Scaling theory and exactly solved models in the kinetics of irreversible aggregation

Physics Reports

Volumn 383, Issue 2-3, 2003, Pages 95-212

  Leyvraz, F ^a  

^a INSTITUTO DE CIENCIAS FÍSICAS   (Mexico)

Author keywords

Aggregation; Exactly solved models; Scaling

Indexed keywords

EID: 0041511747     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(03)00241-2     Document Type: Review

References (118)

1. Abramowitz M. Stegun I. Handbook of Mathematical Functions 1972 Dover New York
2. Aldous D.J. Deterministic and stochastic models for coalescence (aggregation, coagulation: review of the mean-field theory for probabilists Bernoulli 5 1999 3
3. Aizenman M. Bak T.A. Convergence to equilibrium in a system of reacting polymers Commun. Math. Phys. 65 1979 203
4. Bak T.A. Heilmann O.J. Post-gelation solutions to Smoluchowski's coagulation equation J. Phys. A 27 1994 4203
5. Ball J.M. Carr J. The discrete coagulation-fragmentation equations: existence, uniqueness and density conservation J. Stat. Phys. 61 1990 203
6. Ben-Naim E. Krapivsky P.L. Kinetics of aggregation-annihilation processes Phys. Rev. E 52 1995 6066 (cond-mat/9507031)
7. Boehm A.B. Poor C. Grant S.B. Particle coagulation and the memory of initial conditions J. Phys. A 31 1998 9241
8. Bouchaud J.-P. Georges A. Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications Phys. Rep. 195 1990 127
9. Broide M.L. Cohen R.J. Experimental evidence of dynamic scaling in colloidal aggregation Phys. Rev. Lett. 64 1990 2026
10. Buffet E. Pulé J.V. Gelation, the diagonal case revisited Nonlinearity 2 1989 373
11. Buffet E. Pulé J.V. On Lushnikov's model of gelation J. Stat. Phys. 58 1990 1041
12. Buffet E. Werner R.F. A counterexample in coagulation theory J. Math. Phys. 32 1991 2276
13. Calogero F. Leyvraz F. A new solvable model of aggregation kinetics J. Phys. A 32 1999 7697
14. Calogero F. Leyvraz F. New results on a parity-dependent model of aggregation J. Phys. A 33 2000 5619
15. Carnevale G.F. Pomeau Y. Young W.R. Statistics of ballistic agglomeration Phys. Rev. Lett. 64 1990 2913
16. Carr J. da Costa F.P. Instantaneous gelation in coagulation dynamics Z. Angew. Math. Phys. 43 1992 974
17. Cheng Z. Redner S. Leyvraz F. Coagulation with a steady monomer point source Phys. Rev. Lett. 62 1989 2321
18. Cueille S. Sire C. Nontrivial polydispersity exponents in aggregation models Phys. Rev. E 55 1997 5465
19. Cueille S. Sire C. Droplet nucleation and Smoluchowski's equation with growth and injection of particles Phys. Rev. E 57 1998 881
20. Davies S.C. King J.R. Wattis J.A.D. The Smoluchowski coagulation equations with continuous injection J. Phys. A 32 1999 7745
21. Doering C.R. benAvraham D. Interparticle distribution functions and rate equations for diffusion-limited reactions Phys. Rev. A 38 1988 3035
22. Doering C.R. benAvraham D. Diffusion-limited coagulation in the presence of particle input: exact results in one dimension Phys. Rev. Lett. 62 1989 2563
23. Drake, R.L. in: G.M. Hidy, J.R. Brock (Eds.), Topics in Current Aerosol Research, Vol. 3, part 2, Pergamon Press, New York, 1972.
24. Ernst M.H. Ziff R.M. Hendriks E.M. Coagulation processes with a phase transition J. Colloid Interface Sci. 97 1984 266
25. Ernst M.H. Hendriks E.M. Leyvraz F. Smoluchowski's equation and the θ-exponent for branched polymers J. Phys. A 17 1984 2137
26. Ernst M.H. Kinetics of clustering in irreversible aggregation in: Pietronero L. Tosatti E. (Eds.) Fractals in Physics 1986 289 North-Holland Amsterdam
27. Fisher M.E. Walks, walls, wetting an melting J. Stat. Phys. 34 1984 667
28. Frachebourg L. Exact solution of one-dimensional ballistic aggregation Phys. Rev. Lett. 82 1999 1502
29. Frachebourg L. Martin Ph.A. Piasecki J. Ballistic aggregation: a solvable model of irreversible many particles dynamics Physica A 279 2000 69
30. Frachebourg L. Jacquemet V. Martin Ph.A. Inhomogeneous ballistic aggregation J. Stat. Phys. 105 2001 745
31. Friedlander S.K. Wang C.S. The self-preserving particle size distribution for coagulation by Brownian motion J. Colloid Interface Sci. 22 1966 126
32. Friedlander S.K. Smoke, Dust and Haze 2nd Edition 2000 Oxford University Press Oxford
33. Gasper, G. Rahman, M. in: G.-C. Rota (Eds.), Basic Hypergeometric series (Encyclopedia of Mathematics and its Applications, Vol. 35), Cambridge University Press, Cambridge
34. Hansen A.E. Marteau D. Tabeling P. Two-dimensional turbulence and dispersion in a freely decaying system Phys. Rev. E 58 1998 7261
35. Hellén, E.K.O. Salmi, P.E. Alava, M.J. Cluster persistence in one-dimensional diffusion-limited cluster-cluster aggregation, cond-mat/0206139.
36. Hendriks E. Ernst M.H. Ziff R.M. Coagulation equations with gelation J. Stat. Phys. 31 1983 519
37. Hidy G.R. Brock J.R. The Dynamics of Aerocolloidal Systems, International Reviews in Aerosol Physics and Chemistry 1970 Pergamon Press Oxford
38. Ispolatov S. Krapivsky P.L. Ballistic coalescence model Physica A 252 1998 165
39. Ivlev A.V. Morfill G.E. Konopka U. Coagulation of charged microparticles in neutral gas and charge-induced gel transitions Phys. Rev. Lett. 89 2002 195502
40. Jiang Yu Gang Hu Generalized Smoluchowski equation with gelation Phys. Rev. B 39 1989 4659
41. Jiang Yu Gang Hu Long-time behaviour of the cluster size distribution in joint coagulation processes Phys. Rev. B 40 1989 661
42. Jiang Yu Gang Hu Benun Ma Critical behavior of the generalized Smoluchowski coagulation equation Commun. Theor. Phys. 12 1989 395
43. Jiang Yu Gang Hu BenKun Ma Gelation in generalized Smoluchovski equation Commun. Theor. Phys. 11 1989 255
44. Jiang Yu Gang Hu BenKun Ma Critical property and universality in the generalized Smoluchowski coagulation equation Phys. Rev. B 41 1990 9424
45. Jiang Yu Leyvraz F. Scaling theory for ballistic aggregation J. Phys. A 26 1993 L179
46. Jiang Yu Scaling theory for multipolymer coagulation Phys. Rev. E 50 1994 4901
47. Jullien R. Botet R. Aggregation and Fractal Aggregates 1987 World Scientific Singapore
48. Kang K. Redner S. Fluctuation effects in Smoluchowski reaction kinetics Phys. Rev. A 30 1984 2833
49. Kang K. Redner S. Meakin P. Leyvraz F. Long-time crossover phenomena in coagulation kinetics Phys. Rev. A 33 1986 1171
50. Krapivsky P.L. Aggregation processes with n-particle elementary reactions J. Phys. A 24 1991 4697
51. Krapivsky P.L. ben-Naim E. Aggregation with multiple conservation laws Phys. Rev. E 53 1996 291
52. Krapivsky P.L. Redner S. Transitional aggregation kinetics in dry and damp environments Phys. Rev. E 54 1996 3553
53. Krivitski D.S. Numerical solution of the Smoluchowski kinetic equation and asymptotics of the distribution function J. Phys. A 28 1995 2025
54. Lai F.S. Friedlander S.K. Pich J. Hidy G.M. The self-preserving particle size distribution for Brownian motion in the free-molecule regime J. Colloid Interface Sci. 39 1973 395
55. Lee M.H. On the validity of the coagulation equation and the nature of runaway growth Icarus 143 2000 74
56. Lee M.H. A survey of numerical solutions to the coagulation equation J. Phys. A 34 2001 10219
57. Leyvraz F. Tschudi H.R. An exactly solvable model for externally controlled coagulation J. Phys. A 13 1980 1867
58. Leyvraz F. Tschudi H.R. Singularities in the kinetics of coagulation processes J. Phys. A 14 1981 3389
59. Leyvraz F. Tschudi H.R. Critical kinetics near gelation J. Phys. A 15 1982 1951
60. Leyvraz F. Existence and properties of post-gel solutions of the equations of coagulation J. Phys. A 16 1983 2861
61. Leyvraz F. Large-time behavior of the Smoluchowski equations of coagulation Phys. Rev. A 29 1984 854
62. Leyvraz, F. Rate equations approach to aggregation, in: H.E. Stanley, N. Ostrowski (Eds.), On Growth and Form: Fractal and Nonfractal Patterns in Nature, M. Nijhoff, Dordrecht, 1986.
63. Leyvraz F. Redner S. Non-universality and breakdown of scaling in a two-component coagulation model Phys. Rev. Lett. 57 1986 163
64. Leyvraz F. Redner S. Non-universality and breakdown of scaling in two-species aggregation Phys. Rev. A 36 1987 4033
65. Leyvraz F. Scaling and crossover properties of a new solvable model of aggregation kinetics J. Phys. A 32 1999 7719
66. Liggett T.M. Interacting Particle Systems 1985 Springer Berlin
67. Lushnikov A.A. Evolution of coagulating systems J. Colloid Interface Sci. 45 1973 549
68. Lushnikov A.A. Evolution of coagulating systems 2: asymptotic size distribution and analyticity properties of generating functions J. Colloid Interface Sci. 48 1974 400
69. Lushnikov A.A. Evolution of coagulating systems 3: coagulating mixtures J. Colloid Interface Sci. 54 1976 94
70. Lushnikov A.A. Coagulation in finite systems J. Colloid Interface Sci. 65 1978 276
71. Lushnikov A.A. Tokar J.I. Nonstationary conditions of coagulation in the systems with stationary external source of particles Dokl. Akad. Nauk SSSR 252 1980 136
72. Lushnikov A.A. Piskunov V.N. New exactly solvable models in the coagulation theory Dokl. Akad. Nauk SSSR 267 1982 132
73. Lushnikov A.A. Kulmala M. Singular self-preserving regimes of coagulation processes Phys. Rev. E 65 2001 041604
74. Lushnikov A.A. Kulmala M. Nonsingular self-preserving regimes of coagulation-condensation process Phys. Rev. E 64 2001 031605
75. Martin Ph.A. Piasecki J. One-dimensional ballistic aggregation: rigorous long-time estimates J. Stat. Phys. 76 1994 447
76. McLeod J.B. On an infinite set of non-linear differential equations Q. J. Math. Oxford (2) 13 1962 119
77. McLeod J.B. On an infinite set of non-linear differential equations (II) Q. J. Math. Oxford (2) 13 1962 192
78. Meakin P. Fractals, Scaling and Growth Far from Equilibrium Cambridge Nonlinear Science Series Vol. 5 1998 Cambridge University Press Cambridge
79. Melzak Z.A. The effects of coalescence in certain collision processes Q. J. Appl. Math. 11 1953 231
80. Mobilia M. Krapivsky P.L. Redner S. Kinetic anomalies in addition-aggregation processes J. Phys. A 36 2003 4553
81. Norris J.R. Uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent Ann. Appl. Probab. 9 1999 78
82. Norris J.R. Cluster coagulation Commun. Math. Phys. 209 2000 407
83. Oliva P.P. Zanette D.H. Alemany P.A. Analytical approach to coagulation and annihilation of particles with anomalous diffusion Phys. Rev. E 53 1996 228
84. Piasecki J. Universal distribution of masses in a one-dimensional sticky gas Physica (Amsterdam) 190A 1992 90
85. Piasecki J. Trizac E. Droz M. Dynamics of ballistic annihilation Phys. Rev. E 66 2002 066111
86. Pruppacher H.R. Klett J.D. Microphysics of Clouds and Precipitation 1978 Reidel Dordrecht
87. Scott W.T. Analytic studies on cloud droplet coalescence J. Atmos. Sci. 25 1968 54
88. Slemrod M. Coagulation-diffusion systems: derivation and existence of solutions for the diffuse-interface structure equations Physica D 46 1990 351
89. von Smoluchowski M. Drei Vorträge über Diffusion, Brown'sche Molekularbewegung und Koagulation von Kolloidteilchen Z. Phys. 17 1916 557
90. ij=A+B(i+j)+Cij J. Phys. A 16 1983 767
91. Spouge J.L. Solutions and critical times for the polydisperse coagulation equation when a(x,y)=A+B(x+y)+Cxy J. Phys. A 16 1983 3127
92. Spouge J.L. Analytic solutions to Smoluchowski's coagulation equation: a combinatorial interpretation J. Phys. A 18 1985 3063
93. Spouge J.L. Exact solutions for a diffusion-reaction process in one dimension Phys. Rev. Lett. 60 1988 871
94. Spouge J.L. Exact solutions for diffusion-reaction processes in one dimension II: spatial distributions J. Phys. A 21 1988 4183
95. Stockmayer W.H. Theory of molecular size distribution and gel formation in branched-chain polymers J. Chem. Phys. 11 1943 45
96. Swift D.L. Friedlander S.K. Coagulation of hydrosols by Brownian motion and laminar shear flow J. Colloid Interface Sci. 19 1964 621
97. Torney D.C. McConnell H.M. Diffusion-limited reaction rate theory for two-dimensional systems Proc. R. Soc. London, Ser. A 387 1983 147
98. Trizac E. Hansen J.-P. Dynamic scaling behavior of ballistic coalescence Phys. Rev. Lett. 74 1995 4114
99. Trizac, E. Private communication, 2001.
100. Trizac E. Kinetics and scaling in ballistic annihilation Phys. Rev. Lett. 88 2002 160601
101. van Dongen P.G.J. Ernst M.H. Pre- and post gel size distributions in (ir)reversible polymerisation J. Phys. A 16 1983 L327
102. van Dongen P.G.J. Ernst M.H. Dynamic scaling in the kinetics of clustering Phys. Rev. Lett. 54 1985 1396
103. van Dongen P.G.J. Cluster size distribution in irreversible aggregation at large times J. Phys. A 18 1985 2779
104. van Dongen P.G.J. Ernst M.H. Fluctuations in coagulating systems J. Stat. Phys. 49 1987 879
105. van Dongen P.G.J. Ernst M.H. Fluctuations in coagulating systems II J. Stat. Phys. 49 1987 927
106. van Dongen P.G.J. Ernst M.H. Solutions of smoluchowski's coagulation equation at large cluster sizes Physica A 145 1987 15
107. van Dongen P.G.J. On the possible occurrence of instantaneous gelation in Smoluchowski's coagulation equation J. Phys. A: Math. Gen. 20 1987 1889
108. van Dongen P.G.J. Ernst M.H. Scaling solutions of Smoluchowski's coagulation equation J. Stat. Phys. 50 1988 295
109. van Dongen P.G.J. Upper critical dimension in irreversible aggregation Phys. Rev. Lett. 63 1989 1281
110. Vicsek T. Family F. Dynamic scaling for aggregation of clusters Phys. Rev. Lett. 52 1984 1669
111. Vicsek T. Meakin P. Scaling in steady-state cluster-cluster aggregation Phys. Rev. A 32 1985 1122
112. White W.H. A global existence theorem for Smoluchowski's coagulation equations Proc. Am. Math. Soc. 80 1980 273
113. White W.H. On the form of steady-state solutions to the coagulation equations J. Colloid Interface Sci. 87 1982 204
114. Williams D. Probability with Martingales 1991 Cambridge University Press Cambridge
115. Ziff R.M. Stell G. Kinetics of polymer gelation J. Chem. Phys. 73 1980 3492
116. Ziff R.M. Hendriks E.M. Ernst M.H. Critical properties for gelation: a kinetic approach Phys. Rev. Lett. 49 1982 593
117. Ziff R.M. Ernst M.H. Hendriks E.M. Kinetics of gelation and universality J. Phys. A 16 1983 2293
118. Ziff R.M. Ernst M.H. Hendriks E.M. A transformation linking two models of coagulation J. Colloid Interface Sci. 100 1983 220