Mathematical basis for a general theory of Laplacian transport towards irregular interfaces

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 2, 2006, Pages

  Grebenkov, D S ^a   Filoche, M ^a,b   Sapoval, B ^a,b  

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

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ELECTROCHEMISTRY; MATHEMATICAL OPERATORS; MATHEMATICAL TECHNIQUES; PHYSIOLOGY;

LAPLACIAN TRANSPORT; MACROSCOPIC SYSTEMS; PREFRACTAL INTERFACES;

INTERFACES (MATERIALS);

EID: 33344461840     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.021103     Document Type: Article

References (43)

1. B. Sapoval, in Fractals and Disordered Systems, edited by, A. Bunde, and, S. Havlin, (Springer, Berlin, 1996), p. 233.
2. E. R. Weibel, The Pathway for Oxygen. Structure and Function in the Mammalian Respiratory System (Harvard University Press, Cambridge, MA, 1984).
3. R. de Levie, Electrochim. Acta ELCAAV 0013-4686 10.1016/0013-4686(65) 87012-8 10, 113 (1965).
4. R. D. Armstrong and R. A. Burnham, J. Electroanal. Chem. Interfacial Electrochem. JEIEBC 0022-0728 10.1016/0368-1874(76)80171-2 72, 257 (1976).
5. A. Le Méhauté and G. Crepy, C. R. Seances Acad. Sci., Ser. 2 CRSUDO 0750-7623 294, 685 (1982).
6. L. Nyikos and T. Pajkossy, Electrochim. Acta ELCAAV 0013-4686 10.1016/0013-4686(85)80016-5 30, 1533 (1985).
7. S. H. Liu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.55.529 55, 529 (1985).
8. B. Sapoval, Solid State Ionics SSIOD3 0167-2738 10.1016/0167-2738(87) 90002-6 23, 253 (1987).
9. M. Keddam and H. Takenouti, Electrochim. Acta ELCAAV 0013-4686 10.1016/0013-4686(88)85045-X 33, 445 (1988).
10. T. C. Halsey, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.35.3512 35, 3512 (1987).
11. T. C. Halsey and M. Leibig, Europhys. Lett. EULEEJ 0295-5075 14, 815 (1991).
12. T. C. Halsey and M. Leibig, Electrochim. Acta ELCAAV 0013-4686 10.1016/0013-4686(91)85030-B 36, 1699 (1991).
13. T. C. Halsey and M. Leibig, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(92)90314-C 219, 109 (1992).
14. M. Leibig and T. C. Halsey, J. Electroanal. Chem. JECHES 0022-0728 10.1016/0022-0728(93)80432-H 358, 77 (1993).
15. B. Sapoval, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.3314 73, 3314 (1994).
16. B. Sapoval, M. Filoche, and E. R. Weibel, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.122352499 99 (16), 10411 (2002).
17. M. Felici, M. Filoche, and B. Sapoval, J. Appl. Physiol. JAPHEV 8750-7587 94, 2010 (2003).
18. M. -O. Coppens, Catal. Today CATTEA 0920-5861 10.1016/S0920-5861(99) 00118-2 53, 225 (1999).
19. M. Rosso, Y. Huttel, E. Chassaing, B. Sapoval, and R. Gutfraind, J. Electrochem. Soc. JESOAN 0013-4651 10.1149/1.1837666 144, 1713-1717 (1997).
20. D. S. Grebenkov, Ph.D. thesis, Ecole Polytechnique, France, 2004, http://pmc.polytechnique.fr/pagesperso/dg/phd/these.pdf
21. M. Felici, M. Filoche, C. Straus, T. Similowski, and B. Sapoval, Respir. Physiol. RSPYAK 0034-5687 145, 279 (2005).
22. M. Filoche and B. Sapoval, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050820 9, 755 (1999).
23. D. S. Grebenkov, M. Filoche, and B. Sapoval, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2003-00339-4 36, 221 (2003).
24. A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Vol. 120 of Applied Mathematical Sciences (Springer, New York, 1996).
25. W. Craig and S. Sulem, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1993.1164 108, 73 (1993).
26. D. M. Milder, Radio Sci. RASCAD 0048-6604 10.1029/96RS02164 31, 1369 (1996).
27. T. Y. Hou, J. S. Lowengrub, and M. J. Shelly, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.2000.6626 169, 302 (2001).
28. A. Friedman and V. Isakov, Indiana Univ. Math. J. IUMJAB 0022-2518 10.1512/iumj.1989.38.38027 38, 563 (1989).
29. D. P. Nicholls and F. Reitich, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.2001.6737 170, 276 (2001).
30. P. Guidotti, J. Comput. Phys. JCTPAH 0021-9991 10.1016/S0021-9991(03) 00277-8 190, 325 (2003).
31. M. S. Agranovich, in Partial Differential Equations IX, edited by, M. S. Agranovich, Yu. V. Egorov, and, M. S. Shubin, EMS 79 (Springer, Berlin, 1997).
32. M. S. Birman, M. Z. Solomyak, Spectral Theory of Self-Adjoint Operators in Hilbert Space (Reidel, Dordrecht, 1987).
33. M. Filoche and B. Sapoval, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5776 84, 5776 (2000).
34. D. S. Grebenkov, Fractals (in press).
35. B. Sapoval, J. S. Andrade Jr, A. Baldassari, A. Desolneux, F. Devreux, M. Filoche, D. S. Grebenkov, and S. Russ, Physica A PHYADX 0378-4371 10.1016/j.physa.2005.05.066 357, 1 (2005).
36. L. Nyikos and T. Pajkossy, Electrochim. Acta ELCAAV 0013-4686 10.1016/0013-4686(86)80160-8 31, 1347 (1986).
37. B. Sapoval, J. -N. Chazalviel, and J. Peyrière Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.38.5867 38, 5867 (1988).
38. D. S. Grebenkov, E. Chassaing, M. Filoche, and B. Sapoval, in Proceedings of the 17th Forum of Electrochemical Impedances (Paris, 2005).
39. A. Lasia, in Modern Aspects of Electrochemistry, edited by, B. E. Conway, J. Bockris, and, R. E. White, (Kluwer, New York, 1999), Vol. 32, pp. 143-248.
40. W. H. Chen, Linear Network Design and Synthesis (McGraw-Hill, New York, 1964).
41. B. Sapoval, R. Gutfraind, P. Meakin, M. Keddam, and H. Takenouti, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.48.3333 48, 3333 (1993).
42. P. Agarwal, M. E. Orazem, and L. H. Garcia-Rubio, J. Electrochem. Soc. JESOAN 0013-4651 10.1149/1.2069522 139, 1917 (1992).
43. P. Agarwal, M. E. Orazem, and L. H. Garcia-Rubio, J. Electrochem. Soc. JESOAN 0013-4651 10.1149/1.2048479 142, 4159 (1995).