Universal features of the order-parameter fluctuations: Reversible and irreversible aggregation

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

Volumn 62, Issue 2 B, 2000, Pages 1825-1841

  Botet, Robert ^a   Płoszajczak, Marek ^b  

^a UNIVERSITÉ PARIS SUD   (France)

^b CENTRE DE CALCUL DE L INSTITUT NATIONAL DE PHYSIQUE NUCLEAIRE ET DE PHYSIQUE DES PARTICULES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; FUNCTIONS; KINETIC THEORY; MATHEMATICAL MODELS; PHASE TRANSITIONS; PROBABILITY DISTRIBUTIONS; THERMODYNAMICS;

IRREVERSIBLE AGGREGATION; LANDAU-GINZBURG THEORY; ORDER PARAMETER FLUCTUATIONS; SMOLUCHOWSKI KINETIC EQUATIONS; UNIVERSAL SCALING LAWS;

PHASE EQUILIBRIA;

EID: 0034238762     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.62.1825     Document Type: Article

References (54)

1. Proceedings of the International Workshop on Nuclear Matter in Different Phases and Transitions, Les Houches, March, 1998, edited by J.P. Blaizot, X. Campi, and M. Płoszajczak, Fundamental Theories of Physics Vol. 95 (Kluwer, Dordrecht, 1999).
2. N.G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
3. R. Botet and M. Płoszajczak, J. Sol-Gel Sci. Technol. 15, 167 (1999).
4. R. Botet and M. Płoszajczak, Phys. Rev. E 54, 3320 (1996).
5. B. Widom, J. Chem. Phys. 43, 3898 (1965); F.J. Wegner, in Phase Transitions and Critical Phenomena, edited by C. Domb and M.S. Green (Academic Press, London, 1976), Vol. 6, pp. 8-122.
6. B. Widom, J. Chem. Phys. 43, 3898 (1965); F.J. Wegner, in Phase Transitions and Critical Phenomena, edited by C. Domb and M.S. Green (Academic Press, London, 1976), Vol. 6, pp. 8-122.
7. L.S. Ornstein and S. Zernike, Proc. Acad. Sci. Amsterdam 17, 793 (1914).
8. M.E. Fisher and N.N. Barber, Phys. Rev. Lett. 28, 1516 (1972).
9. R. Botet, and M. Płoszajczak, Phys. Rev. E 57, 7305 (1998).
10. M.E. Fisher and A.E. Ferdinand, Phys. Rev. Lett. 19, 169 (1967).
11. J.E. Mayer and M.G. Mayer, Statistical Mechanics (Wiley, London, 1957).
12. R. Botet and M. Płoszajczak, Phys. Rev. Lett. 69, 3696 (1992).
13. R. Botet and M. Płoszajczak, Int. J. Mod. Phys. E 3, 1033 (1994).
14. Z. Koba, H.B. Nielsen, and P. Olesen, Nucl. Phys. B 40, 317 (1972).
15. This follows from the expected validity of Feynman scaling for the many-body inclusive cross sections of particle production in ultrarelativistic collisions.
16. D. Stauffer and A. Aharony, Percolation Theory (Taylor & Francis, London, 1992).
17. R. Botet, M. Płoszajczak, and V. Latora, Phys. Rev. Lett. 78, 4593 (1997). 17
18. In general, the second scaling law [Eq. (45)] can be satisfied in a broader class of scaling functions than Gaussian functions [16].
19. A.Z. Mekjian, Phys. Rev. Lett. 64, 2125 (1990); Phys. Rev. C 41, 2103 (1990).
20. A.Z. Mekjian, Phys. Rev. Lett. 64, 2125 (1990); Phys. Rev. C 41, 2103 (1990).
21. S.J. Lee and A.Z. Mekjian, Phys. Rev. C 45, 1284 (1992).
22. R. Delannay, G. Le Caër, and R. Botet, J. Phys. A 29, 6692 (1996).
23. E.D. McGrady, and R.M. Ziff, Phys. Rev. Lett. 58, 892 (1987); Z. Cheng, and S. Redner, ibid. 60, 2450 (1988).
24. E.D. McGrady, and R.M. Ziff, Phys. Rev. Lett. 58, 892 (1987); Z. Cheng, and S. Redner, ibid. 60, 2450 (1988).
25. C. Domb, J. Phys. A 7, 1335 (1974).
26. R.B. Potts, Proc. Cambridge Philos. Soc. 48, 106 (1952).
27. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); C. Tang and P. Bak, ibid. 60, 2347 (1988); P. Bak, K. Chen, and C. Tang, Phys. Lett. A 147, 297 (1990).
28. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); C. Tang and P. Bak, ibid. 60, 2347 (1988); P. Bak, K. Chen, and C. Tang, Phys. Lett. A 147, 297 (1990).
29. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); C. Tang and P. Bak, ibid. 60, 2347 (1988); P. Bak, K. Chen, and C. Tang, Phys. Lett. A 147, 297 (1990).
30. R. Botet, and M. Płoszajczak, Z. Phys. C 76, 257 (1997); R. Botet, in Proceedings of the International Workshop on Nuclear Matter in Different Phases and Transitions (Ref. [1]), p. 161.
31. R. Botet, and M. Płoszajczak, Z. Phys. C 76, 257 (1997); R. Botet, in Proceedings of the International Workshop on Nuclear Matter in Different Phases and Transitions (Ref. [1]), p. 161.
32. J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).
33. M.E. Fisher and J.W. Essam, J. Math. Phys. 2, 609 (1961).
34. D. Stauffer, Phys. Rep. 54, 1 (1979).
35. M. von Smoluchowski, Z. Phys. Chem. (Munich) 92, 129 (1917); R.L. Drake, in Topics in Current Aerosol Research, edited by G.M. Hidy and J.R. Brock (Pergamon Press, New York, 1972), Vol. 3.
36. M. von Smoluchowski, Z. Phys. Chem. (Munich) 92, 129 (1917); R.L. Drake, in Topics in Current Aerosol Research, edited by G.M. Hidy and J.R. Brock (Pergamon Press, New York, 1972), Vol. 3.
37. A.H. Marcus, Technometrics 10, 133 (1968).
38. R.M. Ziff, M.H. Ernst, and E.M. Hendriks, J. Phys. A 16, 2293 (1983).
39. S. Simons, J. Phys. A 19, L901 (1986).
40. F. Leyvraz and H.R. Tschudi, J. Phys. A 14, 3389 (1981).
41. R.M. Ziff, E.M. Hendriks, and M.H. Ernst, Phys. Rev. Lett. 49, 593 (1981).
42. J.B. McLeod, Q. J. Math. 13, 119 (1962); 13, 192 (1962); 13, 283 (1962).
43. J.B. McLeod, Q. J. Math. 13, 119 (1962); 13, 192 (1962); 13, 283 (1962).
44. J.B. McLeod, Q. J. Math. 13, 119 (1962); 13, 192 (1962); 13, 283 (1962).
45. E.M. Hendriks, M.H. Ernst, and R.H. Ziff, J. Stat. Phys. 31, 519 (1983).
46. P.M. Bleher and Ja.G. Sinai, Commun. Math. Phys. 33, 23 (1973); G.A. Baker, Jr., Phys. Rev. B 5, 2622 (1972); G.A. Baker, Jr. and G.R. Golner, Phys. Rev. Lett. 31, 22 (1973); G. Jona-Lasinio, Nuovo Cimento Soc. Ital. Fis., B 26, 99 (1975).
47. P.M. Bleher and Ja.G. Sinai, Commun. Math. Phys. 33, 23 (1973); G.A. Baker, Jr., Phys. Rev. B 5, 2622 (1972); G.A. Baker, Jr. and G.R. Golner, Phys. Rev. Lett. 31, 22 (1973); G. Jona-Lasinio, Nuovo Cimento Soc. Ital. Fis., B 26, 99 (1975).
48. P.M. Bleher and Ja.G. Sinai, Commun. Math. Phys. 33, 23 (1973); G.A. Baker, Jr., Phys. Rev. B 5, 2622 (1972); G.A. Baker, Jr. and G.R. Golner, Phys. Rev. Lett. 31, 22 (1973); G. Jona-Lasinio, Nuovo Cimento Soc. Ital. Fis., B 26, 99 (1975).
49. P.M. Bleher and Ja.G. Sinai, Commun. Math. Phys. 33, 23 (1973); G.A. Baker, Jr., Phys. Rev. B 5, 2622 (1972); G.A. Baker, Jr. and G.R. Golner, Phys. Rev. Lett. 31, 22 (1973); G. Jona-Lasinio, Nuovo Cimento Soc. Ital. Fis., B 26, 99 (1975).
50. A.A. Lushnikov, J. Colloid Interface Sci. 65, 276 (1978).
51. P.G.J. Van Dongen and M.H. Ernst, J. Stat. Phys. 69, 879 (1987).
52. R.M. Ziff, M.H. Ernst, and E.M. Hendriks, J. Phys. A 16, 2293 (1983).
53. ij=i+j is "asymptotically critical," i.e., its critical time is infinite. The power-law cluster-size distribution with τ=3/2 is rigorously valid only in the limit t→∞.
54. R. Botet and M. Płoszajczak (unpublished).