Stationary Kolmogorov solutions of the Smoluchowski aggregation equation with a source term
UNSPECIFIED. (2004) Stationary Kolmogorov solutions of the Smoluchowski aggregation equation with a source term. PHYSICAL REVIEW E, 69 (6 Part 1). -. ISSN 1063-651XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1103/PhysRevE.69.061114
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|
|Official Date:||June 2004|
|Number:||6 Part 1|
|Number of Pages:||6|
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