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.
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