论文标题
改进的模式耦合理论方程的集成方案
An improved integration scheme for Mode-coupling-theory equations
论文作者
论文摘要
在玻璃转变的模式耦合理论（MCT）中，我们重新考虑数值方案以评估MCT功能。在这里，我们提出与标准等距网格相比，波浪数的不均匀离散化，以减少网格点的数量而不会丢失精度。我们详细讨论了如何从标准的Riemann集成中修改新网格的集成方案。我们通过用于单分散硬盘和硬球的数值求解MCT方程以及计算关键填料分数和非效应参数来基准我们的方法。我们的结果表明，通过使用不均匀的网格，可以获得性能的显着改善。
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.
