High-dimensional molecular dynamics simulations

Spatiotemporal fluctuations in supercooled liquids' structure and dynamics are present in all finite spatial dimensions d, yet are very challenging to treat properly in the mean-field theories which are arguably still our best available theories of the glass transiton. High-dimensional (d > 3) molecular dynamics (MD) simulations are, in principle, very useful for testing these theories since they allow one to test how they break down (or don't break down) as d decreases from ∞ to 3. However, several computational obstacles must be overcome before high-d simulations which accurately capture the length and time scales over which even moderately supercooled liquids' structure and dynamics are heterogenous become computationally feasible. Our group has developed a publicly available, open-source, parallel MD code (hdMD) that has overcome some of these obstacles, but not others. Some of the remaining obstacles, e.g. efficient nearest-neighbor searches in very high d, are relevant to a wide range of STEM fields. This talk will discuss both advances we have made over the past few years (including, e.g., showing that cooperatively rearranging regions in deeply supercooled liquids become less compact with increasing d, and that some of the conclusions of previous high-d simulations were substantially influenced by spurious finite-size effects) and challenges we hope to help the community overcome over the next few years.