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Article
Moment Analysis of the Cluster-Size-Distribution Approach to Scaling During Coagulation
Physical Review A
  • Thomas W. Taylor, Cleveland State University
  • C. M. Sorensen
Document Type
Article
Publication Date
12-1-1987
Disciplines
Abstract
We study the temporal approach of a cluster size distribution to its asymptotic scaling form. By enforcing consistency between the distribution’s zeroth moment derived from both the Smoluchowski equation and the scaling distribution ansatz, we find values for the scaling exponents w and z in terms of the scaling exponent τ and the kernel homogeneity λ which are not equivalent to their asymptotic, scaling forms. The predicted values do agree well, however, with intermediate time values found in simulations by Kang, Redner, Meakin, and Leyvraz [Phys Rev. A 33, 1171 (1986)]. By enforcing consistency between all moment orders, the asymptotic exponent values are found. These results imply the lowest-order moments approach their scaling values quickest.
DOI
10.1103/PhysRevA.36.5415
Version
Publisher's PDF
Citation Information
Taylor, Thomas W. and C. M. Sorensen. "Moment Analysis of the Cluster-Size-Distribution Approach to Scaling During Coagulation." Physical Review A 36 (1987): 5415-5419.