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Article: A survey of numerical solutions to the coagulation equation

TitleA survey of numerical solutions to the coagulation equation
Authors
Issue Date2001
PublisherInstitute of Physics Publishing. The Journal's web site is located at http://www.iop.org/journals/jpa
Citation
Journal Of Physics A: Mathematical And General, 2001, v. 34 n. 47, p. 10219-10241 How to Cite?
AbstractWe present the results of a systematic survey of numerical solutions to the coagulation equation for a rate coefficient of the form Aij α (iμ jν + iν jμ) and monodisperse initial conditions. The results confirm that there are three classes of rate coefficients with qualitatively different solutions. For ν ≤ 1 and λ = μ + ν ≤ 1, the numerical solution evolves in an orderly fashion and tends towards a self-similar solution at large time t. The properties of the numerical solution in the scaling limit agree with the analytic predictions of van Dongen and Ernst. In particular, for the subset with μ > 0 and λ < 1, we disagree with Krivitsky and find that the scaling function approaches the analytically predicted power-law behaviour at small mass, but in a damped oscillatory fashion that was not known previously. For ν ≤ 1 and λ > 1, the numerical solution tends towards a self-similar solution as t approaches a finite time t0. The mass spectrum nk develops at t0 a power-law tail nk α k-τ at large masses that violates mass conservation, and runaway growth/gelation is expected to start at tcrit = t0 in the limit the initial number of particles n0 → ∞. The exponent τ is in general less than the analytic prediction (λ + 3)/2, and t0 = K/[(λ - 1)n0A11] with K = 1-2 if λ ≲ 1.1. For ν > 1, the behaviours of the numerical solution are similar to those found in a previous paper by us. They strongly suggest that there are no self-consistent solutions at any time and that runaway growth is instantaneous in the limit n0 → ∞. They also indicate that the time Tcrit for the onset of runaway growth decreases slowly towards zero with increasing n0. .
Persistent Identifierhttp://hdl.handle.net/10722/151078
ISSN
2006 Impact Factor: 1.577
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLee, MHen_US
dc.date.accessioned2012-06-26T06:16:49Z-
dc.date.available2012-06-26T06:16:49Z-
dc.date.issued2001en_US
dc.identifier.citationJournal Of Physics A: Mathematical And General, 2001, v. 34 n. 47, p. 10219-10241en_US
dc.identifier.issn0305-4470en_US
dc.identifier.urihttp://hdl.handle.net/10722/151078-
dc.description.abstractWe present the results of a systematic survey of numerical solutions to the coagulation equation for a rate coefficient of the form Aij α (iμ jν + iν jμ) and monodisperse initial conditions. The results confirm that there are three classes of rate coefficients with qualitatively different solutions. For ν ≤ 1 and λ = μ + ν ≤ 1, the numerical solution evolves in an orderly fashion and tends towards a self-similar solution at large time t. The properties of the numerical solution in the scaling limit agree with the analytic predictions of van Dongen and Ernst. In particular, for the subset with μ > 0 and λ < 1, we disagree with Krivitsky and find that the scaling function approaches the analytically predicted power-law behaviour at small mass, but in a damped oscillatory fashion that was not known previously. For ν ≤ 1 and λ > 1, the numerical solution tends towards a self-similar solution as t approaches a finite time t0. The mass spectrum nk develops at t0 a power-law tail nk α k-τ at large masses that violates mass conservation, and runaway growth/gelation is expected to start at tcrit = t0 in the limit the initial number of particles n0 → ∞. The exponent τ is in general less than the analytic prediction (λ + 3)/2, and t0 = K/[(λ - 1)n0A11] with K = 1-2 if λ ≲ 1.1. For ν > 1, the behaviours of the numerical solution are similar to those found in a previous paper by us. They strongly suggest that there are no self-consistent solutions at any time and that runaway growth is instantaneous in the limit n0 → ∞. They also indicate that the time Tcrit for the onset of runaway growth decreases slowly towards zero with increasing n0. .en_US
dc.languageengen_US
dc.publisherInstitute of Physics Publishing. The Journal's web site is located at http://www.iop.org/journals/jpaen_US
dc.relation.ispartofJournal of Physics A: Mathematical and Generalen_US
dc.titleA survey of numerical solutions to the coagulation equationen_US
dc.typeArticleen_US
dc.identifier.emailLee, MH:mhlee@hku.hken_US
dc.identifier.authorityLee, MH=rp00724en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1088/0305-4470/34/47/323en_US
dc.identifier.scopuseid_2-s2.0-0035976870en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0035976870&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume34en_US
dc.identifier.issue47en_US
dc.identifier.spage10219en_US
dc.identifier.epage10241en_US
dc.identifier.isiWOS:000172839100026-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridLee, MH=7409119699en_US

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