### Abstract

The dynamics of the diffusion-limited model of cluster-cluster aggregation is investigated in two and three dimensions by studying the temporal evolution of the cluster-size distribution ns(t), which is the number of clusters of size s at time t. In a recent study it was shown that the results of the two-dimensional simulations for mass-independent diffusivity can be well represented by a dynamic-scaling function of the form ns(t) s-2f(s/tz), where f(x) is a scaling function with a power-law behavior for small x, namely f(x)x for x 1 and f(x) 1 for x 1. In this paper we extend the calculations of the cluster-size distribution to three dimensions and to the case of the cluster diffusivity depending on the size of the clusters. The diffusion constant of a cluster of size s is assumed to be proportional to s. The overall behavior of ns(t) and the exponents and z have been determined for a set of values of. We find that the results are consistent with the scaling theory, and the exponents in ns(t) depend continuously on. Moreover, there is a critical value of [c(d=2)-(1/4), c(d=3)-1/2] at which the shape of the cluster-size distribution crosses over from a monotonically decreasing function to a bell-shaped curve which can be described by the above scaling form for ns(t), but with a scaling function f(x) different from f(x).

Original language | English |
---|---|

Pages (from-to) | 564-569 |

Number of pages | 6 |

Journal | Physical Review B |

Volume | 31 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*31*(1), 564-569. https://doi.org/10.1103/PhysRevB.31.564

**Dynamic cluster-size distribution in cluster-cluster aggregation : Effects of cluster diffusivity.** / Meakin, Paul; Vicsek, T.; Family, Fereydoon.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 31, no. 1, pp. 564-569. https://doi.org/10.1103/PhysRevB.31.564

}

TY - JOUR

T1 - Dynamic cluster-size distribution in cluster-cluster aggregation

T2 - Effects of cluster diffusivity

AU - Meakin, Paul

AU - Vicsek, T.

AU - Family, Fereydoon

PY - 1985

Y1 - 1985

N2 - The dynamics of the diffusion-limited model of cluster-cluster aggregation is investigated in two and three dimensions by studying the temporal evolution of the cluster-size distribution ns(t), which is the number of clusters of size s at time t. In a recent study it was shown that the results of the two-dimensional simulations for mass-independent diffusivity can be well represented by a dynamic-scaling function of the form ns(t) s-2f(s/tz), where f(x) is a scaling function with a power-law behavior for small x, namely f(x)x for x 1 and f(x) 1 for x 1. In this paper we extend the calculations of the cluster-size distribution to three dimensions and to the case of the cluster diffusivity depending on the size of the clusters. The diffusion constant of a cluster of size s is assumed to be proportional to s. The overall behavior of ns(t) and the exponents and z have been determined for a set of values of. We find that the results are consistent with the scaling theory, and the exponents in ns(t) depend continuously on. Moreover, there is a critical value of [c(d=2)-(1/4), c(d=3)-1/2] at which the shape of the cluster-size distribution crosses over from a monotonically decreasing function to a bell-shaped curve which can be described by the above scaling form for ns(t), but with a scaling function f(x) different from f(x).

AB - The dynamics of the diffusion-limited model of cluster-cluster aggregation is investigated in two and three dimensions by studying the temporal evolution of the cluster-size distribution ns(t), which is the number of clusters of size s at time t. In a recent study it was shown that the results of the two-dimensional simulations for mass-independent diffusivity can be well represented by a dynamic-scaling function of the form ns(t) s-2f(s/tz), where f(x) is a scaling function with a power-law behavior for small x, namely f(x)x for x 1 and f(x) 1 for x 1. In this paper we extend the calculations of the cluster-size distribution to three dimensions and to the case of the cluster diffusivity depending on the size of the clusters. The diffusion constant of a cluster of size s is assumed to be proportional to s. The overall behavior of ns(t) and the exponents and z have been determined for a set of values of. We find that the results are consistent with the scaling theory, and the exponents in ns(t) depend continuously on. Moreover, there is a critical value of [c(d=2)-(1/4), c(d=3)-1/2] at which the shape of the cluster-size distribution crosses over from a monotonically decreasing function to a bell-shaped curve which can be described by the above scaling form for ns(t), but with a scaling function f(x) different from f(x).

UR - http://www.scopus.com/inward/record.url?scp=35949018798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35949018798&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.31.564

DO - 10.1103/PhysRevB.31.564

M3 - Article

AN - SCOPUS:35949018798

VL - 31

SP - 564

EP - 569

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 1

ER -