Exact combinatorial approach to finite coagulating systems
Agata Fronczak , Anna Chmiel , Piotr Fronczak
AbstractThis 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.
|Journal series||Physical Review E, ISSN 1539-3755, (A 35 pkt)|
|Publication size in sheets||0.3|
|Keywords in English||STOCHASTIC COALESCENCE; SCALING THEORY; GELATION; EQUATIONS; MODELS; AGGREGATION; TRANSITION; KINETICS|
|ASJC Classification||; ;|
|Score|| = 35.0, 30-04-2019, ArticleFromJournal|
= 35.0, 11-03-2019, ArticleFromJournal
|Publication indicators||= 1; = 1; : 2016 = 0.896; : 2014 = 2.288 (2) - 2014=2.269 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.