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Constant flux relation for diffusion-limited cluster-cluster aggregation

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Connaughton, Colm, Rajesh, R. and Zaboronski, Oleg V.. (2008) Constant flux relation for diffusion-limited cluster-cluster aggregation. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol.78 (No.4(1)). 041403. ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.78.041403

Abstract

In a nonequilibrium system, a constant flux relation (CFR) expresses the fact that a constant flux of a conserved quantity exactly determines the scaling of the particular correlation function linked to the flux of that conserved quantity. This is true regardless of whether mean-field theory is applicable or not. We focus on cluster-cluster aggregation and discuss the consequences of mass conservation for the steady state of aggregation models with a monomer source in the diffusion-limited regime. We derive the CFR for the flux-carrying correlation function for binary aggregation with a general scale-invariant kernel and show that this exponent is unique. It is independent of both the dimension and of the details of the spatial transport mechanism, a property which is very atypical in the diffusion-limited regime. We then discuss in detail the "locality criterion" which must be satisfied in order for the CFR scaling to be realizable. Locality may be checked explicitly for the mean-field Smoluchowski equation. We show that if it is satisfied at the mean-field level, it remains true over some finite range as one perturbatively decreases the dimension of the system below the critical dimension, d(c)=2, entering the fluctuation-dominated regime. We turn to numerical simulations to verify locality for a range of systems in one dimension which are, presumably, beyond the perturbative regime. Finally, we illustrate how the CFR scaling may break down as a result of a violation of locality or as a result of finite size effects and discuss the extent to which the results apply to higher order aggregation processes.

Item Type:

Journal Article

Subjects:

Q Science > QC Physics

Divisions:

Faculty of Science > Centre for Complexity Science
Faculty of Science > Mathematics

Library of Congress Subject Headings (LCSH):

Cluster analysis, Dynamics of a particle

Journal or Publication Title:

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

Publisher:

American Physical Society

ISSN:

1539-3755

Official Date:

October 2008

Dates:

Date	Event
October 2008	Published

Volume:

Vol.78

Number:

No.4(1)

Number of Pages:

Page Range:

041403

Identification Number:

10.1103/PhysRevE.78.041403

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

Related URLs:

Other Repository

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