Volume 29, Issue 2
An Improved Integration Scheme for Mode-Coupling-Theory Equations

Michele Caraglio, Lukas Schrack, Gerhard Jung & Thomas Franosch

Commun. Comput. Phys., 29 (2021), pp. 628-648.

Published online: 2020-12

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  • 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 employing a nonuniform grid.

  • Keywords

Glass transition, mode coupling theory

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COPYRIGHT: © Global Science Press

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@Article{CiCP-29-628, author = {Michele Caraglio , and Lukas Schrack , and Gerhard Jung , and Thomas Franosch , }, title = {An Improved Integration Scheme for Mode-Coupling-Theory Equations}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {2}, pages = {628--648}, 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 employing a nonuniform grid.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0125}, url = {http://global-sci.org/intro/article_detail/cicp/18479.html} }
TY - JOUR T1 - An Improved Integration Scheme for Mode-Coupling-Theory Equations AU - Michele Caraglio , AU - Lukas Schrack , AU - Gerhard Jung , AU - Thomas Franosch , JO - Communications in Computational Physics VL - 2 SP - 628 EP - 648 PY - 2020 DA - 2020/12 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2020-0125 UR - https://global-sci.org/intro/article_detail/cicp/18479.html KW - Glass transition, mode coupling theory AB -

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 employing a nonuniform grid.

Michele Caraglio, Lukas Schrack, Gerhard Jung & Thomas Franosch. (2020). An Improved Integration Scheme for Mode-Coupling-Theory Equations. Communications in Computational Physics. 29 (2). 628-648. doi:10.4208/cicp.OA-2020-0125
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