Isometric graphing and multidimensional scaling for reaction-diffusion modeling on regular and fractal surfaces with spatiotemporal pattern recognition

Journal of Chemical Physics

Volumn 120, Issue 11, 2004, Pages 5432-5443

  Kuriakose, Jainy ^a   Ghosh, Anandamohan ^a   Kumar, V Ravi ^a   Kulkarni, B D ^a  

^a NATIONAL CHEMICAL LABORATORY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; FRACTALS; LYAPUNOV METHODS; MOLECULAR DYNAMICS; NONLINEAR EQUATIONS; REACTION KINETICS; REDUCTION; TURBULENCE;

FRACTAL SURFACES; ISOMETRIC GRAPHING;

SURFACE REACTIONS;

ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; DIFFUSION; FRACTAL ANALYSIS; KINETICS; NONLINEAR SYSTEM; PATTERN RECOGNITION; SURFACE PROPERTY;

DIFFUSION; FRACTALS; KINETICS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; PATTERN RECOGNITION, VISUAL; SURFACE PROPERTIES;

EID: 1842731738     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1647046     Document Type: Article

References (53)

1. F. Moiny and M. Dumont, J. Chem. Phys. 111, 4743 (1999).
2. F. Moiny and M. Dumont, J. Chem. Phys. 115, 7705 (2001).
3. B. Sente, M. Dumont, and R. Dagonnier, Vacuum 41, 130 (1990).
4. F. Moiny, M. Dumont, and R. Dagonnier, J. Chem. Phys. 108, 4572 (1998).
5. H. Park, K. Hojing, and S. Lee, Surf. Sci. 380, 514 (1997).
6. R. Albert and A. L. Barabasi, Rev. Mod. Phys. 74, 47 (2002).
7. S. H. Strogatz, Nature (London) 410, 268 (2001).
8. J. B. Tennenbaum, V. de Silva, and J. C. Langford, Science 290, 2319 (2000).
9. R. McEliece, B. Ash, and C. Ash, Introduction to Discrete Mathematics (McGraw-Hill, New York, 1989).
10. C. Bishop, M. Svensen, and C. Williams, Neural Comput. 10, 215 (1998).
11. M. Sheintuch, Catal. Rev. - Sci. Eng. 43, 233 (2001).
12. R. Muralidhar and D. Ramkrishna, Transp. Porous Media 13, 79 (1993).
13. S. Havlin and D. Ben-Avraham, Adv. Phys. 51, 187 (2002).
14. H. Spohn, J. Phys. I 3, 69 (1993).
15. J. Stephenson, Physica A 222, 234 (1995).
16. T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993).
17. O. V. Bychuk and B. O'Shaughnessy, Phys. Rev. Lett. 74, 1795 (1995).
18. B. O'Shaughnessy and I. Procaccia, Phys. Rev. Lett. 54, 455 (1985).
19. L. C. Malacarne, R. S. Mendes, L. T. Pedron, and E. K. Lenzi, Phys. Rev. E 63, 030101 (2001).
20. J. Tyson and J. P. Keener, Physica D 32, 327 (1988).
21. A. T. Winfree, Chaos 1, 303 (1991).
22. D. Barkley, Physica D 49, 61 (1991).
23. D. Barkley, Phys. Rev. Lett. 68, 2090 (1992).
24. I. Aranson, H. Levine, and L. Tsimring, Phys. Rev. Lett. 76, 1170 (1996).
25. J. García-Ojlavo and L. Schimansky-Geier, Europhys. Lett. 47(3), 298 (1999).
26. M. Bär, E. Meron, and C. Utzny, Chaos 12, 204 (2002).
27. Oscillating and Traveling Waves in Chemical Systems, edited by R. J. Field and M. Burger (Wiley Interscience, New York, 1985).
28. Chemical Waves and Patterns, edited by R. Kapral and K. Showalter (Kluwer, Dordrecht, 1995).
29. C. B. Muratov and V. V. Osipov, Phys. Rev. E 54, 486 (1996).
30. I. Borg and P. Groenen, Modern Multidimensional Scaling-Theory and Applications, Springer Series in Statistics (Springer, Berlin, 1997).
31. T. Cox and M. Cox, Multidimensional Scaling (Chapman & Hall, London, 1994).
32. I. T. Jolliffe, Principal Component Analysis (Springer-Verlag, New York, 1989).
33. K. I. Diamantaras and S. Y. Kung, Principal Component Neural Networks: Theory and Applications (Wiley, New York, 1996).
34. A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, New York, 2001), p. 129.
35. T. Kohonen, Self-organization and Associative Memory (Springer-Verlag, Berlin, 1988).
36. R. Brown, P. Bryant, and H. D. I. Abarbanel, Phys. Rev. A 43, 2787 (1991).
37. H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. Sh. Tsimiring, Rev. Mod. Phys. 65, 1331 (1993).
38. N. Parekh, V. Ravi Kumar, and B. D. Kulkarni, Chaos 8, 300 (1998).
39. G. Paladin, M. Serva, and A. Vulpiani, Phys. Rev. Lett. 74, 66 (1995).
40. C. W. Gardiner, Handbook of Stochastic Method for Physics, Chemistry and Natural Science (Springer-Verlag, Berlin, 1983).
41. J. Garcia-Ojalvo and J. M. Sanch, Noise in Spatially Extended Systems (Springer, New York, 1999).
42. The Fractal Approach to Heterogeneous Chemistry - Surfaces, Colloids, Polymers, edited by D. Avnir (Wiley, New York, 1989).
43. J. Argyris, G. Faust, and M. Haase, An Exploration of Chaos (Elsevier Science, Amsterdam, 1994).
44. G. P. Williams, Chaos Theory Tamed (Taylor & Francis, London, 1997).
45. P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge University Press, Cambridge, 1996).
46. A. Ghosh, V. Ravi Kumar, and B. D. Kulkarni, Phys. Rev. E 64, 056222 (2001).
47. F. Takens, Lecture Notes in Mathematics 898, edited by D. Rand and L. S. Young (Springer, Berlin, 1981), p. 230.
48. R. Gilmore, Rev. Mod. Phys. 70, 1455 (1998).
49. S. Deshmukh, A. Ghosh, M. V. Badiger, P. S. Tapadia, V. Ravi Kumar, and B. D. Kulkarni, Chem. Eng. Sci. 56, 5643 (2001).
50. A. Ghosh, M. V. Badiger, V. Ravi Kumar, and B. D. Kulkarni, Chem. Eng. Sci. 56, 5635 (2001).
51. R. J. Phaneuf and A. K. Schmid, Phys. Today 56(3), 50 (2003).
52. P. Manandhar, J. Jang, G. C. Schatz, M. A. Ratner, and S. Hong, Phys. Rev. Lett. 90, 115505 (2003).
53. D. J. Semin, A. Lo, S. E. Roark, R. T. Skodje, and K. Rowlen, J. Chem. Phys. 105, 5542 (1996).