An Improved Integration Scheme for Mode-Coupling-Theory Equations

被引：1

作者：

Caraglio, Michele ^{[1
]}

Schrack, Lukas ^{[1
]}

Jung, Gerhard ^{[1
]}

Franosch, Thomas ^{[1
]}

机构：

[1] Univ Innsbruck, Inst Theoret Phys, Technikerstr 21A, A-6020 Innsbruck, Austria

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2021年 / 29卷 / 02期

基金：

奥地利科学基金会;

关键词：

Glass transition; mode coupling theory; LIQUID-GLASS TRANSITION; LIGHT-SCATTERING; BETA-RELAXATION; STRUCTURAL RELAXATION; SUPERCOOLED LIQUID; DIATOMIC-MOLECULES; ALPHA-RELAXATION; ASYMPTOTIC LAWS; SLOW DYNAMICS; HARD-SPHERES;

D O I：

10.4208/cicp.OA-2020-0125

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：628 / 648

页数：21

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