Gelation in coagulating systems

Physica D: Nonlinear Phenomena

Volumn 222, Issue 1-2, 2006, Pages 37-53

  Lushnikov, A A ^a  

^a UNIVERSITY OF HELSINKI   (Finland)

Author keywords

Exactly solvable model; Finite coagulating systems; Sol gel transition

Indexed keywords

COAGULATION; MONOMERS; RANDOM PROCESSES; SOL-GELS; THERMODYNAMICS;

COAGULATING PARTICLES; EXACTLY SOLVABLE MODELS; FINITE COAGULATING SYSTEMS; SOL GEL TRANSITIONS;

GELATION;

EID: 33749428542     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2006.08.002     Document Type: Review

References (40)

1. Drake R.L. In: Hidy G.M., and Brock J.R. (Eds). Topics in Current Aerosol Researches (Part II) (1972), Pergamon, New York 201-376
2. Aldous D.J. Deterministic and stochastic models for coalescence (aggregation, coagulation; review of the mean-field theory for probabilists). Bernoulli 5 (1999) 3-122
3. Leyvraz F. Scaling theory and exactly solved models in the kinetics of irreversible aggregation. Phys. Rep. 383 (2003) 95-212
4. Melzak Z.A. The effects of coalescence in certain collision processes. Q. J. Appl. Math. 11 (1953) 231-236
5. McLeod J.B. On an infinite set of nonlinear differential equations. Q. J. Math. 2 (1962) 119-124
6. McLeod J.B. On an infinite set of nonlinear differential equations. Q. J. Math. 2 (1962) 192-196
7. White W.H. A global existence theorem for Smoluchowski's coagulation equation. Proc. Amer. Math. Soc. 80 (1980) 273-281
8. van Dongen P.G.J., and Ernst M.H. On the occurrence of a gelation transition in Smoluchowski's coagulation equation. J. Statist. Phys. 44 (1986) 785-792
9. Hendrics E.M., Ernst M.H., and Ziff R.M. Coagulation equation with gelation. J. Statist. Phys. 31 (1983) 519-563
10. Ziff R.M., and Stell G. Kinetics of polymer gelation. J. Chem. Phys. 73 (1980) 3492-3499
11. Lushnikov A.A., and Piskunov V.N. Three new exactly solvable models in theory of coagulation. Dokl. Akad. Nauk SSSR 267 (1982) 127-130
12. Lushnikov A.A., and Piskunov V.N. Analytical solutions in the theory of coagulating systems with sinks. Appl. Math. Mech. 47 (1983) 931-939
13. Marcus A.H. Stochastic coalescence. Technometrics 10 (1968) 133-143
14. Lushnikov A.A. Coagulation in systems with distributed initial conditions. Dokl. Akad. Nauk SSSR 236 (1977) 673-676
15. Lushnikov A.A. Some exactly solvable models of stochastic coagulation. Dokl. Akad. Nauk SSSR 237 (1977) 1122-1125
16. Lushnikov A.A. Coagulation in finite systems. J. Colloid Interface Sci. 65 (1978) 276-285
17. Lushnikov A.A. Some new aspects of coagulation theory. Izv. AN SSRR, Ser. Phys. Atmos. Ocean. 14 (1978) 1046-1054
18. Lushnikov A.A. From sol to gel exactly. Phys. Rev. Lett. 93 (2004) 198302
19. Lushnikov A.A. Exact kinetics of the sol-gel transition. Phys. Rev. E 71 (2005) 046129
20. Lushnikov A.A. Exact particle mass spectrum in a gelling system. J. Phys. A 38 (2005) L35-L39
21. Lushnikov A.A. Sol-gel transition in a coagulating mixture. J. Phys. A 38 (2005) L383-L387
22. Egorychev G.P. Integral Representation and Counting the Combinatorial Sums (1977), Nauka, Moscow (in Russian)
23. Niven I. Formal power series. Amer. Math. Monthly 76 (1969) 871-889
24. Knuth D.E. Linear probing and graphs. Algorithmica 22 (1998) 561-568
25. Flajolet P., Poblete P., and Viola A. On the analysis of linear probing hushing. Algorithmica 22 (1998) 490-515
26. Kreweras G. Une famille de polynomes ayant pluseurs proprietes enumeratives. Period. Math. Hungar. 11 (1980) 309-320
27. Lushnikov A.A. Evolution of coagulating systems. III. Coagulating mixtures. J. Colloid Interface Sci. 54 (1976) 94-103
28. Lushnikov A.A. Exact kinetics of sol-gel transition in a coagulating mixture. Phys. Rev. E 73 (2006) 036111
29. Domilovskii E.R., Lushnikov A.A., and Piskunov V.N. A new exactly solvable model of a coagulating mixture. Dokl. Akad. Nauk SSSR 243 (1978) 407-410
30. Erdös P., and Rényi A. On evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5 (1960) 17-61
31. Bollobas B. Random Graphs (1985), Academic, London
32. Albert R., and Barabási A.-L. Statistical mechanics of complex networks. Rev. Modern Phys. 74 (2002) 47-97
33. Lushnikov A.A. Time evolution of a random graph. J. Phys. A 38 (2005) L777-L782
34. A.A. Lushnikov, Evolution of coagulating systems, Doct. Dissertation, Karpov Institute of Physical Chemistry, Moscow, 1978
35. Lushnikov A.A. Evolution of coagulating systems. J. Colloid Interface Sci. 45 (1973) 549-559
36. Lushnikov A.A., and Kulmala M. Singular self-preserving regimes of coagulation-condensation process. Phys. Rev. E 65 (2002) 041604
37. Jeon I. Existence of gelling solutions for Coagulation-fragmentation equations. Comm. Math. Phys. 194 (1998) 541-567
38. Leyvraz F. Existence and properties of post-gel solutions of the equations of coagulation. J. Phys. A 16 (1983) 2861-2871
39. Lee M.H. A survey of numerical solutions to the coagulation equation. J. Phys. A 34 (2001) 10219-10241
40. Riddel R.J., and Ulenbeck G.E. On the theory of virial development of the equation of state of monoatomic gases. J. Chem. Phys. 21 (1953) 2056-2064