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 - [Warsaw University of Technology (PW)]
Paweł Kukliński,,
- Politechnika Warszawska
, 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]
Issue year2019
Publication size in sheets5.0
ASJC Classification3104 Condensed Matter Physics; 2613 Statistics and Probability; 3109 Statistical and Nonlinear Physics
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 16-12-2019, ArticleFromJournal
Publication indicators Scopus Citations = 0; WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.896; WoS Impact Factor: 2018 = 2.353 (2) - 2018=2.38 (5)
Citation count*
Share Share

Get link to the record

* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Are you sure?