메뉴 건너뛰기




Volumn 62, Issue , 2013, Pages 207-214

Anomalous dispersion, renormalization groups, scaling laws and classification: A reflection on recent efforts

Author keywords

Anomalous diffusion dispersion; Central limit theorems; Renormalization groups

Indexed keywords

ANOMALOUS DIFFUSION; ANOMALOUS DISPERSION; ASYMPTOTIC LIMITS; CENTRAL LIMIT THEOREM; MEAN SQUARE DISPLACEMENT; RENORMALIZATION GROUP; RENORMALIZATION GROUP TECHNIQUE; SELF-SIMILARITIES;

EID: 84888294446     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2013.07.001     Document Type: Article
Times cited : (6)

References (48)
  • 2
  • 3
    • 33845247896 scopus 로고    scopus 로고
    • Modeling non-Fickian transport in geological formations as a continuous time random walk
    • Berkowitz B., Cortis A., Dentz M., Scher H. Modeling non-Fickian transport in geological formations as a continuous time random walk. Rev Geophys 2006, 44:1-49.
    • (2006) Rev Geophys , vol.44 , pp. 1-49
    • Berkowitz, B.1    Cortis, A.2    Dentz, M.3    Scher, H.4
  • 4
    • 0000087814 scopus 로고    scopus 로고
    • Anomalous transport in random fracture networks
    • Berkowitz B., Scher H. Anomalous transport in random fracture networks. Phys Rev Lett 1997, 79:4038-4041.
    • (1997) Phys Rev Lett , vol.79 , pp. 4038-4041
    • Berkowitz, B.1    Scher, H.2
  • 5
    • 0002541858 scopus 로고
    • Application of central limit theorems to solute dispersion in saturated porous media: From kinetic to field scales
    • Kluwer Academic, London, J.H. Cushman (Ed.)
    • Bhattacharya R., Gupta V.K. Application of central limit theorems to solute dispersion in saturated porous media: From kinetic to field scales. Dynamics of fluids in hierarchical porous media 1990, 61-95. Kluwer Academic, London. J.H. Cushman (Ed.).
    • (1990) Dynamics of fluids in hierarchical porous media , pp. 61-95
    • Bhattacharya, R.1    Gupta, V.K.2
  • 6
    • 77958033878 scopus 로고    scopus 로고
    • Generalized central limit theorem and renormalization group
    • Calvo I., Cuchi J.C., Esteve J.G., Falceto F. Generalized central limit theorem and renormalization group. J Stat Phys 2010, 141:409-421.
    • (2010) J Stat Phys , vol.141 , pp. 409-421
    • Calvo, I.1    Cuchi, J.C.2    Esteve, J.G.3    Falceto, F.4
  • 7
    • 35248828149 scopus 로고    scopus 로고
    • Fluid limit of the continuous-time random walk with general Lévy jump distribution functions
    • Cartea Á., del Castillo-Negrete D. Fluid limit of the continuous-time random walk with general Lévy jump distribution functions. Phys Rev E 2007, 76:041105.
    • (2007) Phys Rev E , vol.76 , pp. 041105
    • Cartea, Á.1    del Castillo-Negrete, D.2
  • 8
    • 0027683759 scopus 로고
    • Nonlocal dispersion in media with continuously evolving scales of heterogeneity
    • Cushman J.H., Ginn T.R. Nonlocal dispersion in media with continuously evolving scales of heterogeneity. Transp Porous Media 1993, 13:123-138.
    • (1993) Transp Porous Media , vol.13 , pp. 123-138
    • Cushman, J.H.1    Ginn, T.R.2
  • 9
    • 0034515585 scopus 로고    scopus 로고
    • Fractional advection-dispersion equation: a classical mass balance with convolution-Fickian flux
    • Cushman J.H., Ginn T.R. Fractional advection-dispersion equation: a classical mass balance with convolution-Fickian flux. Water Resour Res 2000, 36:3763-3766.
    • (2000) Water Resour Res , vol.36 , pp. 3763-3766
    • Cushman, J.H.1    Ginn, T.R.2
  • 10
    • 21344481403 scopus 로고
    • Nonequilibrium statistical mechanics of preasymptotic dispersion
    • Cushman J.H., Hu X., Ginn T.R. Nonequilibrium statistical mechanics of preasymptotic dispersion. J Stat Phys 1994, 75:859-878.
    • (1994) J Stat Phys , vol.75 , pp. 859-878
    • Cushman, J.H.1    Hu, X.2    Ginn, T.R.3
  • 14
    • 33749179709 scopus 로고    scopus 로고
    • Parameter estimation for fractional dispersion model for rivers
    • Deng Z., Bengtsson L., Singh V.P. Parameter estimation for fractional dispersion model for rivers. Environ Fluid Mech 2006, 6:451-475.
    • (2006) Environ Fluid Mech , vol.6 , pp. 451-475
    • Deng, Z.1    Bengtsson, L.2    Singh, V.P.3
  • 15
    • 78649992826 scopus 로고    scopus 로고
    • Distribution-versus correlation-induced anomalous transport in quenched random velocity fields
    • Dentz M., Bolster D. Distribution-versus correlation-induced anomalous transport in quenched random velocity fields. Phys Rev Lett 2010, 105:244301. http://link.aps.org/doi/10.1103/PhysRevLett.105.244301, 10.1103/PhysRevLett.105.244301.
    • (2010) Phys Rev Lett , vol.105 , pp. 244301
    • Dentz, M.1    Bolster, D.2
  • 16
    • 1342267258 scopus 로고    scopus 로고
    • Time behavior of solute transport in heterogeneous media: transition from anomalous to normal transport
    • Dentz M., Cortis A., Scher H., Berkowitz B. Time behavior of solute transport in heterogeneous media: transition from anomalous to normal transport. Adv Water Res 2004, 27:155-173.
    • (2004) Adv Water Res , vol.27 , pp. 155-173
    • Dentz, M.1    Cortis, A.2    Scher, H.3    Berkowitz, B.4
  • 17
    • 0034502674 scopus 로고    scopus 로고
    • On the late-time behavior of tracer test breakthrough curves
    • Haggerty R., McKenna S.A., Meigs L.C. On the late-time behavior of tracer test breakthrough curves. Water Resour Res 2000, 36:3467-3479.
    • (2000) Water Resour Res , vol.36 , pp. 3467-3479
    • Haggerty, R.1    McKenna, S.A.2    Meigs, L.C.3
  • 19
    • 0008828220 scopus 로고    scopus 로고
    • Renormalization group and probability theory
    • Jona-Lasinio G. Renormalization group and probability theory. Phys Rep 2001, 352:439-458.
    • (2001) Phys Rep , vol.352 , pp. 439-458
    • Jona-Lasinio, G.1
  • 20
    • 80155151108 scopus 로고    scopus 로고
    • Spatial markov model of anomalous transport through random lattice networks
    • Kang P.K., Dentz M., LeBorgne T., Juanes R. Spatial markov model of anomalous transport through random lattice networks. Phys Rev Lett 2011, 107:180602.
    • (2011) Phys Rev Lett , vol.107 , pp. 180602
    • Kang, P.K.1    Dentz, M.2    LeBorgne, T.3    Juanes, R.4
  • 21
    • 0000550285 scopus 로고
    • Stochastic pathway to anomalous diffusion
    • Klafter J., Blumen A., Shlesinger M. Stochastic pathway to anomalous diffusion. Phys Rev A 1987, 35:3081.
    • (1987) Phys Rev A , vol.35 , pp. 3081
    • Klafter, J.1    Blumen, A.2    Shlesinger, M.3
  • 22
    • 28144450152 scopus 로고    scopus 로고
    • Application of the finite-size Lyapunov exponent to particle tracking velocimetry in fluid mechanics experiments
    • Kleinfelter N., Moroni M., Cushman J.H. Application of the finite-size Lyapunov exponent to particle tracking velocimetry in fluid mechanics experiments. Phys Rev E 2005, 72:056306.
    • (2005) Phys Rev E , vol.72 , pp. 056306
    • Kleinfelter, N.1    Moroni, M.2    Cushman, J.H.3
  • 23
    • 51349167211 scopus 로고    scopus 로고
    • Lagrangian statistical model for transport in highly heterogeneous velocity fields
    • LeBorgne T., Dentz M., Carrera J. Lagrangian statistical model for transport in highly heterogeneous velocity fields. Phys Rev Lett 2008, 101:090601.
    • (2008) Phys Rev Lett , vol.101 , pp. 090601
    • LeBorgne, T.1    Dentz, M.2    Carrera, J.3
  • 25
    • 0015969022 scopus 로고
    • Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of carrier
    • Mandelbrot B.B. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of carrier. J Fluid Mech 1974, 62:331-358.
    • (1974) J Fluid Mech , vol.62 , pp. 331-358
    • Mandelbrot, B.B.1
  • 26
    • 4043102385 scopus 로고    scopus 로고
    • Limit theorems for continuous time random walks with infinite mean waiting times
    • Meerschaert M.M., Scheffler H.P. Limit theorems for continuous time random walks with infinite mean waiting times. J Appl Probab 2004, 41:623-638.
    • (2004) J Appl Probab , vol.41 , pp. 623-638
    • Meerschaert, M.M.1    Scheffler, H.P.2
  • 28
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: a fractional dynamics approach
    • Metzler R., Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys Rep 2000, 339:1-77.
    • (2000) Phys Rep , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 29
  • 30
    • 0025474361 scopus 로고
    • Universal scaling of hydraulic conductivities and dispersivities in geologic media
    • Neuman S.P. Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resour Res 1990, 26:1749-1758.
    • (1990) Water Resour Res , vol.26 , pp. 1749-1758
    • Neuman, S.P.1
  • 31
    • 0027456208 scopus 로고
    • Eulerian-Lagrangian theory of transport in space-time nonstationary velocity fields: exact nonlocal formalism by conditional moments and weak approximation
    • Neuman S.P. Eulerian-Lagrangian theory of transport in space-time nonstationary velocity fields: exact nonlocal formalism by conditional moments and weak approximation. Water Resour Res 1993, 29:633-645.
    • (1993) Water Resour Res , vol.29 , pp. 633-645
    • Neuman, S.P.1
  • 32
    • 64849090484 scopus 로고    scopus 로고
    • Perspective on theories of non-Fickian transport in heterogeneous media
    • Neuman S.P., Tartakovsky D.M. Perspective on theories of non-Fickian transport in heterogeneous media. Adv Water Resour 2009, 32:670-680.
    • (2009) Adv Water Resour , vol.32 , pp. 670-680
    • Neuman, S.P.1    Tartakovsky, D.M.2
  • 33
    • 78651235765 scopus 로고    scopus 로고
    • Fractional Brownian motion run with a non-linear clock
    • O'Malley D., Cushman J.H. Fractional Brownian motion run with a non-linear clock. Phys Rev E 2010, 82:032102.
    • (2010) Phys Rev E , vol.82 , pp. 032102
    • O'Malley, D.1    Cushman, J.H.2
  • 34
    • 84857923278 scopus 로고    scopus 로고
    • A renormalization group classification of nonstationary and/or infinite second moment diffusive processes
    • O'Malley D., Cushman J.H. A renormalization group classification of nonstationary and/or infinite second moment diffusive processes. J Stat Phys 2012, 10.1007/s10955-012-0448-3.
    • (2012) J Stat Phys
    • O'Malley, D.1    Cushman, J.H.2
  • 35
    • 84864778303 scopus 로고    scopus 로고
    • Two-scale renormalization-group classification of diffusive processes
    • O'Malley D., Cushman J.H. Two-scale renormalization-group classification of diffusive processes. Phys Rev E 2012, 86:011126.
    • (2012) Phys Rev E , vol.86 , pp. 011126
    • O'Malley, D.1    Cushman, J.H.2
  • 36
    • 84870741954 scopus 로고    scopus 로고
    • Random renormalization group operators applied to stochastic dynamics
    • O'Malley D., Cushman J.H. Random renormalization group operators applied to stochastic dynamics. J Stat Phys 2012, 1-8.
    • (2012) J Stat Phys , pp. 1-8
    • O'Malley, D.1    Cushman, J.H.2
  • 37
    • 79751481113 scopus 로고    scopus 로고
    • Scaling laws for fractional Brownian motion with power-law clock
    • O'Malley D., Cushman J.H., Johnson G. Scaling laws for fractional Brownian motion with power-law clock. J Stat Mech Theory Exp 2011, 2011:L01001.
    • (2011) J Stat Mech Theory Exp , vol.2011
    • O'Malley, D.1    Cushman, J.H.2    Johnson, G.3
  • 38
    • 34547152719 scopus 로고    scopus 로고
    • Finite-size Lyapunov exponent for Lévy processes
    • Parashar R., Cushman J.H. Finite-size Lyapunov exponent for Lévy processes. Phys Rev E 2007, 76:017201.
    • (2007) Phys Rev E , vol.76 , pp. 017201
    • Parashar, R.1    Cushman, J.H.2
  • 39
    • 65449148311 scopus 로고    scopus 로고
    • Operator-stable Lévy motions and renormalizing the chaotic dynamics of microbes in anisotropic porous media
    • Park M., Cushman J.H. Operator-stable Lévy motions and renormalizing the chaotic dynamics of microbes in anisotropic porous media. J Stat Mech Theory Exp 2009, 2009:P02039.
    • (2009) J Stat Mech Theory Exp , vol.2009
    • Park, M.1    Cushman, J.H.2
  • 40
    • 33644618675 scopus 로고    scopus 로고
    • Scaling laws and Fokker-Planck equations for 3-dimensional porous media with fractal mesoscale
    • Park M., Kleinfelter N., Cushman J.H. Scaling laws and Fokker-Planck equations for 3-dimensional porous media with fractal mesoscale. Multiscale Model Simul 2005, 4:1233-1244.
    • (2005) Multiscale Model Simul , vol.4 , pp. 1233-1244
    • Park, M.1    Kleinfelter, N.2    Cushman, J.H.3
  • 41
    • 13444309297 scopus 로고    scopus 로고
    • Models of anomalous diffusion: the subdiffusive case
    • Piryatinska A., Saichev A.I., Woyczynski W.A. Models of anomalous diffusion: the subdiffusive case. Phys A Stat Mech Appl 2005, 349:375-420. http://www.sciencedirect.com/science/article/pii/S0378437104014098, 10.1016/j.physa.2004.11.003.
    • (2005) Phys A Stat Mech Appl , vol.349 , pp. 375-420
    • Piryatinska, A.1    Saichev, A.I.2    Woyczynski, W.A.3
  • 42
    • 0000917473 scopus 로고
    • Atmospheric diffusion shown on a distance-neighbour graph
    • Richardson L.F. Atmospheric diffusion shown on a distance-neighbour graph. Proc R Soc Lond Ser A 1926, 110:709-737.
    • (1926) Proc R Soc Lond Ser A , vol.110 , pp. 709-737
    • Richardson, L.F.1
  • 45
    • 3142681196 scopus 로고    scopus 로고
    • Fractional Brownian motion and long-range dependence
    • Birkhauser, Cambridge, MA, P. Doukhan, G. Oppenheim, M.S. Taqqu (Eds.)
    • Taqqu M.S. Fractional Brownian motion and long-range dependence. Theory and applications of long range dependence 2003, 5-38. Birkhauser, Cambridge, MA. P. Doukhan, G. Oppenheim, M.S. Taqqu (Eds.).
    • (2003) Theory and applications of long range dependence , pp. 5-38
    • Taqqu, M.S.1
  • 46
    • 33644794918 scopus 로고    scopus 로고
    • Identification of periodic autoregressive moving average models and their application to the modeling of river flows
    • Tesfaye Y.G., Meerschaert M.M., Anderson P.L. Identification of periodic autoregressive moving average models and their application to the modeling of river flows. Water Resour Res 2006, 42:W01419.
    • (2006) Water Resour Res , vol.42
    • Tesfaye, Y.G.1    Meerschaert, M.M.2    Anderson, P.L.3
  • 47
    • 0023794199 scopus 로고
    • An explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry
    • Wheatcraft S.W., Tyler S.W. An explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry. Water Resour Res 1988, 24:566-578.
    • (1988) Water Resour Res , vol.24 , pp. 566-578
    • Wheatcraft, S.W.1    Tyler, S.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.