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Hydrocarbon pyrolysis is a complex process involving large numbers of chemical species and types of chemical reactions. Its quantitative description is important for planetary sciences, in particular, for understanding the processes occurring in the interior of icy planets, such as Uranus and Neptune, where small hydrocarbons are subjected to high temperature and pressure. We propose a computationally cheap methodology based on an originally developed ten-reaction model, and the configurational model from random graph theory. This methodology yields to accurate predictions for molecule size distributions for a variety of initial chemical compositions and temperatures ranging from 3200K to 5000K. Specifically, we show that the size distribution of small molecules is particularly well predicted, and the size of the largest molecule can be accurately predicted provided that it is not too large., Comment: 27 pages (11 main + 16 supplementary), 15 figures (5 main + 10 supplementary). Submitted to the Journal of Physical Chemistry A

Granular materials are a ubiquitous yet ill-understood class of media. Many different approaches and techniques have been developed to understand the many complex behaviors they exhibit but none have been completely successful. We present a novel means to understand granular materials, the Hydra String Method (HSM). This is an efficient and autonomous way to trawl an arbitrary potential energy surface (or any similarly high dimensional function) that enumerates the saddle points, minima, and minimum energy paths between them. In doing so, it creates a reduced dimensional network representation of this function. We also present a series of tests to choose optimized parameters for the application of the HSM. We apply this to the potential energy function of a granular system consisting of a bidisperse configuration of frictionless soft spheres. Future work will make use of the found ensemble of transition pathways to statistically predict the dynamics of a system of grains., Comment: 12 pages, 8 figures