Group theoretic reduction of Laplacian dynamical problems on fractal lattices

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 6, 1997, Pages 6741-6752

  Schwalm, W A ^a   Schwalm, M K ^a   Giona, M ^b  

^a UNIVERSITY OF NORTH DAKOTA   (United States)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040568298     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.6741     Document Type: Article

References (46)

1. M. Giona, A. Adrover, and A R. Giona, Fractals in the Natural and Applied Sciences, edited by M. M. Novak (North-Holland, Amsterdam, 1994), p. 154.
2. B. Mandlebrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
3. S. Havlin and D. Ben-Avraham, Adv. Phys.36, 695 (1987).
4. Y. Gefen, B. Mandelbrot and A. Aharony, Phys. Rev. Lett.45, 855 (1980);
5. Y. Gefen, A. Aharony, B. Mandelbrot and S. Kirkpatrick, Phys. Rev. Lett.ibid. 47, 1771 (1981).
6. R. Griffiths and M. Kaufman, Phys. Rev. B26, 5022 (1982).
7. W A. Schwalm and M K. Schwalm, Phys. Rev. B39, 12 872 (1989).
8. D. Dhar, J. Math. Phys.19, 5 (1977).
9. E. Domany, S. Alexander, D. Bensimon and L. Kadanoff, Phys. Rev. B28, 3110 (1983).
10. R. Rammal, J. Phys. (Paris) Lett.45, 191 (1984).
11. A-M. Tremblay and B W. Southern, J. Phys. (Paris) Lett.44, 843 (1984).
12. S. Alexander, Phys. Rev. B29, 5504 (1984).
13. W A. Schwalm and M K. Schwalm, Phys. Rev. B37, 9524 (1988).
14. V. Sivan, Europhys. Lett.7, 249 (1988).
15. M. Giona, Chem. Eng. Sci.51, 4717 (1996);
16. M. Giona, Chem. Eng. Sci.51, 4731 (1996);
17. M. Giona, Chem. Eng. Sci.51, 5065 (1996).
18. S. Lie, Vorlesungen über Differentialgleichungen mit bekannten imfinitesimalen Transformationen (Teubner, Leipzig, 1912).
19. A. Cohen, Introduction to the Lie Theory of One-Parameter Groups (Heath, New York, 1911).
20. H. Stephani, Differential Equations: Their Solution Using Symmetries (Cambridge University Press, Cambridge, 1989).
21. S. Maeda, Math. Japonica25, 405 (1980);
22. S. Maeda, IMA J. Appl. Math.35, 129 (1987).
23. G. Quispel and X. Sahadevan, Phys. Lett. A184, 64 (1993).
24. M. Tinkham, Group Theory in Quantum Mechanics (McGraw-Hill, New York, 1964).
25. M. Hood and B W. Southern, J. Phys. A19, 2679 (1986).
26. A. Adrover, W A. Schwalm, M. Giona and D. Bachand (this issue), Phys. Rev. E55, 7304 (1997).
27. T. Vicsek, J. Phys. A16, L647 (1983);
28. A. Christou and R B. Stinchcombe, J. Phys. A19, 2625 (1986).
29. B. Sapoval, Th. Gobron and A. Magrgolina, Phys. Rev. Lett.67, 2974 (1991).
30. C S. Jayanthi, S Y. Wu and J. Cocks, Phys. Rev. Lett.69, 1955 (1993);
31. C S. Jayanthi, S Y. Wu and J. Cocks, Phys. Rev.48, 10 188 (1993);
32. 10 199 (1993);
33. J. Q. You Phys. Rev. E 48, R4183 (1994);
34. C S. Jayanthi and S Y. Wu, Phys. Rev. B50, 897 (1994).
35. M K. Schwalm, D K. Ludlow, and H. Ni, in Proceedings of the Conference on Chaos and Fractals in Chemical Engineering, edited by M. Giona (World Scientific, Singapore, in press).
36. M. Kohmoto, L P. Kadanoff and C. Tang, Phys. Rev. Lett.50, 1870 (1983).
37. W A. Schwalm and M K. Schwalm, Phys. Rev. B44, 382 (1991);
38. W A. Schwalm and M K. Schwalm, Physica A185, 195 (1992).
39. W A. Schwalm, Phys. Rev. B49, 15 650 (1994);
40. W A. Schwalm and M K. Schwalm, Phys. Rev. Bibid. 47, 7847 (1993).
41. P M. Adler, Porous Media: Geometry&Transports (Butterworth-Heinemann, Washington, DC, 1992).
42. M K. Schwalm and W A. Schwalm, Phys. Rev. B54, 15 086 (1996).
43. F. Dyson, Phys. Rev.92, 1331 (1953).
44. R. Bass, J. Math. Phys.26, 3068 (1985).
45. R. Mazo, Cell Biophys.11, 19 (1987).
46. S. Alexander and R. Orbach, J. Phys. (Paris) Lett.43, 625 (1982).