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Volumn 59, Issue 3, 2010, Pages 1078-1086

Particle tracking for fractional diffusion with two time scales

Author keywords

Lagrangian solver; Langevin analysis; Time fractional diffusion equation

Indexed keywords

ALTERNATIVE METHODS; ANALYSIS TIME; CAUCHY PROBLEMS; FIRST DERIVATIVE; FRACTIONAL DIFFUSION; FRACTIONAL EQUATION; FRACTURE FLOW; FREE PARTICLES; HETEROGENEOUS POROUS MEDIA; INDIVIDUAL PARTICLES; INVERSE TRANSFORMS; LAGRANGIAN; LANGEVIN; LANGEVIN EQUATION; MODEL EQUATIONS; MONTE CARLO SIMULATION; NON-MARKOVIAN; PARTICLE LOCATIONS; PARTICLE TRACKING; PROBABILITY DENSITIES; PROCESS MODEL; SPACE AND TIME; SPATIAL DIMENSION; STOCHASTIC DIFFERENTIAL EQUATIONS; STOCHASTIC PROCESS; SUBORDINATORS; TIME CHANGE; TIME DERIVATIVE; TIME-FRACTIONAL DIFFUSION; TWO TIME SCALE; UPSCALING; VARIABLE COEFFICIENTS;

EID: 74149090927     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.05.009     Document Type: Article
Times cited : (46)

References (52)
  • 1
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamic approach
    • Metzler R., and Klafter J. The random walk's guide to anomalous diffusion: A fractional dynamic approach. Phys. Rep. 339 (2000) 1-77
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 2
    • 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 Klafter J. The restaurant at the end of the random walk: Recent development in fractional dynamics of anomalous transport processes. J. Phys. A 37 (2004) R161-R208
    • (2004) J. Phys. A , vol.37
    • Metzler, R.1    Klafter, J.2
  • 3
    • 0035921214 scopus 로고    scopus 로고
    • Waiting-time distributions in lattice models for solar flares
    • Norman J.P., Charbonneau P., McIntosh S.W., and Liu H.L. Waiting-time distributions in lattice models for solar flares. Astrophys. J. 557 (2001) 891-896
    • (2001) Astrophys. J. , vol.557 , pp. 891-896
    • Norman, J.P.1    Charbonneau, P.2    McIntosh, S.W.3    Liu, H.L.4
  • 4
    • 0035810193 scopus 로고    scopus 로고
    • Are hospital waiting lists self-regulating?
    • Smethurst D.P., and Williams H.C. Are hospital waiting lists self-regulating?. Nature 410 (2001) 652-653
    • (2001) Nature , vol.410 , pp. 652-653
    • Smethurst, D.P.1    Williams, H.C.2
  • 5
    • 33846708528 scopus 로고    scopus 로고
    • Power law of quiet time distribution in the Korean stock-market
    • 576-572
    • Hong B.H., Lee K.E., and Lee J.W. Power law of quiet time distribution in the Korean stock-market. Physica A 377 (2007) 576-572
    • (2007) Physica A , vol.377
    • Hong, B.H.1    Lee, K.E.2    Lee, J.W.3
  • 6
    • 33750311773 scopus 로고    scopus 로고
    • Universal earthquake-occurrence jumps, correlations with time, and anomalous diffusion
    • Corral A. Universal earthquake-occurrence jumps, correlations with time, and anomalous diffusion. Phys. Rev. Lett. 97 (2006) 178501
    • (2006) Phys. Rev. Lett. , vol.97 , pp. 178501
    • Corral, A.1
  • 8
    • 0034502674 scopus 로고    scopus 로고
    • On the late-time behavior of tracer test breakthrough curves
    • Haggerty R., McKenna S.A., and Meigs L.C. On the late-time behavior of tracer test breakthrough curves. Water Resour. Res. 36 12 (2000) 3467-3479
    • (2000) Water Resour. Res. , vol.36 , Issue.12 , pp. 3467-3479
    • Haggerty, R.1    McKenna, S.A.2    Meigs, L.C.3
  • 9
    • 34347257117 scopus 로고    scopus 로고
    • Predicting the tails of breakthrough curves in regional-scale alluvial systems
    • Zhang Y., Benson D.A., and Baeumer B. Predicting the tails of breakthrough curves in regional-scale alluvial systems. Ground Water 45 4 (2007) 473-484
    • (2007) Ground Water , vol.45 , Issue.4 , pp. 473-484
    • Zhang, Y.1    Benson, D.A.2    Baeumer, B.3
  • 10
    • 14844311252 scopus 로고    scopus 로고
    • Advection and dispersion in time and space
    • Baeumer B., Benson D.A., and Meerschaert M.M. Advection and dispersion in time and space. Phys. A 350 2-4 (2005) 245-262
    • (2005) Phys. A , vol.350 , Issue.2-4 , pp. 245-262
    • Baeumer, B.1    Benson, D.A.2    Meerschaert, M.M.3
  • 11
    • 33751033123 scopus 로고    scopus 로고
    • Fractional diffusion with two time scales
    • Baeumer B., and Meerschaert M.M. Fractional diffusion with two time scales. Phys. A 373 (2007) 237-251
    • (2007) Phys. A , vol.373 , pp. 237-251
    • Baeumer, B.1    Meerschaert, M.M.2
  • 12
    • 3242750610 scopus 로고    scopus 로고
    • Limit theorem for continuous time random walks with two time scales
    • Becker-Kern P., Meerschaert M.M., and Scheffler H.P. Limit theorem for continuous time random walks with two time scales. J. Appl. Probab. 41 2 (2004) 455-466
    • (2004) J. Appl. Probab. , vol.41 , Issue.2 , pp. 455-466
    • Becker-Kern, P.1    Meerschaert, M.M.2    Scheffler, H.P.3
  • 14
    • 33748713050 scopus 로고    scopus 로고
    • A review and numerical assessment of the random walk particle tracking method
    • Salamon P., Fernàndez-Gareia D., and Gómez-Hernández J.J. A review and numerical assessment of the random walk particle tracking method. J. Contam. Hydrol. 87 (2007) 277-305
    • (2007) J. Contam. Hydrol. , vol.87 , pp. 277-305
    • Salamon, P.1    Fernàndez-Gareia, D.2    Gómez-Hernández, J.J.3
  • 15
    • 0027867778 scopus 로고
    • Numerical simulation of solute transport in three-dimensional randomly heterogeneous porous media
    • Tompson A.F.B. Numerical simulation of solute transport in three-dimensional randomly heterogeneous porous media. Water Resour. Res. 29 11 (1993) 3709-3726
    • (1993) Water Resour. Res. , vol.29 , Issue.11 , pp. 3709-3726
    • Tompson, A.F.B.1
  • 16
    • 0036822606 scopus 로고    scopus 로고
    • Dispersion of groundwater age in an alluvial aquifer system
    • 10.1029/2001WR000907
    • Weissmann G.S., Zhang Y., LaBolle E.M., and Fogg G.E. Dispersion of groundwater age in an alluvial aquifer system. Water Resour. Res. 38 10 (2002) 10.1029/2001WR000907
    • (2002) Water Resour. Res. , vol.38 , Issue.10
    • Weissmann, G.S.1    Zhang, Y.2    LaBolle, E.M.3    Fogg, G.E.4
  • 17
    • 0001020008 scopus 로고
    • The random walk method in pollutant transport simulation
    • Custodio E., et al. (Ed), Reidel Publishing Company
    • Kinzelbach W. The random walk method in pollutant transport simulation. In: Custodio E., et al. (Ed). Groundwater Flow and Quality Modelling (1988), Reidel Publishing Company 227-245
    • (1988) Groundwater Flow and Quality Modelling , pp. 227-245
    • Kinzelbach, W.1
  • 18
    • 0029656620 scopus 로고    scopus 로고
    • Random-walk simulation of transport in heterogeneous porous media: Local mass-conservation problem and implementation methods
    • LaBolle E., Fogg G., and Tompson A.F.B. Random-walk simulation of transport in heterogeneous porous media: Local mass-conservation problem and implementation methods. Water Resour. Res. 32 3 (1996) 583-594
    • (1996) Water Resour. Res. , vol.32 , Issue.3 , pp. 583-594
    • LaBolle, E.1    Fogg, G.2    Tompson, A.F.B.3
  • 19
    • 62349083202 scopus 로고    scopus 로고
    • Particle tracking for time-fractional diffusion
    • Zhang Y., Meerschaert M.M., and Baeumer B. Particle tracking for time-fractional diffusion. Phys. Rev. E 78 (2008) 036705
    • (2008) Phys. Rev. E , vol.78 , pp. 036705
    • Zhang, Y.1    Meerschaert, M.M.2    Baeumer, B.3
  • 21
    • 34047155650 scopus 로고    scopus 로고
    • Continuous time random walk and parametric subordination in fractional diffusion
    • Gorenflo R., Mainardi F., and Vivoli A. Continuous time random walk and parametric subordination in fractional diffusion. Chaos Solitons Fractals 34 (2007) 89-103
    • (2007) Chaos Solitons Fractals , vol.34 , pp. 89-103
    • Gorenflo, R.1    Mainardi, F.2    Vivoli, A.3
  • 22
    • 33646360565 scopus 로고    scopus 로고
    • Fractional Fokker-Planck dynamics: Numerical algorithm and simulations
    • Heinsalu E., Patriarca M., Goychuk I., Schmid G., and Hanggi P. Fractional Fokker-Planck dynamics: Numerical algorithm and simulations. Phys. Rev. E 73 (2006) 046133
    • (2006) Phys. Rev. E , vol.73 , pp. 046133
    • Heinsalu, E.1    Patriarca, M.2    Goychuk, I.3    Schmid, G.4    Hanggi, P.5
  • 23
    • 36749036093 scopus 로고    scopus 로고
    • Continuous-time random walks: Simulation of continuous trajectories
    • Kleinhans D., and Friedrich R. Continuous-time random walks: Simulation of continuous trajectories. Phys. Rev. E 76 (2007) 06112
    • (2007) Phys. Rev. E , vol.76 , pp. 06112
    • Kleinhans, D.1    Friedrich, R.2
  • 24
    • 34547327313 scopus 로고    scopus 로고
    • Competition between subdiffusion and Lévy flights: A Monte Carlo approach
    • Magdziarz M., and Weron A. Competition between subdiffusion and Lévy flights: A Monte Carlo approach. Phys. Rev. E 75 (2007) 056702
    • (2007) Phys. Rev. E , vol.75 , pp. 056702
    • Magdziarz, M.1    Weron, A.2
  • 25
    • 32444441271 scopus 로고    scopus 로고
    • The Monte Carlo and fractional kinetics approaches to the underground anomalous subdiffusion of contaminants
    • Marseguerra M., and Zoia A. The Monte Carlo and fractional kinetics approaches to the underground anomalous subdiffusion of contaminants. Ann. Nucl. Energy 33 (2006) 223-235
    • (2006) Ann. Nucl. Energy , vol.33 , pp. 223-235
    • Marseguerra, M.1    Zoia, A.2
  • 26
    • 33846630918 scopus 로고    scopus 로고
    • Normal and anomalous transport across an interface: Monte Carlo and analytical approach
    • Marseguerra M., and Zoia A. Normal and anomalous transport across an interface: Monte Carlo and analytical approach. Ann. Nucl. Energy 33 (2006) 1396-1407
    • (2006) Ann. Nucl. Energy , vol.33 , pp. 1396-1407
    • Marseguerra, M.1    Zoia, A.2
  • 27
    • 33846706972 scopus 로고    scopus 로고
    • Monte Carlo investigation of anomalous transport in presence of a discontinuity and of an advection field
    • Marseguerra M., and Zoia A. Monte Carlo investigation of anomalous transport in presence of a discontinuity and of an advection field. Physica A 377 2 (2007) 448-464
    • (2007) Physica A , vol.377 , Issue.2 , pp. 448-464
    • Marseguerra, M.1    Zoia, A.2
  • 28
  • 29
    • 0000437485 scopus 로고
    • Anomalous transport in turbulent plasmas and continuous time random walks
    • Balescu R. Anomalous transport in turbulent plasmas and continuous time random walks. Phys. Rev. E 51 5 (1995) 4807-4822
    • (1995) Phys. Rev. E , vol.51 , Issue.5 , pp. 4807-4822
    • Balescu, R.1
  • 30
    • 0000914304 scopus 로고
    • Transport aspects in anomalous diffusion - Lévy walks
    • Blumen A., Zumofen G., and Klafter J. Transport aspects in anomalous diffusion - Lévy walks. Phys. Rev. A 40 7 (1989) 3964-3974
    • (1989) Phys. Rev. A , vol.40 , Issue.7 , pp. 3964-3974
    • Blumen, A.1    Zumofen, G.2    Klafter, J.3
  • 31
    • 0000582309 scopus 로고    scopus 로고
    • Stochastic foundations of fractional dynamics
    • Compte A. Stochastic foundations of fractional dynamics. Phys. Rev. E 53 4 (1996) 4191-4193
    • (1996) Phys. Rev. E , vol.53 , Issue.4 , pp. 4191-4193
    • Compte, A.1
  • 33
    • 0000437484 scopus 로고
    • Fractional master equations and fractal time random walks
    • Hilfer R., and Anton L. Fractional master equations and fractal time random walks. Phys. Rev. E 51 2 (1995) R848-R851
    • (1995) Phys. Rev. E , vol.51 , Issue.2
    • Hilfer, R.1    Anton, L.2
  • 34
    • 0000523810 scopus 로고
    • Probability distributions for continuous-time random walks with long tails
    • Klafter J., and Zumofen G. Probability distributions for continuous-time random walks with long tails. J. Phys. Chem. 98 (1994) 7366-7370
    • (1994) J. Phys. Chem. , vol.98 , pp. 7366-7370
    • Klafter, J.1    Zumofen, G.2
  • 35
    • 0000237249 scopus 로고    scopus 로고
    • Fractional diffusion, waiting-time distributions, and Cattaneo-type equations
    • Metzler R., and Nonnenmacher T.F. Fractional diffusion, waiting-time distributions, and Cattaneo-type equations. Phys. Rev. E 57 6 (1998) 6409-6414
    • (1998) Phys. Rev. E , vol.57 , Issue.6 , pp. 6409-6414
    • Metzler, R.1    Nonnenmacher, T.F.2
  • 36
    • 0346163912 scopus 로고
    • Current flow under anomalous-diffusion conditions - Lévy walks
    • Zumofen G., Blumen A., and Klafter J. Current flow under anomalous-diffusion conditions - Lévy walks. Phys. Rev. A 41 8 (1990) 4558-4561
    • (1990) Phys. Rev. A , vol.41 , Issue.8 , pp. 4558-4561
    • Zumofen, G.1    Blumen, A.2    Klafter, J.3
  • 37
    • 41349099804 scopus 로고    scopus 로고
    • Stochastic solution of space-time fractional diffusion equations
    • Meerschaert M.M., Benson D.A., Scheffler H.P., and Baeumer B. Stochastic solution of space-time fractional diffusion equations. Phys. Rev. E 65 (2002) 1103-1106
    • (2002) Phys. Rev. E , vol.65 , pp. 1103-1106
    • Meerschaert, M.M.1    Benson, D.A.2    Scheffler, H.P.3    Baeumer, B.4
  • 38
    • 4043102385 scopus 로고    scopus 로고
    • Limit theorems for continuous time random walks with infinite mean waiting times
    • Meerschaert M.M., and Scheffler H.-P. Limit theorems for continuous time random walks with infinite mean waiting times. J. Appl. Probab. 41 3 (2004) 623-638
    • (2004) J. Appl. Probab. , vol.41 , Issue.3 , pp. 623-638
    • Meerschaert, M.M.1    Scheffler, H.-P.2
  • 39
    • 62349103035 scopus 로고    scopus 로고
    • A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations
    • Benson D.A., and Meerschaert M.M. A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations. Adv. Water Res. 32 (2009) 532-539
    • (2009) Adv. Water Res. , vol.32 , pp. 532-539
    • Benson, D.A.1    Meerschaert, M.M.2
  • 40
    • 48349113290 scopus 로고    scopus 로고
    • Triangular array limits for continuous time random walks
    • 10.1016/j.spa.2007.10.005
    • Meerschaert M.M., and Scheffler H.-P. Triangular array limits for continuous time random walks. Stochastic Process. Appl. 118 (2008) 10.1016/j.spa.2007.10.005
    • (2008) Stochastic Process. Appl. , vol.118
    • Meerschaert, M.M.1    Scheffler, H.-P.2
  • 41
    • 13444309297 scopus 로고    scopus 로고
    • Models of anomalous diffusion: The subdiffusive case
    • Piryatinska A., Saichev A.I., and Woyczynski W.A. Models of anomalous diffusion: The subdiffusive case. Physica A 349 3-4 (2005) 375-420
    • (2005) Physica A , vol.349 , Issue.3-4 , pp. 375-420
    • Piryatinska, A.1    Saichev, A.I.2    Woyczynski, W.A.3
  • 42
    • 33646494026 scopus 로고    scopus 로고
    • On using random walks to solve the space-fractional advection-dispersion equations
    • Zhang Y., Benson D.A., Meerschaert M.M., and Scheffler H.P. On using random walks to solve the space-fractional advection-dispersion equations. J. Stat. Phys. 123 1 (2006) 89-110
    • (2006) J. Stat. Phys. , vol.123 , Issue.1 , pp. 89-110
    • Zhang, Y.1    Benson, D.A.2    Meerschaert, M.M.3    Scheffler, H.P.4
  • 46
    • 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
    • W05410, doi:10.1029/2008WR006858
    • Reeves D.M., Benson D.A., Meerschaert M.M., and Scheffler H.-P. Transport of conservative solutes in simulated fracture networks: 2. Ensemble solute transport and the correspondence to operator-stable limit distributions. Water Resour. Res. 44 (2008) W05410, doi:10.1029/2008WR006858
    • (2008) Water Resour. Res. , vol.44
    • Reeves, D.M.1    Benson, D.A.2    Meerschaert, M.M.3    Scheffler, H.-P.4
  • 47
    • 0037490225 scopus 로고    scopus 로고
    • Multiscaling fractional advection-dispersion equations and their solutions
    • Schumer R., Benson D.A., Meerschaert M.M., and Baeumer B. Multiscaling fractional advection-dispersion equations and their solutions. Water Resour. Res. 39 1 (2003) 1022-1033
    • (2003) Water Resour. Res. , vol.39 , Issue.1 , pp. 1022-1033
    • Schumer, R.1    Benson, D.A.2    Meerschaert, M.M.3    Baeumer, B.4
  • 48
    • 84902228782 scopus 로고    scopus 로고
    • Nonparametric methods for heavy tailed vector data: A survey with applications from finance to hydrology
    • Akritas M.G., and Politis D.N. (Eds), Elsevier Science, Amsterdam
    • Meerschaert M.M., and Scheffler H.P. Nonparametric methods for heavy tailed vector data: A survey with applications from finance to hydrology. In: Akritas M.G., and Politis D.N. (Eds). Recent Advances and Trends in Nonparametric Statistics (2003), Elsevier Science, Amsterdam
    • (2003) Recent Advances and Trends in Nonparametric Statistics
    • Meerschaert, M.M.1    Scheffler, H.P.2
  • 49
    • 0030455918 scopus 로고    scopus 로고
    • Transition probability-based indicator geostatistics
    • Carle S.F., and Fogg G.E. Transition probability-based indicator geostatistics. Math. Geol. 28 4 (1996) 453-476
    • (1996) Math. Geol. , vol.28 , Issue.4 , pp. 453-476
    • Carle, S.F.1    Fogg, G.E.2
  • 50
    • 0031432328 scopus 로고    scopus 로고
    • Modeling spatial variability with one and multidimensional continuous-lag Markov chains
    • Carle S.F., and Fogg G.E. Modeling spatial variability with one and multidimensional continuous-lag Markov chains. Math. Geol. 29 7 (1997) 891-918
    • (1997) Math. Geol. , vol.29 , Issue.7 , pp. 891-918
    • Carle, S.F.1    Fogg, G.E.2
  • 51
    • 0002586211 scopus 로고    scopus 로고
    • User's documentation for MODFLOW-96, an update to the US Geological Survey Modular Finite Difference Ground-Water Flow Model
    • A.W. Harbaugh, M.G. McDonald, User's documentation for MODFLOW-96, an update to the US Geological Survey Modular Finite Difference Ground-Water Flow Model, US Geological Survey Open File Report, 1996, pp. 96-485
    • (1996) US Geological Survey Open File Report , pp. 96-485
    • Harbaugh, A.W.1    McDonald, M.G.2
  • 52
    • 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., Quastel J., and Fogg G.E. Diffusion theory for transport in porous media: Transition-probability densities of diffusion processes corresponding to advection-dispersion equations. Water Resour. Res. 34 7 (1998) 1685-1693
    • (1998) Water Resour. Res. , vol.34 , Issue.7 , pp. 1685-1693
    • LaBolle, E.M.1    Quastel, J.2    Fogg, G.E.3


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