Analytical solution for restricted diffusion in circular and spherical layers under inhomogeneous magnetic fields

Journal of Chemical Physics

Volumn 128, Issue 13, 2008, Pages

  Grebenkov, Denis S ^a  

^a LABORATOIRE DE PHYSIQUE DE LA MATIÈRE CONDENSÉE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LAPLACE EQUATION; MAGNETIC FIELD EFFECTS; MAGNETIZATION; PARTICLE INTERACTIONS; PERTURBATION TECHNIQUES; SPIN DYNAMICS; THICKNESS MEASUREMENT;

APPARENT DIFFUSION COEFFICIENT (ADC); INHOMOGENEOUS MAGNETIC FIELDS; SPHERICAL LAYERS;

SURFACE DIFFUSION;

EID: 41849130269     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2841367     Document Type: Article

References (32)

1. D. S. Grebenkov, Rev. Mod. Phys. 79, 1077 (2007).
2. P. P. Mitra, P. N. Sen, L. M. Schwartz, and P. Le Doussal, Phys. Rev. Lett. 68, 3555 (1992).
3. P. P. Mitra, P. N. Sen, and L. M. Schwartz, Phys. Rev. B 47, 8565 (1993).
4. P. N. Sen, Concepts Magn. Reson. 23, 1 (2004).
5. B. Robertson, Phys. Rev. 151, 273 (1966).
6. R. C. Wayne and R. M. Cotts, Phys. Rev. 151, 264 (1966).
7. C. H. Neuman, J. Chem. Phys. 60, 4508 (1974).
8. P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy (Clarendon, Oxford, 1991).
9. P. T. Callaghan, A. Coy, D. MacGowan, K. J. Packer, and F. O. Zelaya, Nature (London) 351, 467 (1991).
10. P. T. Callaghan, S. L. Codd, and J. D. Seymour, Concepts Magn. Reson. 11, 181 (1999).
11. K. R. Brownstein and C. E. Tarr, Phys. Rev. A 19, 2446 (1979).
12. A. Caprihan, L. Z. Wang, and E. Fukushima, J. Magn. Reson., Ser. A 118, 94 (1996).
13. P. T. Callaghan, J. Magn. Reson. 129, 74 (1997).
14. A. V. Barzykin, Phys. Rev. B 58, 14171 (1998).
15. A. V. Barzykin, J. Magn. Reson. 139, 342 (1999).
16. S. Axelrod and P. N. Sen, J. Chem. Phys. 114, 6878 (2001).
17. D. S. Grebenkov, Magn. Reson. Imaging 25, 559 (2007).
18. D. S. Grebenkov, Diffus. Fundam. 5, 1 (2007).
19. L. J. Zielinski and P. N. Sen, J. Chem. Phys. 119, 1093 (2003).
20. D. S. Grebenkov, Phys. Rev. E 76, 041139 (2007).
21. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Clarendon, Oxford, 1959).
22. J. Crank, The Mathematics of Diffusion, 2nd ed. (Clarendon, Oxford, 1975).
23. J. W. Haus and K. W. Kehr, Phys. Rep. 150, 263 (1987).
24. L. L. Latour, P. P. Mitra, R. L. Kleinberg, and C. H. Sotak, J. Magn. Reson., Ser. A 101, 342 (1993).
25. T. M. de Swiet and P. N. Sen, J. Chem. Phys. 104, 206 (1996).
26. L. J. Zielinski and P. N. Sen, J. Magn. Reson. 147, 95 (2000).
27. D. S. Grebenkov, J. Chem. Phys. 126, 104706 (2007).
28. S. D. Stoller, W. Happer, and F. J. Dyson, Phys. Rev. A 44, 7459 (1991).
29. T. M. de Swiet and P. N. Sen, J. Chem. Phys. 100, 5597 (1994).
30. M. D. Hürlimann, K. G. Helmer, T. M. de Swiet, P. N. Sen, and C. H. Sotak, J. Magn. Reson., Ser. A 113, 260 (1995).
31. R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-VCH, New York, 1989), Vol. 1.
32. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980).