Sampling the large-dimensional energy landscape of a 2D granular system with the hydra string method

In this work, I improve upon the existing hydra string method [C. Moakler and K. A. Newhall, <i>Granular Matter</i>, 2021, <b>24</b>, 24] to systematically sample the energy landscape of a low friction 2D granular system. This method climbs in random directions out of a minimum energy state, finding unique saddle transition points and the neighboring minimum energy states only to repeat the process from the newly found minima. The data is saved as a network with nodes representing the energy-minimizing states and edges representing transition pathways that are parallel to the gradient of the energy at each point along the path. I show how the hydra string method is able to produce a better sample of transition pathways between stable states compared to just randomly sampling the system. The method is also modified to take into account energy minima that are not points caused by non-mechanically stable individual particles and skip past entire configurations that are not mechanically stable. The samples reveal that the energy of the states correlates with the size of the energy barriers between them. Neighboring state energies are also correlated, with correlations decreasing with distance as measured by path length on the network.