An improved integration scheme for Mode-coupling-theory equations
Soft Condensed Matter
2020-12-10 v1 Statistical Mechanics
Computational Physics
Abstract
Within the mode-coupling theory (MCT) of the glass transition, we reconsider the numerical schemes to evaluate the MCT functional. Here we propose nonuniform discretizations of the wave number, in contrast to the standard equidistant grid, in order to decrease the number of grid points without losing accuracy. We discuss in detail how the integration scheme on the new grids has to be modified from standard Riemann integration. We benchmark our approach by solving the MCT equations numerically for mono-disperse hard disks and hard spheres and by computing the critical packing fraction and the nonergodicity parameters. Our results show that significant improvements in performance can be obtained by employing a nonuniform grid.
Cite
@article{arxiv.2007.07621,
title = {An improved integration scheme for Mode-coupling-theory equations},
author = {Michele Caraglio and Lukas Schrack and Gerhard Jung and Thomas Franosch},
journal= {arXiv preprint arXiv:2007.07621},
year = {2020}
}