Mixing-driven equilibrium reactions in multidimensional fractional advection-dispersion systems

Physica A: Statistical Mechanics and its Applications

Volumn 392, Issue 10, 2013, Pages 2513-2525

  Bolster, Diogo ^a   Benson, David A ^b   Meerschaert, Mark M ^c   Baeumer, Boris ^d  

^a University of Notre Dame   (United States)

^b Department of Metallurgical and Materials Engineering   (United States)

^c MICHIGAN STATE UNIVERSITY   (United States)

^d UNIVERSITY OF OTAGO   (New Zealand)

Author keywords

Fractional dispersion; Multiple dimensions; Reactions

Indexed keywords

DISPERSIONS; MIXING;

ADVECTION DISPERSIONS; FICKIAN DIFFUSION MODELS; FRACTIONAL DERIVATIVES; FRACTIONAL DISPERSIONS; MULTI-DIMENSIONAL SPACE; MULTIPLE DIMENSIONS; REACTIONS; SCALAR DISSIPATION RATE;

REACTION RATES;

EID: 84875217363     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2012.12.040     Document Type: Article

References (56)

1. K. Seo, and K. Bowman Lévy flights and anomalous diffusion in the stratosphere J. Geophys. Res. 105 2000 295 302
2. B. Cushman-Roisin Beyond eddy diffusivity: an alternative model for turbulent dispersion Environmental Fluid Mechanics 8 2008 543 549
3. J. Seymour, J. Gage, S. Codd, and R. Gerlach Anomalous fluid transport in porous media induced by biofilm growth Phys. Rev. Lett. 93 2004 198103
4. A.M. Tartakovsky, D.M. Tartakovsky, and P. Meakin Stochastic Langevin model for flow and transport in porous media Phys. Rev. Lett. 101 2008 044502
5. T. Le Borgne, M. Dentz, and J. Carrera Lagrangian statistical model for transport in highly heterogeneous velocity fields Phys. Rev. Lett. 101 9 2008 090601
6. P.K. Kang, M. Dentz, T. Le Borgne, and R. Juanes Spatial Markov model of anomalous transport through random lattice networks Phys. Rev. Lett. 107 2011 180602
7. P.K. Kang, M. Dentz, and R. Juanes Predictability of anomalous transport on lattice networks with quenched disorder Phys. Rev. E 83 2011 030101
8. D. del Castillo-Negrete Chaotic transport in zonal flows in analogous geophysical and plasma systems Phys. Plasmas 7 2000 1702
9. T. Kosztolowic, K. Dworecki, and S. Mrowczynski How to measure subdiffusion parameters Phys. Rev. Lett. 94 2005 170602
10. P. Barthelemy, J. Bertolotti, and D. Wiersma A Lévy flight for light Nature (London) 453 2008 495
11. E. Foufoula-Georgiou, V. Ganti, and W.E. Dietrich A non-local theory of sediment transport on hillslopes J. Geophys. Res. 115 2010 F00A16
12. S.C. Weber, A.J. Spakowitz, and J.A. Theriot Bacterial chromosomal loci move subdiffusively through a viscoelastic cytoplasm Phys. Rev. Lett. 104 2010 238102
13. J. Bouchaud, and A. Georges Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications Phys. Rev. 195 1990 127
14. M. Dentz, and D. Bolster Distribution- versus correlation-induced anomalous transport in quenched random velocity fields Phys. Rev. Lett. 105 2010 244301
15. J. Cushman, X. Hu, and T. Ginn Nonequilibrium statistical mechanics of preasymptotic dispersion J. Stat. Phys. 75 1994 859 878
16. H. Scher, and M. Lax Stochastic transport in a disordered solid I. Theory, Phys. Rev. B 7 1973 4491 4502
17. M. Dentz, and D. Tartakovsky Delay mechanisms of non?fickian transport in heterogeneous media Geophys. Res. Lett. 33 2006 L16406
18. R. Metzler, and J. Klafter The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys. Rep. 339 2000 1 77
19. D. Benson, R. Schumer, S. Wheatcraft, and M. Meerschaert Fractional dispersion, Lévy motion, and the MADE tracer tests Transp. Porous Media 42 2001 211 240
20. M. Meerschaert, D. Benson, and B. Baeumer Multidimensional advection and fractional dispersion Phys. Rev. E 59 1999 5026
21. M. Meerschaert, D. Benson, and B. Baeumer Operator Lévy motion and multiscaling anomalous diffusion Phys. Rev. E 63 2001 021112
22. C. Tsallis, S. Levy, A.M. Souza, and R. Maynard Statistical-mechanical foundation of the ubiquity of the Lévy distributions in nature Phys. Rev. Lett. 77 1996 5442
23. D.M. Reeves, D.A. Benson, M.M. Meerschaert, and H.-P. Scheffler Transport of conservative solutes in simulated fracture networks: 2. ensemble solute transport and the correspondence to operator-stable limit distributions Water Resour. Res. 44 5 2008 W05410
24. Y. Zhang, D. Benson, M. Meerschaert, E. LaBolle, and H. Scheffler Random walk approximation of fractional-order multiscaling anomalous diffusion Phys. Rev. E 74 2006 026706
25. Y. Zhang, and D. Benson Lagrangian simulation of multidimensional anomalous transport at the MADE site Geophys. Res. Lett. 35 2008 L07403
26. B. Baeumer, M. Haase, and M. Kovacs Unbounded functional calculus for bounded groups with applications J. Evol. Equ. 9 2009 171 195
27. M. Meerschaert, and A. Sikorskii Stochastic Models for Fractional Calculus 2012 De Gruyter
28. M. Meerschaert, J. Mortensen, and S. Wheatcraft Fractional vector calculus for fractional advection-dispersion Physica A 367 2006 181 190
29. T. LeBorgne, M. Dentz, D. Bolster, J. Carrera, J.-R. de Dreuzy, and O. Bour Persistence of incomplete mixing: a key to anomalous transport Phys. Rev. E 84 2011 015301(R)
30. T. LeBorgne, M. Dentz, D. Bolster, J. Carrera, J. de Dreuzy, and P. Davy Non-Fickian mixing: temporal evolution of the scalar dissipation rate in heterogeneous porous media Adv. Water Resour. 33 2010 1468 1475
31. D. Bolster, F. Valdes-Parada, T.L. Borgne, M. Dentz, and J. Carrera Mixing in confined stratified aquifers Journal of Contaminant Hydrology 120-121 2011 198 212
32. M. Dentz, D. Bolster, and T. Le Borgne Concentration statistics for transport in random media Phys. Rev. E 80 2009 010101
33. D. Bolster, D. Benson, T.L. Borgne, and M. Dentz Anomalous mixing and reaction induced by superdiffusive nonlocal transport Phys. Rev. E 82 2010 021119
34. D. Bolster, P. deAnna, D. Benson, and A. Tartakovsky Incomplete mixing and reactions with fractional dispersion Adv. Water Resour. 37 2012 86 93
35. R. Saxena, A. Mathai, and H. Haubold Fractional reaction-diffusion equations Astrophys. Space Sci. 305 2006 289 296
36. H. Haubold, A. Mathai, and R. Saxena Further solutions of fractional reaction-diffusion equations in terms of the h-function J. Comput. Appl. Math. 235 2011 1311 1316
37. D. del Castillo-Negrete, B. Carreras, and V. Lynch Front dynamics in reaction diffusion systems with Lévy flights: a fractional diffusion approach Phys. Rev. Lett. 91 2003 018302
38. D. Brockman, and L. Hufnagel Front propagation in reaction-superdiffusion dynamics: taming Lévy flights with fluctuations Phys. Rev. Lett. 98 2007 178301
39. E. Abad, S. Yuste, and K. Lindenberg Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous-time random walks Phys. Rev. E 81 2010 031115
40. S. Fedotov Non-markovian random walks and nonlinear reactions: subdiffusion and propagating fronts Phys. Rev. E 81 2010 011117
41. B. Baeumer, M. Kovacs, and M. Meerschaert Fractional reproduction- dispersal equations and heavy tail dispersal kernels Bull. Math. Biol. 69 2007 2281 2297
42. V. Volperta, Y. Necb, and A. Nepomnyashchyb Exact solutions in front propagation problems with superdiffusion Phys. D 239 2010 134 144
43. B. Henry, T. Langlands, and S. Wearne Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations Phys. Rev. E 74 2006 03116
44. S. Yuste, K. Lindenberg, and J. Ruiz-Lorenzo R Klages, G Radons, IM Sokolov, Anomalous Transport - Foundations and Applications 2008 Wiley-VCH 381 383
45. I. Sokolov, M. Schmidt, and F. Sagus Reaction-subdiffusion equations Phys. Rev. E 73 2006 031102
46. M.D. Simoni, J. Carrera, X. Sánchez-Vila, and A. Guadagnini A procedure for the solution of multicomponent reactive transport problems Water Resour. Res. 41 2005 W11410 10.1029/2005WR004056
47. L. Donado, X. Sánchez-Vila, M. Dentz, J. Carrera, and D. Bolster Multicomponent reactive transport in multicontinuum media Water Resour. Res. 45 2009 W11402 10.1029/2008WR006823
48. G. Zumofen, J. Klafter, and M.F. Shlesinger Breakdown of Ovchinnikov-Zeldovich segregation in the a + b → 0 reaction under Lévy mixing Phys. Rev. Lett. 77 1996 2830 2833
49. A. Tartakovsky, P. deAnna, T. LeBorgne, A. Balter, and D. Bolster Effect of spatial concentration fluctuations on effective kinetics in diffusion-reaction systems Water Resour. Res. 48 2012 W02526
50. D. Bolster, M. Meerschaert, and A. Sikorskii Product rule for vector fractional derivatives Fract. Calc. Appl. Anal. 15 3 2012 463 479
51. M. Meerschaert, J. Mortensen, and H.-P. Scheffler Vector Grünwald formula for fractional derivatives Fract. Calc. Appl. Anal. 7 1 2004 61 81
52. C. Tadjeran, and M.M. Meerschaert A second order accurate numerical method for the two-dimensional fractional diffusion equation J. Comput. Phys. 220 2007 813 823
53. S. Pope Turbulent Flows 2000 Cambridge University Press
54. B. Jha, L. Cueto-Felgueroso, and R. Juanes Quantifying mixing in viscously unstable porous media flows Phys. Rev. E 84 2011 066312
55. M. Plancher, M. Leffler, Contribution à ľétude de la représentation d'une fonction arbitraire par des intégrales définies, Rendiconti del Circolo Matematico di Palermo 30 289-335.
56. D. Benson, and M.M. Meerschaert Simulation of chemical reaction via particle tracking: diffusion-limited versus thermodynamic rate-limited regimes Water Resour. Res. 44 2008 W12201 10.1029/2008WR007111