2004
DOI: 10.1103/physreve.69.061114
|View full text |Cite
|
Sign up to set email alerts
|

Stationary Kolmogorov solutions of the Smoluchowski aggregation equation with a source term

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 asympto… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

2
73
0

Year Published

2006
2006
2023
2023

Publication Types

Select...
5
1

Relationship

1
5

Authors

Journals

citations
Cited by 45 publications
(75 citation statements)
references
References 17 publications
2
73
0
Order By: Relevance
“…arguments. Strictly speaking, the Zakharov transformation technology of [10,26] only works for homogeneous kernels which leaves us with the question of what to do with the logarithm in eq. (87).…”
Section: Renormalised Smoluchowski Equationmentioning
confidence: 99%
See 4 more Smart Citations
“…arguments. Strictly speaking, the Zakharov transformation technology of [10,26] only works for homogeneous kernels which leaves us with the question of what to do with the logarithm in eq. (87).…”
Section: Renormalised Smoluchowski Equationmentioning
confidence: 99%
“…Therefore, it is correctly predicted by mean field theory. The non-renormalization of γ 2 by diffusive fluctuations can be explained by mass conservation or, more precisely by constancy of the average flux of mass in the mass space, see [10] for more details. Here, we simply wish to point out that the exact answers for γ 1 and γ 2 establish multiscaling non-perturbatively: the points (0, 0), (1, γ 1 ) and (2, γ 2 ) do not lie on the same straight line.…”
Section: B Constant Flux Relation -Analytic Confirmation Of Multiscamentioning
confidence: 99%
See 3 more Smart Citations