Exact combinatorial approach to finite coagulating systems

Agata Fronczak, Anna Chmiel, and Piotr Fronczak
Phys. Rev. E 97, 022126 – Published 16 February 2018

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.

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  • Received 23 September 2017

DOI:https://doi.org/10.1103/PhysRevE.97.022126

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Agata Fronczak, Anna Chmiel, and Piotr Fronczak

  • Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland

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Issue

Vol. 97, Iss. 2 — February 2018

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