document Type: Article
Times cited : (15)

References (124)
  • 1
    • 33644799765 scopus 로고    scopus 로고
    • Parameter estimation for the truncated Pareto distribution
    • Aban, I. B., M. M. Meerschaert, and A. K. Panorska (2006), Parameter estimation for the truncated Pareto distribution, J. Am. Stat. Assoc., 101, 270-277.
    • (2006) J. Am. Stat. Assoc. , vol.101 , pp. 270-277
    • Aban, I.B.1    Meerschaert, M.M.2    Panorska, A.K.3
  • 2
    • 0027069042 scopus 로고
    • Field study of dispersion in a heterogeneous aquifer: 2. Spatial moment analysis
    • Adams, E. E., and L. W. Gelhar (1992), Field study of dispersion in a heterogeneous aquifer: 2. Spatial moment analysis, Water Resour. Res., 28, 3293-3307.
    • (1992) Water Resour. Res. , vol.28 , pp. 3293-3307
    • Adams, E.E.1    Gelhar, L.W.2
  • 5
    • 3242750610 scopus 로고    scopus 로고
    • Limit theorem for continuous-time random walks with two time scales
    • DOI 10.1239/jap/1082999078
    • Becker-Kern, P., M. M. Meerschaert, and H. P. Scheffler (2004), Limit theorem for continuous time random walks with two time scales, J. Appl. Probab., 41, 455-466. (Pubitemid 38977208)
    • (2004) Journal of Applied Probability , vol.41 , Issue.2 , pp. 455-466
    • Becker-Kern, P.1    Meerschaert, M.M.2    Scheffler, H.-P.3
  • 6
    • 62349103035 scopus 로고    scopus 로고
    • A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations
    • Benson, D. A., and M. M. Meerschaert (2009), A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations, Adv. Water Resour., 32, 532-539.
    • (2009) Adv. Water Resour. , vol.32 , pp. 532-539
    • Benson, D.A.1    Meerschaert, M.M.2
  • 7
    • 0034032484 scopus 로고    scopus 로고
    • Application of a fractional advection-dispersion equation
    • Benson, D. A., S. W. Wheatcraft, and M. M. Meerschaert (2000), Application of a fractional advection-dispersion equation, Water Resour. Res., 36, 1403-1412.
    • (2000) Water Resour. Res. , vol.36 , pp. 1403-1412
    • Benson, D.A.1    Wheatcraft, S.W.2    Meerschaert, M.M.3
  • 9
    • 0029506402 scopus 로고
    • On characterization of anomalous dispersion in porous and fractured media
    • Berkowitz, B., and H. Scher (1995), On characterization of anomalous dispersion in porous and fractured media, Water Resour. Res., 31, 1461-1466.
    • (1995) Water Resour. Res. , vol.31 , pp. 1461-1466
    • Berkowitz, B.1    Scher, H.2
  • 10
    • 0032073339 scopus 로고    scopus 로고
    • Theory of anomalous chemical transport in random fracture networks
    • Berkowitz, B., and H. Scher (1998), Theory of anomalous chemical transport in random fracture networks, Phys. Rev. E, 57, 5858-5869.
    • (1998) Phys. Rev. e , vol.57 , pp. 5858-5869
    • Berkowitz, B.1    Scher, H.2
  • 11
    • 0035068615 scopus 로고    scopus 로고
    • The role of probabilistic approaches to transport theory in heterogeneous media
    • Berkowitz, B., and H. Scher (2001), The role of probabilistic approaches to transport theory in heterogeneous media, Transp. Porous Media, 42, 241-263.
    • (2001) Transp. Porous Media , vol.42 , pp. 241-263
    • Berkowitz, B.1    Scher, H.2
  • 12
    • 0033986694 scopus 로고    scopus 로고
    • Anomalous transport in laboratory-scale, heterogeneous porous media
    • DOI 10.1029/1999WR900295
    • Berkowitz, B., H. Scher, and S. E. Silliman (2000), Anomalous transport in laboratory-scale, heterogeneous porous media, Water Resour. Res., 36, 149-158. (Pubitemid 30042117)
    • (2000) Water Resources Research , vol.36 , Issue.1 , pp. 149-158
    • Berkowitz, B.1    Scher, H.2    Silliman, S.E.3
  • 13
    • 0036822950 scopus 로고    scopus 로고
    • Physical pictures of transport in heterogeneous media: Advection-dispersion, randomwalk, and fractional derivative formulations
    • doi:10.1029/2001WR001030
    • Berkowitz, B., J. Klafter, R. Metzler, and H. Scher (2002), Physical pictures of transport in heterogeneous media: Advection-dispersion, randomwalk, and fractional derivative formulations, Water Resour. Res., 38(10), 1191, doi:10.1029/2001WR001030.
    • (2002) Water Resour. Res. , vol.38 , Issue.10 , pp. 1191
    • Berkowitz, B.1    Klafter, J.2    Metzler, R.3    Scher, H.4
  • 14
    • 33845247896 scopus 로고    scopus 로고
    • Modeling Non-fickian transport in geological formations as a continuous time random walk
    • DOI 10.1029/2005RG000178
    • Berkowitz, B., A. Cortis, M. Dentz, and H. Scher (2006), Modeling non-Fickian transport on geological formations as a continuous time random walk, Rev. Geophys., 44, RG2003, doi:10.1029/2005RG000178. (Pubitemid 46044201)
    • (2006) Reviews of Geophysics , vol.44 , Issue.2
    • Berkowitz, B.1    Cortis, A.2    Dentz, M.3    Scher, H.4
  • 15
    • 43049109491 scopus 로고    scopus 로고
    • Non-Fickian transport and multiple-rate mass transfer in porous media
    • DOI 10.1029/2007WR005906
    • Berkowitz, B., S. Emmanuel, and H. Scher (2008), Non-Fickian transport and multiple-rate mass transfer in porous media, Water Resour. Res., 44, W03402, doi:10.1029/2007WR005906. (Pubitemid 351628535)
    • (2008) Water Resources Research , vol.44 , Issue.3
    • Berkowitz, B.1    Emmanuel, S.2    Scher, H.3
  • 16
    • 62949194253 scopus 로고    scopus 로고
    • Laboratory experiments on dispersive transport across interfaces: The role of flow direction
    • doi:10.1029/2008WR007342
    • Berkowitz, B., A. Cortis, I. Dror, and H. Scher (2009), Laboratory experiments on dispersive transport across interfaces: The role of flow direction, Water Resour. Res., 45, W02201, doi:10.1029/2008WR007342.
    • (2009) Water Resour. Res. , vol.45
    • Berkowitz, B.1    Cortis, A.2    Dror, I.3    Scher, H.4
  • 17
    • 0027103243 scopus 로고
    • Field study of dispersion in a heterogeneous aquifer: 4. Investigation of adsorption and sampling bias
    • Boggs, J. M., and E. E. Adams (1992), Field study of dispersion in a heterogeneous aquifer: 4. Investigation of adsorption and sampling bias, Water Resour. Res., 28(12), 3325-3335.
    • (1992) Water Resour. Res. , vol.28 , Issue.12 , pp. 3325-3335
    • Boggs, J.M.1    Adams, E.E.2
  • 18
    • 0027061589 scopus 로고
    • Field study of dispersion in a heterogeneous aquifer: 1. Overview and site description
    • Boggs, J. M., S. C. Young, and L. M. Beard (1992), Field study of dispersion in a heterogeneous aquifer: 1. Overview and site description, Water Resour. Res., 28, 3281-3291.
    • (1992) Water Resour. Res. , vol.28 , pp. 3281-3291
    • Boggs, J.M.1    Young, S.C.2    Beard, L.M.3
  • 19
    • 0040307478 scopus 로고
    • Anomalous diffusion in disordered media: Statistical mechanism and physical applications
    • Bouchaud, J. P., and A. Georges (1990), Anomalous diffusion in disordered media: Statistical mechanism and physical applications, Phys. Rep., 195, 127-293.
    • (1990) Phys. Rep. , vol.195 , pp. 127-293
    • Bouchaud, J.P.1    Georges, A.2
  • 21
    • 15944428559 scopus 로고    scopus 로고
    • Anomalous diffusion and fractional advection-diffusion equation
    • Chang, F. X., J. Chen, and W. Huang (2005), Anomalous diffusion and fractional advection-diffusion equation, Acta Phys. Sinica, 54, 1113-1117.
    • (2005) Acta Phys. Sinica , vol.54 , pp. 1113-1117
    • Chang, F.X.1    Chen, J.2    Huang, W.3
  • 23
    • 18944388435 scopus 로고    scopus 로고
    • Fractal travel time estimates for dispersive contaminants
    • Clarke, D., M. M. Meerschaert, and S. W. Wheatcraft (2005), Fractal travel time estimates for dispersive contaminants, Ground Water, 43, 401-407.
    • (2005) Ground Water , vol.43 , pp. 401-407
    • Clarke, D.1    Meerschaert, M.M.2    Wheatcraft, S.W.3
  • 24
  • 25
    • 37649031846 scopus 로고    scopus 로고
    • Quantitative characterization of pore-scale disorder effects on transport in homogeneous granular media
    • DOI 10.1103/PhysRevE.70.041108, 041108
    • Cortis, A., Y. Chen, H. Scher, and B. Berkowitz (2004a), Quantitative characterization of pore-scale disorder effects on transport in "homogeneous" granular media, Phys. Rev. E, 70(10), 041108, doi:10.1103/PhysRevE.70.041108. (Pubitemid 40010427)
    • (2004) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics , vol.70 , Issue.10 , pp. 0411081-0411088
    • Cortis, A.1    Chen, Y.2    Scher, H.3    Berkowitz, B.4
  • 26
    • 2442709370 scopus 로고    scopus 로고
    • Numerical simulation of non-Fickian transport in geological formations with multiplescale heterogeneities
    • doi:10.1029/2003WR002750
    • Cortis, A., C. Gallo, H. Scher, and B. Berkowitz (2004b), Numerical simulation of non-Fickian transport in geological formations with multiplescale heterogeneities, Water Resour. Res., 40, W04209, doi:10.1029/2003WR002750.
    • (2004) Water Resour. Res. , vol.40
    • Cortis, A.1    Gallo, C.2    Scher, H.3    Berkowitz, B.4
  • 27
    • 0002367839 scopus 로고
    • An introduction to hierarchical porous media
    • edited by J. H. Cushman, Academic, London
    • Cushman, J. H. (1990), An introduction to hierarchical porous media, in Dynamics of Fluids in Hierarchical Porous Media, edited by J. H. Cushman, pp. 1 -6, Academic, London.
    • (1990) Dynamics of Fluids in Hierarchical Porous Media , pp. 1-6
    • Cushman, J.H.1
  • 29
    • 2142755490 scopus 로고    scopus 로고
    • Numerical solution of fractional advection-dispersion equation
    • Deng, Z.-Q., V. P. Singh, and L. Bengtsson (2004), Numerical solution of fractional advection-dispersion equation, J. Hydraul. Eng., 130, 422-431.
    • (2004) J. Hydraul. Eng. , vol.130 , pp. 422-431
    • Deng, Z.-Q.1    Singh, V.P.2    Bengtsson, L.3
  • 30
    • 33646517721 scopus 로고    scopus 로고
    • A fractional dispersion model for overland solute transport
    • doi:10.1029/2005WR004146
    • Deng, Z.-Q., J. de Lima, M. De Lima, and V. P. Singh (2006), A fractional dispersion model for overland solute transport, Water Resour. Res., 42, W03416, doi:10.1029/2005WR004146.
    • (2006) Water Resour. Res. , vol.42
    • Deng, Z.-Q.1    De Lima, J.2    De Lima, M.3    Singh, V.P.4
  • 31
    • 1542646350 scopus 로고    scopus 로고
    • Transport behavior of a passive solute in continuous time random walks and multirate mass transfer
    • doi:10.1029/2001WR001163
    • Dentz, M., and B. Berkowitz (2003), Transport behavior of a passive solute in continuous time random walks and multirate mass transfer, Water Resour. Res., 39(5), 1111, doi:10.1029/2001WR001163.
    • (2003) Water Resour. Res. , vol.39 , Issue.5 , pp. 1111
    • Dentz, M.1    Berkowitz, B.2
  • 32
    • 1342267258 scopus 로고    scopus 로고
    • Time behavior of solute transport in heterogeneous media: Transition from anomalous to normal transport
    • Dentz, M., A. Cortis, H. Scher, and B. Berkowitz (2004), Time behavior of solute transport in heterogeneous media: Transition from anomalous to normal transport, Adv. Water Resour., 27, 155-173.
    • (2004) Adv. Water Resour. , vol.27 , pp. 155-173
    • Dentz, M.1    Cortis, A.2    Scher, H.3    Berkowitz, B.4
  • 34
    • 0031656037 scopus 로고    scopus 로고
    • Identification of large-scale hydraulic conductivity trends and the influence of trends on contaminant transport
    • Eggleston, J., and S. Rojstaczer (1998), Identification of large-scale hydraulic conductivity trends and the influence of trends on contaminant transport, Water Resour. Res., 34, 2155-2168.
    • (1998) Water Resour. Res. , vol.34 , pp. 2155-2168
    • Eggleston, J.1    Rojstaczer, S.2
  • 36
    • 0001149907 scopus 로고    scopus 로고
    • A dual-domain mass transfer approach for modeling solute transport in heterogeneous porous media application to the MADE site
    • Feehley, C. E., C. Zheng, and F. J. Molz (2000), A dual-domain mass transfer approach for modeling solute transport in heterogeneous porous media, application to the MADE site,Water Resour. Res., 36, 2051-2515.
    • (2000) Water Resour. Res. , vol.36 , pp. 2051-2515
    • Feehley, C.E.1    Zheng, C.2    Molz, F.J.3
  • 38
    • 0004272246 scopus 로고    scopus 로고
    • 2nd ed., Prentice-Hall, Upper Saddle River, N. J
    • Fetter, C.W. (1999), Contaminant Hydrogeology, 2nd ed., 500 pp., Prentice-Hall, Upper Saddle River, N. J.
    • (1999) Contaminant Hydrogeology
    • Fetter, C.W.1
  • 39
    • 0000874039 scopus 로고
    • Lévy flights in random environments
    • Fogedby, H. C. (1994a), Lévy flights in random environments, Phys. Rev. Lett., 73, 2517-2520.
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 2517-2520
    • Fogedby, H.C.1
  • 40
    • 4244190920 scopus 로고
    • Langevin equations for continuous time Lévy flights
    • Fogedby, H. C. (1994b), Langevin equations for continuous time Lévy flights, Phys. Rev. E, 50, 1657-1660.
    • (1994) Phys. Rev. e , vol.50 , pp. 1657-1660
    • Fogedby, H.C.1
  • 43
    • 40549140431 scopus 로고    scopus 로고
    • Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation
    • doi:10.1103/PhysRevE.77.021122
    • Fulger, D., E. Scalas, and G. Germano (2008), Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation, Phys. Rev. E, 77, 021122, doi:10.1103/PhysRevE.77.021122.
    • (2008) Phys. Rev. e , vol.77 , pp. 021122
    • Fulger, D.1    Scalas, E.2    Germano, G.3
  • 44
    • 0036650850 scopus 로고    scopus 로고
    • Time fractional diffusion: A discrete random walk approach
    • DOI 10.1023/A:1016547232119, Fractional Order Calculus and Its Applications
    • Gorenflo, R., F. Mainardi, D. Moretti, and P. Paradisi (2002), Time fractional diffusion: A discrete random walk approach, Nonlinear Dyn., 29, 129-143. (Pubitemid 34945395)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 129-143
    • Gorenflo, R.1    Mainardi, F.2    Moretti, D.3    Paradisi, P.4
  • 45
    • 15544368331 scopus 로고    scopus 로고
    • Discrete and continuous random walk models for space-time fractional diffusion
    • Gorenflo, R., A. Vivoli, and F. Mainardi (2004), Discrete and continuous random walk models for space-time fractional diffusion, Nonlinear Dyn., 38, 101-116.
    • (2004) Nonlinear Dyn. , vol.38 , pp. 101-116
    • Gorenflo, R.1    Vivoli, A.2    Mainardi, F.3
  • 46
    • 34047155650 scopus 로고    scopus 로고
    • Continuous time random walk and parametric subordination in fractional diffusion
    • Gorenflo, R., F. Mainardi, and A. Vivoli (2007), Continuous time random walk and parametric subordination in fractional diffusion, Chaos Solitons Fractals, 34, 89-103.
    • (2007) Chaos Solitons Fractals , vol.34 , pp. 89-103
    • Gorenflo, R.1    Mainardi, F.2    Vivoli, A.3
  • 47
    • 0034502674 scopus 로고    scopus 로고
    • On the late-time behavior of tracer test breakthrough curves
    • Haggerty, R., S. A. McKenna, and L. C. Meigs (2000), On the late-time behavior of tracer test breakthrough curves, Water Resour. Res., 36, 3467-3479.
    • (2000) Water Resour. Res. , vol.36 , pp. 3467-3479
    • Haggerty, R.1    McKenna, S.A.2    Meigs, L.C.3
  • 48
    • 0034062226 scopus 로고    scopus 로고
    • Rate-limited mass transfer or macrodispersion: Which dominates plume evolution at the Macrodispersion Experiment (MADE) site?
    • Harvey, C. F., and S. M. Gorelick (2000), Rate-limited mass transfer or macrodispersion: Which dominates plume evolution at the Macrodispersion Experiment (MADE) site?, Water Resour. Res., 36, 637-650.
    • (2000) Water Resour. Res. , vol.36 , pp. 637-650
    • Harvey, C.F.1    Gorelick, S.M.2
  • 49
    • 0035865913 scopus 로고    scopus 로고
    • Water flow and solute mass flux in heterogeneous porous formations with spatially random porosity
    • Hassan, A. E. (2001), Water flow and solute mass flux in heterogeneous porous formations with spatially random porosity, J. Hydrol., 242, 1-25.
    • (2001) J. Hydrol. , vol.242 , pp. 1-25
    • Hassan, A.E.1
  • 50
    • 0031960695 scopus 로고    scopus 로고
    • A Monte Carlo assessment of Eulerian flow and transport perturbation models
    • Hassan, A. E., J. H. Cushman, and J. W. Delleur (1998), A Monte Carlo assessment of Eulerian flow and transport perturbation models, Water Resour. Res., 34, 1143-1163.
    • (1998) Water Resour. Res. , vol.34 , pp. 1143-1163
    • Hassan, A.E.1    Cushman, J.H.2    Delleur, J.W.3
  • 53
    • 33747610186 scopus 로고    scopus 로고
    • Evidence of onedimensional scale-dependent fractional advection-dispersion
    • Huang, G. H., Q. Z. Huang, and H. B. Zhan (2006), Evidence of onedimensional scale-dependent fractional advection-dispersion, J. Contam. Hydrol., 85, 53-71.
    • (2006) J. Contam. Hydrol. , vol.85 , pp. 53-71
    • Huang, G.H.1    Huang, Q.Z.2    Zhan, H.B.3
  • 55
    • 0034941374 scopus 로고    scopus 로고
    • Numerical simulation of a natural gradient tracer experiment for the natural attenuation study: Flow and physical transport
    • Julian, H. E., J. M. Boggs, C. Zheng, and C. E. Feehley (2001), Numerical simulation of a natural gradient tracer experiment for the natural attenuation study: Flow and physical transport, Ground Water, 39, 534-545.
    • (2001) Ground Water , vol.39 , pp. 534-545
    • Julian, H.E.1    Boggs, J.M.2    Zheng, C.3    Feehley, C.E.4
  • 56
    • 0035538793 scopus 로고    scopus 로고
    • A stochastic interpretation of the tailing effect in solute transport
    • Kennedy, C. A., and W. C. Lennox (2001), A stochastic interpretation of the tailing effect in solute transport, Stochastic Environ. Res. Risk Assess., 15, 325-340.
    • (2001) Stochastic Environ. Res. Risk Assess. , vol.15 , pp. 325-340
    • Kennedy, C.A.1    Lennox, W.C.2
  • 57
    • 31444435831 scopus 로고    scopus 로고
    • Generalized Fick's law and fractional ADE for pollutant transport in a river: Detailed derivation
    • Kim, S., and M. L. Kavvas (2006), Generalized Fick's law and fractional ADE for pollutant transport in a river: Detailed derivation, J. Hydrol. Eng., 11, 80-83.
    • (2006) J. Hydrol. Eng. , vol.11 , pp. 80-83
    • Kim, S.1    Kavvas, M.L.2
  • 58
    • 0001020008 scopus 로고
    • The random walk method in pollutant transport simulation
    • edited by E. Custodio et al. D. Reidel, Dordrecht, Netherlands
    • Kinzelbach, W. (1988), The random walk method in pollutant transport simulation, in Groundwater Flow and Quality Modeling, edited by E. Custodio et al., pp. 227-245, D. Reidel, Dordrecht, Netherlands.
    • (1988) Groundwater Flow and Quality Modeling , pp. 227-245
    • Kinzelbach, W.1
  • 59
    • 0034749297 scopus 로고    scopus 로고
    • Analysis of field observations of tracer transport in a fractured till
    • Kosakowski, G., B. Berkowitz, and H. Scher (2001), Analysis of field observations of tracer transport in a fractured till, J. Contam. Hydrol., 47, 29-51.
    • (2001) J. Contam. Hydrol. , vol.47 , pp. 29-51
    • Kosakowski, G.1    Berkowitz, B.2    Scher, H.3
  • 60
    • 0035065504 scopus 로고    scopus 로고
    • Role of molecular diffusion in contaminant migration and recovery in an alluvial aquifer system
    • LaBolle, E. M., and G. E. Fogg (2001), Role of molecular diffusion in contaminant migration and recovery in an alluvial aquifer system, Transp. Porous Media, 42, 155-179.
    • (2001) Transp. Porous Media , vol.42 , pp. 155-179
    • Labolle, E.M.1    Fogg, G.E.2
  • 61
    • 33645751554 scopus 로고    scopus 로고
    • Reply to comment by Doo-Hyun Lim on "diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients,"
    • doi:10.1029/2005WR004403
    • LaBolle, E. M., and Y. Zhang (2006), Reply to comment by Doo-Hyun Lim on "Diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients," Water Resour. Res., 42, W02602, doi:10.1029/2005WR004403.
    • (2006) Water Resour. Res. , vol.42
    • Labolle, E.M.1    Zhang, Y.2
  • 62
    • 0029656620 scopus 로고    scopus 로고
    • Random-walk simulation of transport in heterogeneous porous media: Local massconservation problem and implementation methods
    • LaBolle, E. M., G. E. Fogg, and A. F. B. Tompson (1996), Random-walk simulation of transport in heterogeneous porous media: Local massconservation problem and implementation methods, Water Resour. Res., 32, 393-583.
    • (1996) Water Resour. Res. , vol.32 , pp. 393-583
    • Labolle, E.M.1    Fogg, G.E.2    Tompson, A.F.B.3
  • 63
    • 0031866558 scopus 로고    scopus 로고
    • Diffusion theory for transport in porous media: Transition-probability densities of diffusion processes corresponding to advection-dispersion equations
    • LaBolle, E. M., J. Quastel, and G. E. Fogg (1998), Diffusion theory for transport in porous media: Transition-probability densities of diffusion processes corresponding to advection-dispersion equations,Water Resour. Res., 34, 1685-1693.
    • (1998) Water Resour. Res. , vol.34 , pp. 1685-1693
    • Labolle, E.M.1    Quastel, J.2    Fogg, G.E.3
  • 64
    • 0034099432 scopus 로고    scopus 로고
    • Diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients
    • LaBolle, E. M., J. Quastel, G. E. Fogg, and J. Gravner (2000), Diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients, Water Resour. Res., 36, 651-662.
    • (2000) Water Resour. Res. , vol.36 , pp. 651-662
    • Labolle, E.M.1    Quastel, J.2    Fogg, G.E.3    Gravner, J.4
  • 65
    • 49449104332 scopus 로고    scopus 로고
    • Non-Fickian dispersion in porous media: 2. Model validation from measurements at different scales
    • doi:10.1029/2007WR006279
    • Le Borgne, T., and P. Gouze (2008), Non-Fickian dispersion in porous media: 2. Model validation from measurements at different scales, Water Resour. Res., 44, W06427, doi:10.1029/2007WR006279.
    • (2008) Water Resour. Res. , vol.44
    • Le Borgne, T.1    Gouze, P.2
  • 66
    • 51349167211 scopus 로고    scopus 로고
    • Lagrangian statistical model for transport in highly heterogeneous velocity fields
    • doi:10.1103/PhysRevLett.101.090601
    • Le Borgne, T., M. Dentz, and J. Carrera (2008), Lagrangian statistical model for transport in highly heterogeneous velocity fields, Phys. Rev. Lett., 101, 090601, doi:10.1103/PhysRevLett.101.090601.
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 090601
    • Le Borgne, T.1    Dentz, M.2    Carrera, J.3
  • 67
    • 33751370304 scopus 로고    scopus 로고
    • Numerical study of nuclide migration in a nonuniform horizontal flow field of a high-level radioactive waste repository with multiple canisters
    • Lim, D. H. (2006), Numerical study of nuclide migration in a nonuniform horizontal flow field of a high-level radioactive waste repository with multiple canisters, Nucl. Technol., 156, 222-245.
    • (2006) Nucl. Technol. , vol.156 , pp. 222-245
    • Lim, D.H.1
  • 68
    • 0034061776 scopus 로고    scopus 로고
    • Determination of particle transfer in random walk particle methods for fractured porous media
    • Liu, H. H., G. S. Bodvarsson, and L. Pan (2000), Determination of particle transfer in random walk particle methods for fractured porous media, Water Resour. Res., 37, 707-713.
    • (2000) Water Resour. Res. , vol.37 , pp. 707-713
    • Liu, H.H.1    Bodvarsson, G.S.2    Pan, L.3
  • 69
    • 0036761104 scopus 로고    scopus 로고
    • Possible problems of scale dependency in applications of the three-dimensional fractional advectiondispersion equation to natural porous media
    • doi:10.1029/2001WR000624
    • Lu, S. L., F. J. Molz, and G. J. Fix (2002), Possible problems of scale dependency in applications of the three-dimensional fractional advectiondispersion equation to natural porous media, Water Resour. Res., 38(9), 1165, doi:10.1029/2001WR000624.
    • (2002) Water Resour. Res. , vol.38 , Issue.9 , pp. 1165
    • Lu, S.L.1    Molz, F.J.2    Fix, G.J.3
  • 71
    • 0027007065 scopus 로고
    • Application of the connection machine to flow and transport problems in three-dimensional heterogeneous aquifers
    • Mahinthakumar, G., and A. J. Valocchi (1992), Application of the connection machine to flow and transport problems in three-dimensional heterogeneous aquifers, Adv. Water Resour., 15, 289-302.
    • (1992) Adv. Water Resour. , vol.15 , pp. 289-302
    • Mahinthakumar, G.1    Valocchi, A.J.2
  • 73
    • 33846630918 scopus 로고    scopus 로고
    • Normal and anomalous transport across an interface: Monte Carlo and analytical approach
    • Marseguerra, M., and A. Zoia (2006), Normal and anomalous transport across an interface: Monte Carlo and analytical approach, Ann. Nucl. Energy, 33, 1396-1407.
    • (2006) Ann. Nucl. Energy , vol.33 , pp. 1396-1407
    • Marseguerra, M.1    Zoia, A.2
  • 74
    • 0019145640 scopus 로고
    • Is transport in porous media always diffusive? A counterexample
    • Matheron, G., and G. de Marsily (1980), Is transport in porous media always diffusive? A counterexample, Water Resour. Res., 16, 901-917.
    • (1980) Water Resour. Res. , vol.16 , pp. 901-917
    • Matheron, G.1    De Marsily, G.2
  • 75
    • 34547728198 scopus 로고    scopus 로고
    • Revisiting the Cape Cod bacteria injection experiment using a stochastic modeling approach
    • Maxwell, R. M., C. Welty, and R. W. Harvey (2007), Revisiting the Cape Cod bacteria injection experiment using a stochastic modeling approach, Environ. Sci. Technol., 41, 5548-5558.
    • (2007) Environ. Sci. Technol. , vol.41 , pp. 5548-5558
    • Maxwell, R.M.1    Welty, C.2    Harvey, R.W.3
  • 76
    • 0001943404 scopus 로고    scopus 로고
    • A simple robust estimation method for the thickness of heavy tails
    • Meerschaert, M. M., and H. P. Scheffler (1998), A simple robust estimation method for the thickness of heavy tails, J. Stat. Plann. Inference, 71(1-2), 19-34.
    • (1998) J. Stat. Plann. Inference , vol.71 , Issue.1-2 , pp. 19-34
    • Meerschaert, M.M.1    Scheffler, H.P.2
  • 78
    • 4043102385 scopus 로고    scopus 로고
    • Limit theorems for continuous time random walks with infinite mean waiting times
    • Meerschaert, M. M., and H. P. Scheffler (2004), Limit theorems for continuous time random walks with infinite mean waiting times, J. Appl. Probab., 41, 623-638.
    • (2004) J. Appl. Probab. , vol.41 , pp. 623-638
    • Meerschaert, M.M.1    Scheffler, H.P.2
  • 79
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection-dispersion flow equations
    • Meerschaert, M. M., and C. Tadjeran (2004), Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math., 172, 65-77.
    • (2004) J. Comput. Appl. Math. , vol.172 , pp. 65-77
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 80
    • 28044468843 scopus 로고    scopus 로고
    • Finite difference approximations for two-sided space-fractional partial differential equations
    • Meerschaert, M. M., and C. Tadjeran (2006), Finite difference approximations for two-sided space-fractional partial differential equations, Appl. Numer. Math., 56, 80-90.
    • (2006) Appl. Numer. Math. , vol.56 , pp. 80-90
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 81
    • 41349099804 scopus 로고    scopus 로고
    • Stochastic solution of space-time fractional diffusion equations
    • doi:10.1103/PhysRevE.65.041103
    • Meerschaert, M. M., D. A. Benson, H.-P. Scheffler, and B. Baeumer (2002), Stochastic solution of space-time fractional diffusion equations, Phys. Rev. E, 65, 041103, doi:10.1103/PhysRevE.65.041103.
    • (2002) Phys. Rev. e , vol.65 , pp. 041103
    • Meerschaert, M.M.1    Benson, D.A.2    Scheffler, H.-P.3    Baeumer, B.4
  • 82
    • 33747807970 scopus 로고    scopus 로고
    • Fractional vector calculus for fractional advection-dispersion
    • Meerschaert, M. M., J. Mortensen, and S. W. Wheatcraft (2006), Fractional vector calculus for fractional advection-dispersion, Physica A, 367, 181-190.
    • (2006) Physica A , vol.367 , pp. 181-190
    • Meerschaert, M.M.1    Mortensen, J.2    Wheatcraft, S.W.3
  • 83
    • 57049164298 scopus 로고    scopus 로고
    • Tempered anomalous diffusion in heterogeneous systems
    • doi:10.1029/2008GL034899
    • Meerschaert, M. M.,Y. Zhang, and B. Baeumer (2008), Tempered anomalous diffusion in heterogeneous systems, Geophys. Res. Lett., 35, L17403, doi:10.1029/2008GL034899.
    • (2008) Geophys. Res. Lett. , vol.35
    • Meerschaert, M.M.1    Zhang, Y.2    Baeumer, B.3
  • 84
    • 63549130217 scopus 로고    scopus 로고
    • Correlated continuous time random walks
    • doi:10.1016/j.spl.2009.01.007
    • Meerschaert, M. M., E. Nane, and Y. M. Xiao (2009), Correlated continuous time random walks, Stat. Prob. Lett., 79, 1194-1202, doi:10.1016/j.spl.2009.01. 007.
    • (2009) Stat. Prob. Lett. , vol.79 , pp. 1194-1202
    • Meerschaert, M.M.1    Nane, E.2    Xiao, Y.M.3
  • 85
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • Metzler, R., and J. Klafter (2000), The random walk's guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep., 339, 1-77.
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 86
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of the random walk: Recent development in fractional dynamics of anomalous transport processes
    • Metzler, R., and J. Klafter (2004), The restaurant at the end of the random walk: Recent development in fractional dynamics of anomalous transport processes, J. Phys. A, 37, R161-R208.
    • (2004) J. Phys. A , vol.37
    • Metzler, R.1    Klafter, J.2
  • 87
    • 0033865257 scopus 로고    scopus 로고
    • Macroscopic behaviour and random-walk particle tracking of kinetically sorbing solutes
    • Michalak, A. M., and P. K. Kitanidis (2000), Macroscopic behaviour and random-walk particle tracking of kinetically sorbing solutes, Water Resour. Res., 36, 2133-2146.
    • (2000) Water Resour. Res. , vol.36 , pp. 2133-2146
    • Michalak, A.M.1    Kitanidis, P.K.2
  • 89
    • 2542446420 scopus 로고    scopus 로고
    • Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions
    • doi:10.1029/2003RG000126
    • Molz, F. J., H. Rajaram, and S. Lu (2004), Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions, Rev. Geophys., 42, RG1002, doi:10.1029/2003RG000126.
    • (2004) Rev. Geophys. , vol.42
    • Molz, F.J.1    Rajaram, H.2    Lu, S.3
  • 90
    • 33746656614 scopus 로고    scopus 로고
    • Comment on investigating the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, using a three-dimensional inverse flow and transport model by Heidi Christiansen Barlebo, Mary C. Hill, and Dan Rosbjerg
    • DOI 10.1029/2005WR004265
    • Molz, F. J., C. Zheng, S. M. Gorelick, and C. F. Harvey (2006), Comment on "Investigating the Macrodispersion Experiment (MADE) site in Columbus, Mississipi, using a three-dimensional inverse flow and transport model" by Heidi Chrstiansen Barlebo, Mary C. Hill, and Dan Rosbjerg,Water Resour. Res., 42, W06603, doi:10.1029/2005WR004265. (Pubitemid 44156578)
    • (2006) Water Resources Research , vol.42 , Issue.6
    • Molz, F.J.1    Zheng, C.2    Gorelick, S.M.3    Harvey, C.F.4
  • 91
    • 0027456208 scopus 로고
    • Eulerian-Lagrangian theory of transport in spacetime nonstationary velocity fields: Exact nonlocal formalism by condi-tional moments and weak approximation
    • Neuman, S. P. (1993), Eulerian-Lagrangian theory of transport in spacetime nonstationary velocity fields: Exact nonlocal formalism by condi-tional moments and weak approximation, Water Resour. Res., 29, 633-645.
    • (1993) Water Resour. Res. , vol.29 , pp. 633-645
    • Neuman, S.P.1
  • 92
    • 64849090484 scopus 로고    scopus 로고
    • Perspective on theories of non-Fickian transport in heterogeneous media
    • Neuman, S. P., and D. M. Tartakovsky (2009), Perspective on theories of non-Fickian transport in heterogeneous media, Adv. Water Resour., 32, 670-680.
    • (2009) Adv. Water Resour. , vol.32 , pp. 670-680
    • Neuman, S.P.1    Tartakovsky, D.M.2
  • 93
    • 0242723836 scopus 로고
    • Fractional derivatives and Leibniz rule
    • Osler, T. J. (1971), Fractional derivatives and Leibniz rule, Am. Math. Mon., 78, 645-649.
    • (1971) Am. Math. Mon. , vol.78 , pp. 645-649
    • Osler, T.J.1
  • 94
    • 85102325477 scopus 로고    scopus 로고
    • Transport of water and solutes in soils as in fractal porous media
    • Pachepsky, Y., D. Timlin, and D. A. Benson (2001), Transport of water and solutes in soils as in fractal porous media, Soil Sci. Soc. Am., 56, 51-75.
    • (2001) Soil Sci. Soc. Am. , vol.56 , pp. 51-75
    • Pachepsky, Y.1    Timlin, D.2    Benson, D.A.3
  • 96
    • 0027871606 scopus 로고
    • Stochastic analysis of the transport of kinetically sorbing solutes in aquifers with randomly heterogeneous hydraulic conductivity
    • Quinodoz, H. A., and A. J. Valocchi (1993), Stochastic analysis of the transport of kinetically sorbing solutes in aquifers with randomly heterogeneous hydraulic conductivity, Water Resour. Res., 29, 3227-3240.
    • (1993) Water Resour. Res. , vol.29 , pp. 3227-3240
    • Quinodoz, H.A.1    Valocchi, A.J.2
  • 97
    • 46049098771 scopus 로고    scopus 로고
    • Transport of conservative solutes in simulated fracture networks: 2. Ensemble solute transport and the correspondence to operator-stable limit distributions
    • DOI 10.1029/2008WR006858
    • Reeves, D. M., D. A. Benson, M. M. Meerschaert, and H.-P. Scheffler (2008), Transport of conservative solutes in simulated fracture networks: 2. Ensemble solute transport and the correspondence to operator-stable limit distributions, Water Resour. Res., 44, W05410, doi:10.1029/2008WR006858. (Pubitemid 351897324)
    • (2008) Water Resources Research , vol.44 , Issue.5
    • Reeves, D.M.1    Benson, D.A.2    Meerschaert, M.M.3    Scheffler, H.-P.4
  • 98
    • 0027060213 scopus 로고
    • Field study of dispersion in a heterogeneous aquifer: 3. Geostatistical analysis of hydraulic conductivity
    • Rehfeldt, K. R., J. M. Boggs, and L. W. Gelhar (1992), Field study of dispersion in a heterogeneous aquifer: 3. Geostatistical analysis of hydraulic conductivity, Water Resour. Res., 28, 3309-3324.
    • (1992) Water Resour. Res. , vol.28 , pp. 3309-3324
    • Rehfeldt, K.R.1    Boggs, J.M.2    Gelhar, L.W.3
  • 99
    • 52949121016 scopus 로고    scopus 로고
    • Relative importance of geostatistical and transport models in describing heavily tailed breakthrough curves at the Lauswiesen site
    • Riva, M., A. Guadagnini, D. Fernandez-Garcia, X. Sanchez-Vila, and T. Ptak (2008), Relative importance of geostatistical and transport models in describing heavily tailed breakthrough curves at the Lauswiesen site, J. Contam. Hydrol., 101, 1-13.
    • (2008) J. Contam. Hydrol. , vol.101 , pp. 1-13
    • Riva, M.1    Guadagnini, A.2    Fernandez-Garcia, D.3    Sanchez-Vila, X.4    Ptak, T.5
  • 100
    • 33846337551 scopus 로고    scopus 로고
    • Modeling mass transfer processes using random walk particle tracking
    • DOI 10.1029/2006WR004927
    • Salamon, P., D. Fernàndez-Garcia, and J. J. Gómez- Hernández (2006), Modeling mass transfer processes using random walk particle tracking, Water Resour. Res., 42, W11417, doi:10.1029/2006WR004927. (Pubitemid 46134887)
    • (2006) Water Resources Research , vol.42 , Issue.11
    • Salamon, P.1    Fernandez-Garcia, D.2    Gomez-Hernandez, J.J.3
  • 101
    • 34848886078 scopus 로고    scopus 로고
    • Modeling tracer transport at the MADE site: The importance of heterogeneity
    • DOI 10.1029/2006WR005522
    • Salamon, P., D. Fernàndez-Garcia, and J. J. Gómez- Hernández (2007), Modeling tracer transport at the MADE site: The importance of heterogeneity, Water Resour. Res., 43, W08404, doi:10.1029/2006WR005522. (Pubitemid 47509786)
    • (2007) Water Resources Research , vol.43 , Issue.8
    • Salamon, P.1    Fernandez-Garcia, D.2    Gomez-Hernandez, J.J.3
  • 102
    • 0036829534 scopus 로고    scopus 로고
    • Towards a unified framework for anomalous transport in heterogeneous media
    • Scher, H., G. Margolin, and B. Berkowitz (2002), Towards a unified framework for anomalous transport in heterogeneous media, Chem. Phys., 284, 349-359.
    • (2002) Chem. Phys. , vol.284 , pp. 349-359
    • Scher, H.1    Margolin, G.2    Berkowitz, B.3
  • 103
    • 0035130739 scopus 로고    scopus 로고
    • Eulerian derivation of the fractional advection-dispersion equation
    • Schumer, R., D. A. Benson, M. M. Meerschaert, and B. Baeumer (2001), Eulerian derivation of the fractional advection-dispersion equation, J. Contam. Hydrol., 48, 69-88.
    • (2001) J. Contam. Hydrol. , vol.48 , pp. 69-88
    • Schumer, R.1    Benson, D.A.2    Meerschaert, M.M.3    Baeumer, B.4
  • 104
    • 1542436807 scopus 로고    scopus 로고
    • Fractal mobile/immobile solute transport
    • doi:10.1029/2003WR002141
    • Schumer, R., D. A. Benson, M. M. Meerschaert, and B. Baeumer (2003), Fractal mobile/immobile solute transport, Water Resour. Res., 39(10), 1296, doi:10.1029/2003WR002141.
    • (2003) Water Resour. Res. , vol.39 , Issue.10 , pp. 1296
    • Schumer, R.1    Benson, D.A.2    Meerschaert, M.M.3    Baeumer, B.4
  • 105
    • 0002406902 scopus 로고
    • Three dimensional groundwater quality modeling in heterogeneous media
    • edited by L. C. Wrobel and C. A. Brebbia, Comput. Mech., Billerica, Mass
    • Semra, K., P. Ackerer, and R. Mose (1993), Three dimensional groundwater quality modeling in heterogeneous media, in Water Pollution II: Modeling, Measuring and Prediction, edited by L. C. Wrobel and C. A. Brebbia, pp. 3 -11, Comput. Mech., Billerica, Mass.
    • (1993) Water Pollution II: Modeling, Measuring and Prediction , pp. 3-11
    • Semra, K.1    Ackerer, P.2    Mose, R.3
  • 106
    • 9944235714 scopus 로고    scopus 로고
    • Non-uniqueness of the first passage time density of Lévy random processes
    • Sokolov, I. M., and R. Metzler (2004), Non-uniqueness of the first passage time density of Lévy random processes, J. Phys. A Math. Gen., 37, L609-L615.
    • (2004) J. Phys. A Math. Gen. , vol.37
    • Sokolov, I.M.1    Metzler, R.2
  • 107
    • 0000775921 scopus 로고
    • Diffusion processes associated with Lévy generators
    • Stroock, D.W. (1975), Diffusion processes associated with Lévy generators, Z. Wahrsch. Verw. Gebiete, 32, 209-244.
    • (1975) Z. Wahrsch. Verw. Gebiete , vol.32 , pp. 209-244
    • Stroock, D.W.1
  • 108
    • 33745298497 scopus 로고    scopus 로고
    • Quantitative analysis of porosity heterogeneity: Application of geostatistics to borehole images
    • DOI 10.1007/s11004-005-9011-y
    • Tilke, P. G., D. Allen, and A. Gyllensten (2006), Quantitative analysis of porosity heterogeneity: Application of geostatistics to borehole images, Math. Geol., 38, 155-174, doi:10.1007/s11004-005-9011-y. (Pubitemid 43933705)
    • (2006) Mathematical Geology , vol.38 , Issue.2 , pp. 155-174
    • Tilke, P.G.1    Allen, D.2    Gyllensten, A.3
  • 109
    • 0027867778 scopus 로고
    • Numerical simulation of solute transport in three-dimensional randomly heterogeneous porous media
    • Tompson, A. F. B. (1993), Numerical simulation of solute transport in three-dimensional randomly heterogeneous porous media, Water Resour. Res., 29, 3709-3726.
    • (1993) Water Resour. Res. , vol.29 , pp. 3709-3726
    • Tompson, A.F.B.1
  • 110
    • 0034983863 scopus 로고    scopus 로고
    • A particle-tracking method for advective transport in fractures with diffusion into matrix blocks
    • Tsang, Y. W., and C. F. Tsang (2001), A particle-tracking method for advective transport in fractures with diffusion into matrix blocks, Water Resour. Res., 37, 831-835.
    • (2001) Water Resour. Res. , vol.37 , pp. 831-835
    • Tsang, Y.W.1    Tsang, C.F.2
  • 111
    • 0022206872 scopus 로고
    • A random walk method for the simulation of macrodispersion in a stratified aquifer
    • IAHS Publ.
    • Uffink, G. J. M. (1985), A random walk method for the simulation of macrodispersion in a stratified aquifer, in Relation of Groundwater Quality and Quantity, IAHS Publ., 146, 103-114.
    • (1985) Relation of Groundwater Quality and Quantity , vol.146 , pp. 103-114
    • Uffink, G.J.M.1
  • 112
    • 0036822606 scopus 로고    scopus 로고
    • Dispersion of groundwater age in an alluvial aquifer system
    • doi:10.1029/2001WR000907
    • Weissmann, G. S., Y. Zhang, E. M. LaBolle, and G. E. Fogg (2002), Dispersion of groundwater age in an alluvial aquifer system, Water Resour. Res., 38(10), 1198, doi:10.1029/2001WR000907.
    • (2002) Water Resour. Res. , vol.38 , Issue.10 , pp. 1198
    • Weissmann, G.S.1    Zhang, Y.2    Labolle, E.M.3    Fogg, G.E.4
  • 113
    • 0031435051 scopus 로고    scopus 로고
    • The influence of surface sorption on dispersion in parallel plate fractures
    • Wels, C., L. Smith, and R. Beckie (1997), The influence of surface sorption on dispersion in parallel plate fractures, J. Contam. Hydrol., 28, 95-114.
    • (1997) J. Contam. Hydrol. , vol.28 , pp. 95-114
    • Wels, C.1    Smith, L.2    Beckie, R.3
  • 114
    • 84950627400 scopus 로고
    • Particle-tracking technique for nuclide decay chain transport in fractured porous media
    • Yamashita, R., and H. Kimura (1990), Particle-tracking technique for nuclide decay chain transport in fractured porous media, J. Nucl. Sci. Technol., 27, 1042-1049.
    • (1990) J. Nucl. Sci. Technol. , vol.27 , pp. 1042-1049
    • Yamashita, R.1    Kimura, H.2
  • 115
    • 23944449029 scopus 로고    scopus 로고
    • A mass balance based numerical method for the fractional advection-dispersion equation: Theory and application
    • DOI 10.1029/2004WR003818, W07029
    • Zhang, X. X., J. W. Crawford, L. K. Deeks, M. I. Sutter, A. G. Bengough, and I. M. Young (2005), A mass balance based numerical method for the fractional advection-dispersion equation: Theory and application, Water Resour. Res., 41, W07029, doi:10.1029/2004WR003818. (Pubitemid 41197308)
    • (2005) Water Resources Research , vol.41 , Issue.7 , pp. 1-10
    • Zhang, X.1    Crawford, J.W.2    Deeks, L.K.3    Stutter, M.I.4    Bengough, A.G.5    Young, I.M.6
  • 116
    • 33646494026 scopus 로고    scopus 로고
    • On using random walks to solve the space-fractional advection-dispersion equations
    • Zhang, Y., D. A. Benson, M. M. Meerschaert, and H.-P. Scheffer (2006a), On using random walks to solve the space-fractional advection-dispersion equations, J. Stat. Phys., 123, 89-110.
    • (2006) J. Stat. Phys. , vol.123 , pp. 89-110
    • Zhang, Y.1    Benson, D.A.2    Meerschaert, M.M.3    Scheffer, H.-P.4
  • 117
    • 34347244858 scopus 로고    scopus 로고
    • Relationship between flux and resident concentrations for anomalous dispersion
    • DOI 10.1029/2006GL027251
    • Zhang, Y., B. Baeumer, and D. A. Benson (2006b), The relationship between flux and resident concentrations for anomalous diffusion, Geophys. Res. Lett., 33, L18407, doi:10.1029/2006GL027251. (Pubitemid 351175116)
    • (2006) Geophysical Research Letters , vol.33 , Issue.18
    • Zhang, Y.1    Baeumer, B.2    Benson, D.A.3
  • 119
    • 34347238581 scopus 로고    scopus 로고
    • Space-fractional advection-dispersion equations with variable parameters: Diverse formulas, numerical solutions, and application to the Macrodispersion Experiment site data
    • DOI 10.1029/2006WR004912
    • Zhang, Y., D. A. Benson, M. M. Meerschaert, and E. M. LaBolle (2007a), Space-fractional advection-dispersion equations with variable parameters: Diverse formulas, numerical solutions, and application to the MADE-site data, Water Resour. Res., 43, W05439, doi:10.1029/2006WR004912. (Pubitemid 46998239)
    • (2007) Water Resources Research , vol.43 , Issue.5
    • Zhang, Y.1    Benson, D.A.2    Meerschaert, M.M.3    LaBolle, E.M.4
  • 120
    • 34347257117 scopus 로고    scopus 로고
    • Predicting the tails of breakthrough curves in regional-scale alluvial systems
    • Zhang, Y., D. A. Benson, and B. Baeumer (2007b), Predicting the tails of breakthrough curves in regional-scale alluvial systems, Ground Water, 45, 473-484.
    • (2007) Ground Water , vol.45 , pp. 473-484
    • Zhang, Y.1    Benson, D.A.2    Baeumer, B.3
  • 121
    • 62349083202 scopus 로고    scopus 로고
    • Particle tracking for time-fractional diffusion
    • doi:10.1103/PhysRevE.78.036705
    • Zhang, Y., M. M. Meerschaert, and B. Baeumer (2008), Particle tracking for time-fractional diffusion, Phys. Rev. E, 78, 036705, doi:10.1103/PhysRevE. 78.036705.
    • (2008) Phys. Rev. e , vol.78 , pp. 036705
    • Zhang, Y.1    Meerschaert, M.M.2    Baeumer, B.3
  • 122
    • 62349097511 scopus 로고    scopus 로고
    • Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications
    • Zhang, Y., D. A. Benson, and D. M. Reeves (2009), Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications, Adv. Water Resour., 32, 561-581.
    • (2009) Adv. Water Resour. , vol.32 , pp. 561-581
    • Zhang, Y.1    Benson, D.A.2    Reeves, D.M.3
  • 123
    • 0037371909 scopus 로고    scopus 로고
    • Analysis of the effect of decimeterscale preferential flow paths on solute transport
    • Zheng, C., and S. M. Gorelick (2003), Analysis of the effect of decimeterscale preferential flow paths on solute transport, Ground Water, 41, 142-155.
    • (2003) Ground Water , vol.41 , pp. 142-155
    • Zheng, C.1    Gorelick, S.M.2
  • 124
    • 0043131921 scopus 로고    scopus 로고
    • Application of the fractional advectiondispersion equation in porous media
    • Zhou, L., and H. M. Selim (2003), Application of the fractional advectiondispersion equation in porous media, Soil Sci. Soc. Am. J., 67, 1079-1084.
    • (2003) Soil Sci. Soc. Am. J. , vol.67 , pp. 1079-1084
    • Zhou, L.1    Selim, H.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.