A mixed basis approach in the SGP-limit

Journal of Magnetic Resonance

Volumn 212, Issue 2, 2011, Pages 274-279

  Nordin, Matias ^a   Nilsson Jacobi, Martin ^a   Nydén, Magnus ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Geometry; Initial slope; Laplace operator; Matrix formulation; Narrow pulse approximation; NMR; Perturbation method; Poisson's equation; Restricted diffusion; SGP limit

Indexed keywords

INITIAL SLOPE; LAPLACE OPERATOR; MATRIX FORMULATION; NARROW PULSE; PERTURBATION METHOD; POISSON'S EQUATION; RESTRICTED DIFFUSION; SGP-LIMIT;

BOUNDARY CONDITIONS; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; GEOMETRY; NUCLEAR MAGNETIC RESONANCE; POISSON EQUATION;

PERTURBATION TECHNIQUES;

ALGORITHM; ARTICLE; DIFFUSION; FOURIER ANALYSIS; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; POISSON DISTRIBUTION;

ALGORITHMS; DIFFUSION; FOURIER ANALYSIS; MAGNETIC RESONANCE SPECTROSCOPY; POISSON DISTRIBUTION;

EID: 80053269511     PISSN: 10907807     EISSN: 10960856     Source Type: Journal    
DOI: 10.1016/j.jmr.2011.07.002     Document Type: Article

References (39)

1. D.S. Grebenkov Nmr survey of reflected brownian motion Reviews of Modern Physics 79 2007 1077
2. W.S. Price NMR Studies of Translational Motion 2009 Cambridge University Press
3. P.T. Callaghan Principles of Nuclear Magnetic Resonance Microscopy 1991 Oxford University Press
4. J.H. Simpson, and H.Y. Carr Diffusion and nuclear spin relaxation in water Physical Review 111 1958 1201 1202 ([first] NMR applied on water to measure diffusion)
5. D.W. Mccall, D.C. Douglass, and E.W. Anderson Self-diffusion studies by means of nuclear magnetic resonance spin-echo techniques Berichte der Bunsengesellschaft fr physikalische Chemie 67 1963 336 340
6. E.O. Stejskal Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow The Journal of Chemical Physics 43 1965 3597 3604
7. H.Y. Carr, and E.M. Purcell Effects of diffusion on free precession in nuclear magnetic resonance experiments Physical Review 94 1954 630 638 (first discussion of flow)
8. M.D. Hürlimann, K.G. Helmer, T.M. Deswiet, and P.N. Sen Spin echoes in a constant gradient and in the presence of simple restriction Journal of Magnetic Resonance: Series A 113 1995 260 264
9. P.N. Sen, M.D. Hürlimann, and T.M. de Swiet Debye-Porod law of diffraction for diffusion in porous media Physical Review B 51 1995 601 604
10. W.S. Price, P. Stilbs, and O. Söderman Determination of pore space shape and size in porous systems using NMR diffusometry. beyond the short gradient pulse approximation Journal of Magnetic Resonance 160 2003 139 143
11. D. Topgaard, and O. Söderman Experimental determination of pore shape and size using q-space NMR microscopy in the long diffusion-time limit Magnetic Resonance Imaging 21 2003 69 76 (Pubitemid 36293020)
12. J.E. Tanner, and E.O. Stejskal Restricted self-diffusion of protons in colloidal systems by the pulsed-gradient, spin-echo method The Journal of Chemical Physics 49 1968 1768 1778
13. H.C. Torrey Bloch equations with diffusion terms Physical Review 104 1956 563 565
14. P.T.C.A. Coy Pulsed gradient spin echo nuclear magnetic resonance for molecules diffusing between partially reflecting rectangular barriers The Journal of Chemical Physics 101 1994 4599 4609
15. P. Linse, and O. Soderman The validity of the short-gradient-pulse approximation in nmr studies of restricted diffusion. simulations of molecules diffusing between planes, in cylinders and spheres Journal of Magnetic Resonance: Series A 116 1995 77 86
16. L.Z. Wang, A. Caprihan, and E. Fukushima The narrow-pulse criterion for pulsed-gradient spin-echo diffusion measurements Journal of Magnetic Resonance: Series A 117 1995 209 219
17. R. Mair, P. Sen, M. Hrlimann, S. Patz, D. Cory, and R. Walsworth The narrow pulse approximation and long length scale determination in xenon gas diffusion nmr studies of model porous media Journal of Magnetic Resonance 156 2002 202 212
18. P.T. Callaghan, S.L. Codd, and J.D. Seymour Spatial coherence phenomena arising from translational spin motion in gradient spin echo experiments Concepts in Magnetic Resonance 11 1999 181 202
19. P.T. Callaghan, A. Coy, T.P.J. Halpin, D. MacGowan, K.J. Packer, and F.O. Zelaya Diffusion in porous systems and the influence of pore morphology in pulsed gradient spin-echo nuclear magnetic resonance studies The Journal of Chemical Physics 97 1992 651 662
20. A. Coy, and P.T. Callaghan Pulsed gradient spin-echo NMR experiments on water surrounding close-packed polymer spheres Journal of Colloid and Interface Science 168 1994 373 379
21. S.L. Codd, and S.A. Altobelli A PGSE study of propane gas flow through model porous bead packs Journal of Magnetic Resonance 163 2003 16 22
22. P. Callaghan Pulsed-gradient spin-echo nmr for planar, cylindrical, and spherical pores under conditions of wall relaxation Journal of Magnetic Resonance: Series A 113 1995 53 59
23. G.B. Arfken, and H.-J. Weber Mathematical Methods for Physicists fourth (International) ed. 1995 Academic Press
24. M. Nordin, M.N. Jacobi, and M. Nydén Deriving time-dependent diffusion and relaxation rate in porous systems using eigenfunctions of the laplace operator Journal of Magnetic Resonance 201 2009 205 211
25. M. Nordin, M. Nilsson-Jacobi, M. Nydén, A mixed basis approach to approximate the spectrum of Laplace operator, Paper Presented at the VI's Proceedings of Interdisciplinary Transport Phenomena, Volterra, Italy, 2009. arXiv:0909.0935v1.
26. P.P. Ewald Die berechnung optischer und elektrostatischer gitterpotentiale Annalen der Physik 369 1921 253 287
27. L. Greengard, and V. Rokhlin A fast algorithm for particle simulations Journal of Computational Physics 73 1987 325 348
28. T. Amisaki Precise and efficient Ewald summation for periodic fast multipole method Journal of Computational Physics 21 2000 1075 1087
29. C.H. Neuman Spin echo of spins diffusing in a bounded medium The Journal of Chemical Physics 60 1974 4508 4512
30. P. Callaghan Pulsed-gradient spin-echo NMR for planar, cylindrical, and spherical pores under conditions of wall relaxation Journal of Magnetic Resonance: Series A 113 1995 53 59
31. D.E. Woessner NMR spin-echo self-diffusion measurements on fluids undergoing restricted diffusion The Journal of Physical Chemistry 67 1963 1365 1367
32. J. Neyman, and E.L. Scott Statistical approach to problems of cosmology Journal of the Royal Statistical Society: Series B (Methodological) 20 1958 1 43
33. P. Banerjee The Boundary Element Methods 1994 McGraw-Hill
34. O.D.L. Strack Principles of the analytic element method Journal of Hydrology 226 1999 128 138 (Pubitemid 30086546)
35. Z.-C. Li, R. Mathon, and P. Sermer Boundary methods for solving elliptic problems with singularities and interfaces SIAM Journal on Numerical Analysis 24 1987 487 498 (Pubitemid 17603387)
36. Z. Li The Trefftz method for the Helmholtz equation with degeneracy Applied Numerical Mathematics 58 2008 131 159
37. Z.-C. Li, T.-T. Lu, H.-S. Tsai, and A.H. Cheng The Trefftz method for solving eigenvalue problems Engineering Analysis with Boundary Elements 30 2006 292 308
38. P.T. Callaghan A simple matrix formalism for spin echo analysis of restricted diffusion under generalized gradient waveforms Journal of Magnetic Resonance 129 1997 74 84 (Pubitemid 127454055)
39. A. Caprihan, L.Z. Wang, and E. Fukushima A multiple-narrow-pulse approximation for restricted diffusion in a time-varying field gradient Journal of Magnetic Resonance: Series A 118 1996 94 102 (Pubitemid 126751678)