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| Titel |
An algorithm for the numerical solution of the multivariate master equation for stochastic coalescence |
| VerfasserIn |
L. Alfonso |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1680-7316
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| Digitales Dokument |
URL |
| Erschienen |
In: Atmospheric Chemistry and Physics ; 15, no. 21 ; Nr. 15, no. 21 (2015-11-06), S.12315-12326 |
| Datensatznummer |
250120144
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| Publikation (Nr.) |
 copernicus.org/acp-15-12315-2015.pdf |
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| Zusammenfassung |
| In cloud modeling studies, the time evolution of droplet size distributions
due to collision–coalescence events is usually modeled with the Smoluchowski
coagulation equation, also known as the kinetic collection equation (KCE).
However, the KCE is a deterministic equation with no stochastic fluctuations
or correlations. Therefore, the full stochastic description of cloud droplet
growth in a coalescing system must be obtained from the solution of the
multivariate master equation, which models the evolution of the state vector
for the number of droplets of a given mass. Unfortunately, due to its
complexity, only limited results were obtained for certain types of kernels
and monodisperse initial conditions. In this work, a novel numerical
algorithm for the solution of the multivariate master equation for
stochastic coalescence that works for any type of kernels, multivariate
initial conditions and small system sizes is introduced. The performance of
the method was seen by comparing the numerically calculated particle mass
spectrum with analytical solutions of the master equation obtained for the
constant and sum kernels. Correlation coefficients were calculated for the
turbulent hydrodynamic kernel, and true stochastic averages were compared
with numerical solutions of the kinetic collection equation for that case.
The results for collection kernels depending on droplet mass demonstrates
that the magnitudes of correlations are significant and must be taken into
account when modeling the evolution of a finite volume coalescing system. |
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