Communications in Information and Systems

Volume 19 (2019)

Number 1

Evolution of coagulation-fragmentation stochastic processes using accurate chemical master equation approach

Pages: 37 – 55



Farid Manuchehrfar (Department of Bioengineering, University of Illinois, Chicago, Il., U.S.A.)

Wei Tian (Department of Bioengineering, University of Illinois, Chicago, Il., U.S.A.)

Tom Chou (Departments of Biomathematics and Mathematics, University of California at Los Angeles)

Jie Liang (Department of Bioengineering, University of Illinois, Chicago, Il., U.S.A.)


Coagulation and fragmentation (CF) is a fundamental process in which smaller particles attach to each other to form larger clusters while existing clusters break up into smaller particles. It is a ubiquitous process that plays important roles in many physical and biological phenomena. CF is typically a stochastic process that often occurs in confined spaces with a limited number of available particles. Here, we study the CF process formulated with the discrete Chemical Master Equation (dCME). Using the newly developed Accurate Chemical Master Equation (ACME) method, we examine calculate the time-dependent behavior of the CF system. We investigate the effects of a number of important factors that influence the overall behavior of the system, including the dimensionality, the ratio of attachment to detachment rates among clusters, and the initial conditions. By comparing CF in one and three dimensions, we conclude that systems in three dimensions are more likely to form large clusters. We also demonstrate how the ratio of the attachment to detachment rates affects the dynamics and the steady-state of the system. Finally, we demonstrate the relationship between the formation of large clusters and the initial condition.

T.C. acknowledges support from the Army Research Office (W911NF-18-1-0345) and the National Science Foundation (DMS-1516675 and DMS-1814364).

Published 18 April 2019