Year: 2026
Type: preprint
Abstract: Mechanically stable packings of $N$ particles in $d$ dimensions lie at the minima of an $Nd$-dimensional potential energy landscape. Starting from random initial particle positions, the system can relax using gradient-based optimization until it arrives at one of the equilibrium states; all initial conditions that end at the same minimum belong to the same catchment basin. We measure the distribution of the catchment basin volumes for indistinguishable monodisperse soft spheres in both $d=2$ and $d=3$. Ordering the basins at each system size, $N$, according to their volume, $P_N(n)$, from the largest at $n=1$ to smaller at larger $n$, we find a very wide distribution of volumes which is similar in both dimensions: $P_N(n) \approx A_Nn^{-α}$ with $α\approx 1$ which, in our most favorable cases, extends over $7$ decades. We explore aspects of the connectivity of the basins, show that their structure is highly contorted, and demonstrate how these results may be used to understand the imprinting of memories in cyclic strain studies of solids.
Source: arXiv (Cornell University)
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
Awards: G1353381076, G1453181110, G1503004319, Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, G2848635288, G298330452, G3562386289, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4010157413, G4403015908, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G5367127336, G5464919783, Physics Frontier Center for Living Systems, G6709186444, G6754955425, G8108599699, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI, G8562358136, G8851268641
OpenAlex ID: W7167941868