Our recent molecular dynamics simulation results of binary particle glass-former systems demonstrated that the non-monotonic temperature T-dependence of the point-to-set dynamic length scale ${\xi }_{\mathrm{c}}^{dyn}$ in harmonic (HM) systems is not an intrinsic property of bulk liquids but originates from wall effects. We would expect our results to apply equally to other simple models, such as Lennard-Jones (LJ) systems. However, Hocky et al. presented a monotonic T-dependent ${\xi }_{\mathrm{c}}^{dyn}$ in a LJ system. Therefore, the present work employs molecular dynamics simulations to investigate the T-dependent behavior of ${\xi }_{\mathrm{c}}^{dyn}$ in the LJ system employed by Hocky et al. to clarify our expectation. Results employing a geometry size d that is somewhat smaller than that employed by Hocky et al. reveal that a non-monotonic behavior exists in the LJ system. By varying the value of d, we demonstrate that the formation of a peak in ${\xi }_{\mathrm{c}}^{dyn}$ with respect to T in the LJ system is the natural result of wall effects. More importantly, a new non-monotonic behavior is observed, where the temperature at which the ratio of the characteristic time required for the overlap profile of the system to decay to a given value for a point near the wall to the corresponding characteristic time at a point in the center attains a maximum is in good agreement with the temperature $T_{max-c}$ at which ${\xi }_{\mathrm{c}}^{dyn}$ attains a maximum value, indicating that the non-monotonic behavior of ${\xi }_{\mathrm{c}}^{dyn}$ with respect to T is a natural property of liquids in a sandwiched geometry. Furthermore, we find that, contrary to HM systems, where the values of $T_{max-c}$ obtained for all values of d considered were greater than the mode-coupling temperature T_c, the value of $T_{max-c}$ obtained for LJ systems can be either greater than, equal to, or less than T_c because an HM system has a stronger finite-size effect than that in a LJ system, indirectly implying that the conclusion derived from random first-order transition theory that a dramatic change occurs near T_c bears no necessary relationship with the non-monotonic evolution of ${\xi }_{\mathrm{c}}^{dyn}$ with respect to T.

中文翻译：

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二元Lennard-Jones玻璃成型机中的点对点动态长度刻度

我们最近对二元粒子玻璃形成系统的分子动力学模拟结果表明，点对点动态长度标度的非单调温度T-依赖性${\xi }_{\mathrm{C}}^{dÿñ}$谐波（HM）系统中的流体不是本体液体的固有特性，而是源于壁效应。我们希望我们的结果同样适用于其他简单模型，例如Lennard-Jones（LJ）系统。然而，霍克等。呈现出单调的T依赖${\xi }_{\mathrm{C}}^{dÿñ}$在LJ系统中。因此，目前的工作采用分子动力学模拟来研究T依赖的行为${\xi }_{\mathrm{C}}^{dÿñ}$在由Hocky等人使用的LJ系统中。阐明我们的期望。采用几何尺寸d的结果略小于Hocky等人采用的结果。揭示LJ系统中存在非单调行为。通过改变d的值，我们证明了在${\xi }_{\mathrm{C}}^{dÿñ}$LJ系统中相对于T的比值是壁效应的自然结果。更重要的是，观察到一种新的非单调行为，在该温度下，系统的重叠轮廓所需的特征时间与壁附近某个点的给定值之间的比率衰减到对应的特征时间的温度。中心点达到最高温度${Ť}_{最大限度-C}$ 在哪 ${\xi }_{\mathrm{C}}^{dÿñ}$ 达到最大值，表明 ${\xi }_{\mathrm{C}}^{dÿñ}$关于T，是夹层几何形状的液体的自然特性。此外，我们发现，与HM系统相反，${Ť}_{最大限度-C}$对于所考虑的所有d值获得的值均大于模式耦合温度T _c，${Ť}_{最大限度-C}$对于LJ系统获得的结果可以大于，等于或小于T _c，因为HM系统比LJ系统具有更大的有限尺寸效应，这间接暗示了从随机一阶跃迁理论得出的结论是：T _c附近发生了戏剧性的变化，与T的非单调演变没有必然的关系。${\xi }_{\mathrm{C}}^{dÿñ}$相对于Ť。