Rapid simulation of the time-dependent diffusion coefficient in complex materials

Journal of Physics A: Mathematical and Theoretical

Volumn 44, Issue 39, 2011, Pages

  Prange, Michael D ^a   Druskin, Vladimir ^a   Johnson, David Linton ^a   Schwartz, Lawrence M ^a  

^a SCHLUMBERGER DOLL RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80052945639     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/44/39/395203     Document Type: Article

References (16)

1. Einstein A 1956 Investigations on the Theory of the Brownian Movement (New York: Dover)
2. Sen P N 2004 Time-dependent diffusion coefficient as a probe of geometry Concepts Magn. Reson. A 23A 121 (Pubitemid 40646215)
3. Mitra P P and Sen P N 1992 Effects of microgeometry and surface relaxation on NMR pulsed-field-gradient experiments: simple pore geometries Phys. Rev. B 45 14356
4. Mitra P P, Sen P N and Schwartz L M 1993 Short-time behavior of the diffusion coefficient as a geometrical probe of porous media Phys. Rev. B 47 856574
5. Sen P N, Schwartz L M, Mitra P P and Halperin B I 1994 Surface relaxation and the long-time diffusion coefficient in porous media: periodic geometries Phys. Rev. B 49 21525
6. Ryu S 2009 Effects of inhomogeneous partial absorption and the geometry of the boundary on population evolution of molecules diffusing in general porous media Phys. Rev. E 80 026109
7. Leibig M 1993 Random walks and NMR measurements in porous media J. Phys. A: Math. Gen. 26 334967
8. Torquato S and Kim C 1999 Effective conductivity, dielectric constant, and idffusion coefficient of digitized composite media via first-passage-time equations J. Appl. Phys. 85 156071 (Pubitemid 129614951)
9. Grebenkov D S 2011 A fast random walk algorithm for computing the pulsed-gradient spin-echo signal in multiscale porous media J. Magn. Reson. 211 24355
10. Zhang Z, Johnson D L and Schwartz L M 2011 Simulating the time dependent diffusion coefficient in mixed pore size materials Phys. Rev. E at press
11. de Hoop A T and Prange M D 2007 Variational analysis of the natural decay rates and eigenmodes of cavity-enclosed diffusive fields J. Phys. A: Math. Theor. 40 1246377
12. Wolfram Research. Mathematica, Version 7.0. Champaign, IL - ref-separator -
13. Gallopoulos E and Saad Y 1992 Efficient solution of parabolic equations by Krylov approximation methods SIAM J. Sci. Stat. Comput. 13 123664
14. Druskin V and Knizhnerman L 1995 Krylov subspace approximation of eigen pairs and matrix functions in exact and computer arithmetic Numer. Linear Algebr. Appl. 2 20517
15. Anderson E et al 1999 LAPACK Users Guide 3rd edn (Philadelphia, PA: SIAM)
16. Brezinski C and Zaglia M R 1991 Extrapolation MethodsTheory and Practice (Studies in Computational Mathematics) (New York: Elsevier)