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Kinetics of diffusion-limitied aggregation-annihilation processes on NW small-world networks is investigated by Monte Carlo simulation. In the system, if two clusters of the same species meet at the same node, they will aggregate and form a large one; while if two clusters of different species meet at the same node, they will annihilate each other. Simulation results show that, if the value of p (a parameter that quantifies the number of shortcuts) is large or small enough, the concentration of clusters c(t) and the concentration of particles g(t) follow power laws at large times, i.e.c(t)∝t-α and g(t)∝t－β. Moreover, the relation between the exponents α and β is found to satisfy α=2β. However, if p is of medium value, the concentration of clusters and the concentration of particles do not follow the power laws exactly. Our simulation results agree with the reported theoretical analysis very well.
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Keywords:
- aggregation-annihilation processes /
- small-world network /
- kinetic behavior /
- Monte Carlo simulation
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[7] Vicsek T 1992 Fractal growth phenomena (Singapore: World Scientific)
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[11] Sokolov I M, Blumen A 1994 Phys. Rev. E 50 2335
[12] Ben-Naim E, Krapivsky P L 1995 Phys. Rev. E 52 6066
[13] Argyrakis P, Kopelman R 1993 Phys. Rev. E 47 3757
[14] Privman V, Cadilhe A M R, Glasser M L 1996 Phys. Rev. E 53 739
[15] Kwon S, Kim Y 2009 Phys. Rev. E 79 041132
[16] Frachebourg L, Krapivsky P L, Redner S 1998 J. Phys. A: Math. Gen. 31 2791
[17] Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47
[18] Dorogovtsev S N, Mendes J F F 2002 Adv. Phys. 51 1079
[19] Catanzaro M, Boguá M, Pastor-Satorras R 2005 Phys. Rev. E 71 056104
[20] Laguna M F, Aldana M, Larralde H, Parris P E, Kenkre V M 2005 Phys. Rev. E 72 026102
[21] Gallos L K, Argyrakis P 2004 Phys. Rev. Lett. 92 138301
[22] Gallos L K, Argyrakis P 2007 J. Phys.: Condens. Matter 19 065123
[23] Tang M, Liu Z, Zhou J 2006 Phys. Rev. E 74 036101
[24] Liang X M, Ma L J, Tang M 2009 Acta Phys. Sin. 58 83 (in Chinese) [梁小明、马丽娟、唐明 2009 58 83]
[25] Hua D Y 2009 Chin. Phys. Lett. 26 018901
[26] Ke J, Lin Z, Zheng Y, Chen X, Lu W 2006 Phys. Rev. Lett. 97 028301
[27] Shi H P, Ke J H, Sun C, Lin Z Q 2009 Acta Phys. Sin. 58 1 (in Chinese) [施华萍、柯见洪、孙 策、林振权 2009 58 1]
[28] Watts D J, Strogatz S H 1998 Nature (London) 393 440
[29] Newman M E J, Watts D J 1999 Phys. Rev. E 60 7332
[30] Krapivsky P L 1993 Physica A 198 150
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[1] Smoluchowski M V 1917 Z. Phys. Chem. 92 129
[2] Family F, Landau D P 1984 Kinetics of aggregation and gelation (New York: Elesevier Science Publishing)
[3] Ernst M H, Hendriks E M, Ziff R M 1982 J. Phys. A: Math. Gen. 15 743
[4] Ziff R M, Ernst M H, Hendriks E M 1982 J. Phys. A: Math. Gen. 15 2293
[5] Kang K, Redner S 1985 Phys. Rev. A 32 435
[6] Kang K, Redner S 1984 Phys. Rev. Lett. 52 955
[7] Vicsek T 1992 Fractal growth phenomena (Singapore: World Scientific)
[8] Toussaint D, Wilcek F 1983 J. Chem. Phys. 78 2642
[9] Zumofen G, Blimen A, Klafter J 1985 J. Chem. Phys. 82 3198
[10] Krapivsky P L 1993 Physica A 198 135
[11] Sokolov I M, Blumen A 1994 Phys. Rev. E 50 2335
[12] Ben-Naim E, Krapivsky P L 1995 Phys. Rev. E 52 6066
[13] Argyrakis P, Kopelman R 1993 Phys. Rev. E 47 3757
[14] Privman V, Cadilhe A M R, Glasser M L 1996 Phys. Rev. E 53 739
[15] Kwon S, Kim Y 2009 Phys. Rev. E 79 041132
[16] Frachebourg L, Krapivsky P L, Redner S 1998 J. Phys. A: Math. Gen. 31 2791
[17] Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47
[18] Dorogovtsev S N, Mendes J F F 2002 Adv. Phys. 51 1079
[19] Catanzaro M, Boguá M, Pastor-Satorras R 2005 Phys. Rev. E 71 056104
[20] Laguna M F, Aldana M, Larralde H, Parris P E, Kenkre V M 2005 Phys. Rev. E 72 026102
[21] Gallos L K, Argyrakis P 2004 Phys. Rev. Lett. 92 138301
[22] Gallos L K, Argyrakis P 2007 J. Phys.: Condens. Matter 19 065123
[23] Tang M, Liu Z, Zhou J 2006 Phys. Rev. E 74 036101
[24] Liang X M, Ma L J, Tang M 2009 Acta Phys. Sin. 58 83 (in Chinese) [梁小明、马丽娟、唐明 2009 58 83]
[25] Hua D Y 2009 Chin. Phys. Lett. 26 018901
[26] Ke J, Lin Z, Zheng Y, Chen X, Lu W 2006 Phys. Rev. Lett. 97 028301
[27] Shi H P, Ke J H, Sun C, Lin Z Q 2009 Acta Phys. Sin. 58 1 (in Chinese) [施华萍、柯见洪、孙 策、林振权 2009 58 1]
[28] Watts D J, Strogatz S H 1998 Nature (London) 393 440
[29] Newman M E J, Watts D J 1999 Phys. Rev. E 60 7332
[30] Krapivsky P L 1993 Physica A 198 150
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