Treating random sequential addition via the replica method

Abstract

While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition.

Structure of saturated random-sequential-adsorption ellipse packings

“…Explaining such a connection -if indeed one exists -will be nontrivial because saturated RSA packings of anistropic 2D particles often have local structure that is substantially different than that of their equilibrium counterparts at the same φ [31]. One potential strategy for obtaining such an explanation is extending replica-trick-based techniques, which were very recently employed to successfully predict RSA sphere packings' structure [47], to anisotropic particles.…”

Structure of jammed ellipse packings with a wide range of aspect ratios

“…= d / b (eqn (7)) could be calculated by combining Onsager's classical arguments 32 for why the characteristic densities for structural transitions driven by excluded volume should scale as 1/ α , ellipsoidal Percus–Yevick theory, 50 and mean-field theoretical methods like those employed in ref. 48, 49, 51 and 52. Finally, the presence of the a ln( α ) term might be explained by the need for a next-to-leading order correction to Onsager ( i.e.…”

“…f J,disks and f s,disks can be calculated using approaches based on liquid-state theory and the replica trick. 48,49 Donev et al's perturbation-theory approach 2 could be used to calculate I = (a + b À c)/f X,disks (eqn ( 6)). L = d/b (eqn (7)) could be calculated by combining Onsager's classical arguments 32 for why the characteristic densities for structural transitions driven by excluded volume should scale as 1/a, ellipsoidal Percus-Yevick theory, 50 and mean-field theoretical methods like those employed in ref.…”

First-Principles Performance Prediction of High Explosives Enabled by Machine Learning

“…Broadly, the first task is to train an ML model for each HE to approximately reproduce the results of the more computationally expensive DFT calculations. The form of the ML potential includes explicit two- and three-body terms, with higher order terms included approximately via an analytical resummation, conceptually akin to liquid perturbation theory approaches. − We employ a cutoff radius for all of the potentials to define a finite-interacting local environment for each atom. The cutoff was set to 3 Å, as was done in the previous PETN work .…”