UNSPECIFIED. (2004) Stationary Kolmogorov solutions of the Smoluchowski aggregation equation with a source term. PHYSICAL REVIEW E, 69 (6 Part 1). -. ISSN 1063-651X

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Abstract

In this paper we show how the method of Zakharov transformations may be used to analyze the stationary solutions of the Smoluchowski aggregation equation with a source term for arbitrary homogeneous coagulation kernel. The resulting power-law mass distributions are of Kolmogorov type in the sense that they carry a constant flux of mass from small masses to large. They are valid for masses much larger than the characteristic mass of the source. We derive a "locality criterion," expressed in terms of the asymptotic properties of the kernel, that must be satisfied in order for the Kolmogorov spectrum to be an admissible solution. Whether a given kernel leads to a gelation transition or not can be determined by computing the mass capacity of the Kolmogorov spectrum. As an example, we compute the exact stationary state for the family of kernels, K-zeta(m(1),m(2))=(m(1)m(2))(zeta/2) which includes both gelling and nongelling cases, reproducing the known solution in the case zeta=0. Surprisingly, the Kolmogorov constant is the same for all kernels in this family.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Journal or Publication Title:	PHYSICAL REVIEW E
Publisher:	AMERICAN PHYSICAL SOC
ISSN:	1063-651X
Date:	June 2004
Volume:	69
Number:	6 Part 1
Number of Pages:	6
Page Range:	-
Identification Number:	10.1103/PhysRevE.69.061114
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/8235

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