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We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size N onto stochastic networks, computing transition probabilities from the network for an N-particle cluster to the one for $$N+1$$ , and connecting these networks into a single joint network. The attachment rate is a control parameter. The resulting network representing the aggregation of up to 14 particles contains 6427 vertices. It is not only time-irreversible but also reducible. To analyze its transient dynamics, we introduce the sequence of the expected initial and pre-attachment distributions and compute them for a wide range of attachment rates and three values of temperature. As a result, we find the configurations most likely to be observed in the process of aggregation for each cluster size. We examine the attachment process and conduct a structural analysis of the sets of local energy minima for every cluster size. We show that both processes taking place in the network, attachment and relaxation, lead to the dominance of icosahedral packing in small (up to 14 atom) clusters. [ABSTRACT FROM AUTHOR]

A set of analytical and computational tools based on transition path theory (TPT) is proposed to analyze flows in complex networks. Specifically, TPT is used to study the statistical properties of the reactive trajectories by which transitions occur between specific groups of nodes on the network. Sampling tools are built upon the outputs of TPT that allow to generate these reactive trajectories directly, or even transition paths that travel from one group of nodes to the other without making any detour and carry the same probability current as the reactive trajectories. These objects permit to characterize the mechanism of the transitions, for example by quantifying the width of the tubes by which these transitions occur, the location and distribution of their dynamical bottlenecks, etc. These tools are applied to a network modeling the dynamics of the Lennard-Jones cluster with 38 atoms ( $$\mathrm{LJ}_{38}$$ ) and used to understand the mechanism by which this cluster rearranges itself between its two most likely states at various temperatures. [ABSTRACT FROM AUTHOR]