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A two-species system is considered, in which irreversible aggregations occur between particles of the same species while irreversible complete annihilations occur between particles of different species. Such competing processes between aggregation and annihilation reactions are performed by Monte Carlo simulations under various parameter conditions, and the influences of aggregation rate, annihilation rate, and initial particle distribution on the dynamics of the system are analyzed in detail. Simulation results indicate that the particle size distributions always obey a certain scaling law. When the aggregation rates of the two kinds of particles are both twice as fast as the annihilation rate, the scaling exponents of the particle size distributions have relation with the initial particle distribution; while in the remaining cases, the scaling exponents depend crucially on the reaction rates. Moreover, when both aggregation rates are larger than or equal to the double of the annihilation rate, all particles will annihilate each other completely; while at least one of the aggregation rates is slower than the double of the annihilation rate, the species with slower aggregation rate could survive finally. Simulation results are in good agreement with the reported theoretical solutions.
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Keywords:
- aggregation-annihilation /
- Monte Carlo simulation /
- scaling law
[1] Frielander S K 1977 Smoke, dust and haze: Fundamentals of aerosol behavior (Wiley: New York)
[2] Meakin P 1992 Rep. Prog. Phys. 55 157
[3] Vicsek T 1992 Fractal growth phenomena (Singapore: World Scientific)
[4] Drake R L, Hidy G M, Brook J R (eds) 1972 in Topic of Current Aerosol Research (Pergamon: New York)
[5] Krapivsky P L 1993 Physica A 198 135
[6] Krapivsky P L 1993 Physica A 198 150
[7] Sokolov I M, Blumen A 1994 Phys. Rev. E 50 2335
[8] Zhang L G, Yang Z R 1997 Physica A 237 444
[9] Zhang L G, Yang Z R 1997 Phys. Rev. E 55 1442
[10] Ben-Naim E, Krapivsky P L 1995 Phys. Rev. E 52 6066
[11] Ke J, Lin Z 2002 Phys. Rev. E 65 051107
[12] Ke J, Lin Z, Zheng Y, Chen X, Lu W 2007 J. Phys.: Condens. Matter 19 065104
[13] Ke J H, Lin Z Q, Wang X H 2003 Chin. Phys. 12 443
[14] Ke J, Lin Z 2003 Phys. Rev. E 67 062101
[15] Qian C J, Li H, Zhong R, Luo M B, Ye G X 2009 Chin. Phys. B 18 1947
[16] Ma L J, Tang M, Liang X M 2009 Acta Phys. Sin. 58 83 (in Chinese) [马丽娟, 唐明, 梁小明 2009 58 83]
[17] Gao Y, Wang H F, Lin Z Q, Xue X Y 2011 Chin. Phys. B 20 086801
[18] Lin Z Q, Ye G X 2013 Chin. Phys. B 22 058201
[19] Shen W W, Li P P, Ke J H 2010 Acta Phys. Sin. 59 6681 (in Chinese) [沈伟维, 李萍萍, 柯见洪 2010 59 6681]
[20] Zhu B, Li P P, Ke J H, Lin Z Q 2012 Acta Phys. Sin. 61 066802 (in Chinese) [朱标, 李萍萍, 柯见洪, 林振权 2012 61 066802]
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[1] Frielander S K 1977 Smoke, dust and haze: Fundamentals of aerosol behavior (Wiley: New York)
[2] Meakin P 1992 Rep. Prog. Phys. 55 157
[3] Vicsek T 1992 Fractal growth phenomena (Singapore: World Scientific)
[4] Drake R L, Hidy G M, Brook J R (eds) 1972 in Topic of Current Aerosol Research (Pergamon: New York)
[5] Krapivsky P L 1993 Physica A 198 135
[6] Krapivsky P L 1993 Physica A 198 150
[7] Sokolov I M, Blumen A 1994 Phys. Rev. E 50 2335
[8] Zhang L G, Yang Z R 1997 Physica A 237 444
[9] Zhang L G, Yang Z R 1997 Phys. Rev. E 55 1442
[10] Ben-Naim E, Krapivsky P L 1995 Phys. Rev. E 52 6066
[11] Ke J, Lin Z 2002 Phys. Rev. E 65 051107
[12] Ke J, Lin Z, Zheng Y, Chen X, Lu W 2007 J. Phys.: Condens. Matter 19 065104
[13] Ke J H, Lin Z Q, Wang X H 2003 Chin. Phys. 12 443
[14] Ke J, Lin Z 2003 Phys. Rev. E 67 062101
[15] Qian C J, Li H, Zhong R, Luo M B, Ye G X 2009 Chin. Phys. B 18 1947
[16] Ma L J, Tang M, Liang X M 2009 Acta Phys. Sin. 58 83 (in Chinese) [马丽娟, 唐明, 梁小明 2009 58 83]
[17] Gao Y, Wang H F, Lin Z Q, Xue X Y 2011 Chin. Phys. B 20 086801
[18] Lin Z Q, Ye G X 2013 Chin. Phys. B 22 058201
[19] Shen W W, Li P P, Ke J H 2010 Acta Phys. Sin. 59 6681 (in Chinese) [沈伟维, 李萍萍, 柯见洪 2010 59 6681]
[20] Zhu B, Li P P, Ke J H, Lin Z Q 2012 Acta Phys. Sin. 61 066802 (in Chinese) [朱标, 李萍萍, 柯见洪, 林振权 2012 61 066802]
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