Existence and stability of reaction-diffusion waves on a fractal lattice

Chaos, Solitons and Fractals

Volumn 20, Issue 4, 2004, Pages 799-814

  Abdulbake, Janan ^a   Mulholland, Anthony J ^b   Gomatam, Jagannathan ^a  

^a GLASGOW CALEDONIAN UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFUSION; NONLINEAR EQUATIONS; WAVE PROPAGATION;

FRACTAL LATTICES; REACTION-DIFFUSION WAVES; TRAVELING WAVES;

FRACTALS;

EID: 0344924841     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2003.09.003     Document Type: Article

References (28)

1. Feder J. Fractals. 1988;Plenum Press, New York. ISBN 0-306-42851-2.
2. Pfeifer P., Obert M. Fractals: basic concepts and terminology. Avnir D. The fractal approach to heterogeneous chemistry. 1992;11 John Wiley & Sons Ltd. New York. Reprinted.
3. Falconer K. Fractal geometry. second ed. 1993;John Wiley and Sons, Chichester, UK.
4. Havlin S., Aroulo M., Larralde H., Shehter A., Stanley H.E., Trunfio P. Anomalous dynamics in reaction-diffusion systems. II. Nuovo Cimento. 16, D(8):1994;1039-1051.
5. Adler P.M. Flow in porous media. Avnir D. The fractal approach to heterogeneous chemistry. 1992;341-359 John Wiley & Sons Ltd. New York. Reprinted.
6. Giona M. First-order reaction-diffusion kinetics in complex fractal media. Chem. Eng. Sci. 47(6):1992;1503-1515.
7. Kigami J. Harmonic calculus on P.C.F. self-similar sets. Trans. AMS. 335(2):1993;721-755.
8. Lapidus M.L. The vibrations of fractal drums and waves in fractal media. Novak M.M. Fractals in the natural and applied sciences. vol. A-41:1994;255-260 Elsevier Science BV, North-Holland.
9. Yamaguti M., Hata M., Kigami J. Mathematics of fractals. Translations of mathematical monographs. vol. 167:1997;American Mathematical Society, Rhode Island. ISBN 0-8218-0537-1.
10. Schwalm W.A., Schwalm M.K. Extension theory for lattice Green functions. Phys. Rev. B. 37(16):1988;9525-9542.
11. Schwalm W.A., Schwalm M.K. Electronic properties of fractal-glass models. Phys. Rev. B. 39(17):1989;12872-12882.
12. Schwalm W.A., Schwalm M.K. Closed formulae for Green functions on fractal lattices. Physica A. 185:1992;195-201.
13. Schwalm W.A., Schwalm M.K. Explicit orbits for renormalisation maps for Green functions on fractal lattices. Phys. Rev. B. 47(13):1993;7847-7858.
14. Giona M. Transport phenomena in fractal and heterogeneous media - input/output renormalisation and exact results. Chaos, Solitons & Fractals. 7(9):1996;1371-1396.
15. Giona M. Chemical engineering, fractal and disordered system theory: perspectives, applications and future developments. Fractals. 5(3):1997;333-354.
16. Giona M., Schwalm W.A., Adrover A., Schwalm M.K. Analysis of linear transport phenomena on fractals. Chem. Eng. J. 64:1996;45-61.
17. Giona M., Schwalm W.A., Schwalm M.K., Adrover A. Exact solution of linear transport equations in fractal media-I. Renormalisation analysis and general theory. Chem. Eng. Sci. 51(20):1996;4717-4729.
18. Giona M., Schwalm W.A., Schwalm M.K., Adrover A. Exact solution of linear transport equations in fractal media- II, diffusion and convection. Chem. Eng. Sci. 51(20):1996;4731-4744.
19. Giona M., Adrover A., Schwalm W.A., Schwalm M.K. Exact solution of linear transport equations in fractal media- III: adsorption and chemical reaction. Chem. Eng. Sci. 51(22):1996;5065-5076.
20. Giona M., Adrover A., Schwalm W.A., Schwalm M.K. Solution of transport schemes on fractals by means of Green function renormalisation-application to integral quantities. Fractals. 5(3):1997;473-491.
21. Giona M., Adrover A. Closed-form solution for the reconstruction problem in porous media. AIChE J. 42(5):1996;1407-1415.
22. Schwalm W.A., Reese C.C., Schwalm M.K., Wagner C.J. Conic pencils and renormalisation dynamics. Phys. Lett. A. 193:1994;238-244.
23. Schwalm M.K., Giona M., Schwalm W.A., Adrover A., Giustiniani M. Renormalisation analysis and adsorption on fractal and disordered lattices in the presence of energetic disorder. Langmuir. 13:1997;1128-1137.
24. Abdulbake J, Mulholland AJ, Gomatam J. A renormalisation approach to reaction-diffusion processes on fractals. Fractals, in press.
25. Rinzel J., Keller J.B. Travelling wave solutions of nerve conduction equation. Biophys. J. 13:1973;1313-1337.
26. Grindrod P. Patterns and waves: the theory and applications of reaction-diffusion equations. 1997;Clarendon Press, Oxford.
27. McKean H.P. Nagumo's equation. Adv. Math. 4:1970;209-223.
28. Lesne A. Renormalisation methods, critical phenomena, chaos, fractal structures. 1998;John Wiley & Sons, Chinchester, England.