Stochastic modeling techniques have
emerged as a powerful tool
to study the time evolution of processes in many research fields including
(bio)chemical engineering and biology. One of the most applied techniques
is kinetic Monte Carlo (kMC) modeling according to the stochastic
simulation algorithm (SSA) as pioneered by Gillespie, in which MC
channels and time steps are discretely sampled from probability distributions.
In the last decades, the SSA algorithm, as originally developed for
systems with elemental species (e.g., A, B, C, etc.), has been further
adapted (i) to also tackle systems with distributed species, therefore,
populations and (ii) to enable faster algorithm execution. In the
present contribution, we highlight the most important developments,
taking bulk/solution polymerization as the reference distributed chemical
process. We address SSA principles based on conventional array data
structures, common acceleration methods (e.g., τ leaping and
the scaling method), and the strength of tree- and matrix-based data
structures for detailed storage of molecular information per distribution
type and even individual population member. In addition, we report
advancement regarding array programming and MC sampling methods complemented
by the introduction of the use of higher-order trees and root-finding
sampling tools. The contribution gives thus a detailed overview of
the available main kMC algorithm steps to study kinetics, irrespective
of the specific field of application due to their generic nature.