Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework

Agata Fronczak , Michał Łepek , Paweł Kukliński , Piotr Fronczak


The time evolution of a system of coagulating particles under the product kernel and arbitrary initial conditions is studied. Using the improved Marcus-Lushnikov approach, the master equation is solved for the probability W(Q,t) to find the system in a given mass spectrum Q={n1,n2,⋯,ng⋯}, with ng being the number of particles of size g. The exact expression for the average number of particles ⟨ng(t)⟩ at arbitrary time t is derived and its validity is confirmed in numerical simulations of several selected initial mass spectra.
Author Agata Fronczak (FP / PCSD)
Agata Fronczak,,
- Physics of Complex Systems Divison
, Michał Łepek (FP / PCSD)
Michał Łepek,,
- Physics of Complex Systems Divison
, Paweł Kukliński - [Politechnika Warszawska]
Paweł Kukliński,,
, Piotr Fronczak (FP / PCSD)
Piotr Fronczak,,
- Physics of Complex Systems Divison
Journal seriesPhysical Review E, ISSN 2470-0045, e-ISSN 2470-0053, [1538-4519, 1539-3755], (A 35 pkt)
Issue year2019
Publication size in sheets5.0
Languageen angielski
Score (nominal)0
ScoreMinisterial score = 0.0, 30-04-2019, ArticleFromJournal
Ministerial score (2013-2016) = 0.0, 13-03-2019, ArticleFromJournal
Publication indicators Scopus Citations = 0; WoS Citations = 0; WoS Impact Factor: 2017 = 2.284 (2) - 2017=2.293 (5)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.