  Coagulation and fragmentation (CF) is a fundamental process by which
particles attach to each other to form clusters while existing clusters break
up into smaller ones. It is a ubiquitous process that plays a key role 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.
In this study, we use the discrete Chemical Master Equation (dCME) to describe
the CF process. Using the newly developed Accurate Chemical Master Equation
(ACME) method, we calculate the time-dependent behavior of the CF system. We
investigate the effects of a number 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 higher
dimensions are more likely to form large clusters. We also demonstrate how the
ratio of the attachment to detachment rates affect the dynamics and the
steady-state of the system. Finally, we demonstrate the relationship between
the formation of large clusters and the initial condition.
