Exact combinatorial approach to finite coagulating systems

Agata Fronczak , Anna Chmiel , Piotr Fronczak

Abstract

This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.
Author Agata Fronczak (FP / PCSD)
Agata Fronczak,,
- Physics of Complex Systems Divison
, Anna Chmiel (FP / PCSD)
Anna Chmiel,,
- Physics of Complex Systems Divison
, Piotr Fronczak (FP / PCSD)
Piotr Fronczak,,
- Physics of Complex Systems Divison
Journal seriesPhysical Review E, ISSN 1539-3755, (A 35 pkt)
Issue year2018
Vol97
No2
Pages022126-022126
Publication size in sheets0.3
Keywords in EnglishSTOCHASTIC COALESCENCE; SCALING THEORY; GELATION; EQUATIONS; MODELS; AGGREGATION; TRANSITION; KINETICS
DOIDOI:10.1103/PhysRevE.97.022126
Languageen angielski
Score (nominal)35
ScoreMinisterial score = 35.0, 12-09-2018, ArticleFromJournal
Ministerial score (2013-2016) = 35.0, 12-09-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2014 = 2.288 (2) - 2014=2.269 (5)
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