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Random walks, random flows, and enhanced diffusivity in advection-diffusion equations
1. | Mathematics Department, University of North Carolina, Chapel Hill, NC 27599, United States |
References:
[1] |
M. Avellaneda and A. Majda, An integral representation and bounds on the effective diffusivity in passive advective diffusion by laminar and turbulent flows, Commun. Math. Phys., 138 (1991), 339-391. |
[2] |
R. Camassa, Z. Lin and R. McLaughlin, The exact evolution of the scalar variance in pipe and channel flow, Commun. Math. Sci., 8 (2010), 601-626. |
[3] |
S. Goldstein, On diffusion by discontinuous movements and on the telegraph equation, Quart. J. Mech. Appl. Math., 4 (1951), 129-156.
doi: 10.1093/qjmam/4.2.129. |
[4] |
R. Griego and R. Hersh, Theory of random evolutions with applications to partial differential equations, Trans. AMS, 156 (1971), 405-418.
doi: 10.1090/S0002-9947-1971-0275507-7. |
[5] |
A. Majda and P. Kramer, Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena, Physics Reports, 314 (1999), 237-574.
doi: 10.1016/S0370-1573(98)00083-0. |
[6] |
A. Mazzucato and M. Taylor, Vanishing viscosity limits for a class of circular pipe flows, Commun. PDE, 36 (2012), 328-361.
doi: 10.1080/03605302.2010.505973. |
[7] |
M. Pinsky, "Lectures on Random Evolution,'' World Scientific, London, 1991. |
[8] |
G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. Roy. Soc. London A, 219 (1953), 186-203.
doi: 10.1098/rspa.1953.0139. |
[9] |
M. Taylor, "Partial Differential Equations,'' Vols. 1-3, Springer-Verlag, New York, 1996. |
show all references
References:
[1] |
M. Avellaneda and A. Majda, An integral representation and bounds on the effective diffusivity in passive advective diffusion by laminar and turbulent flows, Commun. Math. Phys., 138 (1991), 339-391. |
[2] |
R. Camassa, Z. Lin and R. McLaughlin, The exact evolution of the scalar variance in pipe and channel flow, Commun. Math. Sci., 8 (2010), 601-626. |
[3] |
S. Goldstein, On diffusion by discontinuous movements and on the telegraph equation, Quart. J. Mech. Appl. Math., 4 (1951), 129-156.
doi: 10.1093/qjmam/4.2.129. |
[4] |
R. Griego and R. Hersh, Theory of random evolutions with applications to partial differential equations, Trans. AMS, 156 (1971), 405-418.
doi: 10.1090/S0002-9947-1971-0275507-7. |
[5] |
A. Majda and P. Kramer, Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena, Physics Reports, 314 (1999), 237-574.
doi: 10.1016/S0370-1573(98)00083-0. |
[6] |
A. Mazzucato and M. Taylor, Vanishing viscosity limits for a class of circular pipe flows, Commun. PDE, 36 (2012), 328-361.
doi: 10.1080/03605302.2010.505973. |
[7] |
M. Pinsky, "Lectures on Random Evolution,'' World Scientific, London, 1991. |
[8] |
G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. Roy. Soc. London A, 219 (1953), 186-203.
doi: 10.1098/rspa.1953.0139. |
[9] |
M. Taylor, "Partial Differential Equations,'' Vols. 1-3, Springer-Verlag, New York, 1996. |
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