摘要We investigate the dynamical behaviour of the aggregation process in the symmetric conserved mass aggregation model under three different topological structures. The dispersion σ (t,L)=(∑i(mi-ρ0)2/L)1/2 is defined to describe the dynamical behaviour where ρ0 is the density of particle and mi is the particle number on a site. It is found numerically that for a regular lattice and a scale-free network, σ(t,L) follows a power-law scaling σ(t,L)tδ1 and σ (t,L)~tδ4 from a random initial condition to the stationary states, respectively. However, for a small-world network, there are two power-law scaling regimes, σ(t,L)~ tδ2 when t<T and σ(t,L)~ tδ3 when t>T. Moreover, it is found numerically that δ2 is near to δ1 for small rewiring probability q, and δ3 hardly changes with varying $q$ and it is almost the same as δ4. We speculate that the aggregation of the connection degree accelerates the mass aggregation in the initial relaxation stage and the existence of the long-distance interactions in the complex networks results in the acceleration of the mass aggregation when t>T for the small-world networks. We also show that the relaxation time τ follows a power-law scaling τ ~ Lz and σ (t,L) in the stationary state follows a power-law σ s(L)~Lα for three different structures.
Abstract：We investigate the dynamical behaviour of the aggregation process in the symmetric conserved mass aggregation model under three different topological structures. The dispersion σ (t,L)=(∑i(mi-ρ0)2/L)1/2 is defined to describe the dynamical behaviour where ρ0 is the density of particle and mi is the particle number on a site. It is found numerically that for a regular lattice and a scale-free network, σ(t,L) follows a power-law scaling σ(t,L)tδ1 and σ (t,L)~tδ4 from a random initial condition to the stationary states, respectively. However, for a small-world network, there are two power-law scaling regimes, σ(t,L)~ tδ2 when t<T and σ(t,L)~ tδ3 when t>T. Moreover, it is found numerically that δ2 is near to δ1 for small rewiring probability q, and δ3 hardly changes with varying $q$ and it is almost the same as δ4. We speculate that the aggregation of the connection degree accelerates the mass aggregation in the initial relaxation stage and the existence of the long-distance interactions in the complex networks results in the acceleration of the mass aggregation when t>T for the small-world networks. We also show that the relaxation time τ follows a power-law scaling τ ~ Lz and σ (t,L) in the stationary state follows a power-law σ s(L)~Lα for three different structures.
HUA Da-Yin. Dynamics of Symmetric Conserved Mass Aggregation Model on Complex Networks[J]. 中国物理快报, 2009, 26(1): 18901-018901.
HUA Da-Yin. Dynamics of Symmetric Conserved Mass Aggregation Model on Complex Networks. Chin. Phys. Lett., 2009, 26(1): 18901-018901.
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2009, Vol. 26 
