### Abstract

A scaling generalization of the Smoluchowski equation is used to treat fluctuation effects in aggregation problems. In particular, we investigate the diffusion-limited cluster-cluster aggregation subject to the condition that single particles are fed into the system at a constant rate, h, while clusters larger than a fixed size are removed. Considering the zero-feed-rate limit as a critical point, we find that h plays the role of an external field conjugate to the order parameter which turns out to be the cluster density. The cluster density obeys dynamic scaling and, because of the finiteness of a kinetic coefficient, the dynamic critical exponents are expressible in terms of a static exponent. The exponents are determined by arguing that the zero-feed-rate process is in one universality class with the A+A0 diffusive annihilation problem. Our scaling theory is in agreement with available Monte Carlo simulation data.

Original language | English |
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Pages (from-to) | 1129-1133 |

Number of pages | 5 |

Journal | Physical Review A |

Volume | 32 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

**Aggregation in the presence of sources and sinks : A scaling theory.** / Rácz, Z.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 32, no. 2, pp. 1129-1133. https://doi.org/10.1103/PhysRevA.32.1129

}

TY - JOUR

T1 - Aggregation in the presence of sources and sinks

T2 - A scaling theory

AU - Rácz, Z.

PY - 1985

Y1 - 1985

N2 - A scaling generalization of the Smoluchowski equation is used to treat fluctuation effects in aggregation problems. In particular, we investigate the diffusion-limited cluster-cluster aggregation subject to the condition that single particles are fed into the system at a constant rate, h, while clusters larger than a fixed size are removed. Considering the zero-feed-rate limit as a critical point, we find that h plays the role of an external field conjugate to the order parameter which turns out to be the cluster density. The cluster density obeys dynamic scaling and, because of the finiteness of a kinetic coefficient, the dynamic critical exponents are expressible in terms of a static exponent. The exponents are determined by arguing that the zero-feed-rate process is in one universality class with the A+A0 diffusive annihilation problem. Our scaling theory is in agreement with available Monte Carlo simulation data.

AB - A scaling generalization of the Smoluchowski equation is used to treat fluctuation effects in aggregation problems. In particular, we investigate the diffusion-limited cluster-cluster aggregation subject to the condition that single particles are fed into the system at a constant rate, h, while clusters larger than a fixed size are removed. Considering the zero-feed-rate limit as a critical point, we find that h plays the role of an external field conjugate to the order parameter which turns out to be the cluster density. The cluster density obeys dynamic scaling and, because of the finiteness of a kinetic coefficient, the dynamic critical exponents are expressible in terms of a static exponent. The exponents are determined by arguing that the zero-feed-rate process is in one universality class with the A+A0 diffusive annihilation problem. Our scaling theory is in agreement with available Monte Carlo simulation data.

UR - http://www.scopus.com/inward/record.url?scp=35949024008&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35949024008&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.32.1129

DO - 10.1103/PhysRevA.32.1129

M3 - Article

AN - SCOPUS:35949024008

VL - 32

SP - 1129

EP - 1133

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

ER -