Structural Analysis and Optimisation of Jammed Granular Particles

Abstract

Granular matter consisting of maximally dense random particle packings has been studied in science and industry. However, understanding the relationship between particle shape and random packing density has been challenging, so the question of "what shape packs with the highest density?" remains unanswered. While experiments and theory are restricted to investigating a few common shapes, numerical simulations allow studying the properties of packings of a diverse range of shapes. This thesis utilises simulations and machine learning methods to investigate particle geometry's role in packing behaviour by exploring a high-dimensional shape space. The first two parts of the thesis generate disordered packings of monodisperse and binary mixtures of frictionless dimers in three dimensions by a gravitational pouring protocol in LAMMPS and analyse their structural properties by packing density, contact statistics, and several order metrics. The results show that monodisperse dimers exhibit a non-monotonic behaviour in the packing density with the aspect ratio $\alpha$ and undergo significant structural rearrangements up to the characteristic peak at $\alpha_{\rm max} \approx 1.4-1.5$. This unique density maximum also exists in the binary case, irrespectively of the variation in shape or mixture composition, accompanied by similar microscopic rearrangements. The outcomings indicate that the packing density of binary mixtures is independent of the segregation state by holding an ideal mixing law. The final section of the thesis applies a Random forest regressor to a dataset of the packing density represented as a function of particle shape obtained by overlapping spheres to predict novel dense packing shapes. The regression model is applied to the data represented in the lower-dimensional space by Principal component analysis (PCA) and Kernel PCA separately. The findings illustrate that the regressor predicts dense packing shapes, and their novelty depends on the dimensionality reduction method. While it optimises the trimer that already exists in the dataset with the highest density for PCA, Kernel one predicts a distinct shape