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Asymptotic solutions to the Smoluchowski's coagulation equation with singular gamma distributions as initial size spectra

Lindblad, Ulf LU (2007) In Journal of Colloid and Interface Science 309(2). p.440-444
Abstract
Smoluchowski's coagulation equation is studied for the kernel K (u, v) = E(u(alpha)v(beta) + u(beta) v(alpha)) with real, non-negative alpha, beta and E, using gamma distributions with a singularity at zero volume as initial size spectra. As the distribution parameter of the gamma distribution, p, approaches its lower limit (p -> 0) the distribution becomes similar to pv(p-1) 1 for small v. Asymptotic solutions to the coagulation equation are derived for the two cases p -> 0 and v -> 0. The constant kernel (alpha = beta = 0) is shown to be unique among the studied kernels in the sense that the p -> 0 asymptote and the v 0 asymptote differ.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
distribution, gamma, the Smoluchowski coagulation equation, exact solutions
in
Journal of Colloid and Interface Science
volume
309
issue
2
pages
440 - 444
publisher
Elsevier
external identifiers
  • wos:000245967700031
  • scopus:34047250502
ISSN
1095-7103
DOI
10.1016/j.jcis.2006.09.072
language
English
LU publication?
yes
id
ddef57f0-b869-4bc6-8af5-712d10f5f125 (old id 662600)
date added to LUP
2007-12-13 11:41:42
date last changed
2017-01-01 04:28:20
@article{ddef57f0-b869-4bc6-8af5-712d10f5f125,
  abstract     = {Smoluchowski's coagulation equation is studied for the kernel K (u, v) = E(u(alpha)v(beta) + u(beta) v(alpha)) with real, non-negative alpha, beta and E, using gamma distributions with a singularity at zero volume as initial size spectra. As the distribution parameter of the gamma distribution, p, approaches its lower limit (p -> 0) the distribution becomes similar to pv(p-1) 1 for small v. Asymptotic solutions to the coagulation equation are derived for the two cases p -> 0 and v -> 0. The constant kernel (alpha = beta = 0) is shown to be unique among the studied kernels in the sense that the p -> 0 asymptote and the v 0 asymptote differ.},
  author       = {Lindblad, Ulf},
  issn         = {1095-7103},
  keyword      = {distribution,gamma,the Smoluchowski coagulation equation,exact solutions},
  language     = {eng},
  number       = {2},
  pages        = {440--444},
  publisher    = {Elsevier},
  series       = {Journal of Colloid and Interface Science},
  title        = {Asymptotic solutions to the Smoluchowski's coagulation equation with singular gamma distributions as initial size spectra},
  url          = {http://dx.doi.org/10.1016/j.jcis.2006.09.072},
  volume       = {309},
  year         = {2007},
}