AI 中文总结
本研究将 Green-Kubo 方法推广至空间相关，通过分解剪切应力为子体积互相关，揭示液体中的类行波结构，并利用高斯拟合建模时空响应，从而以短 MD 模拟预测粘度。
AI 中文摘要
Green-Kubo (GK) 方法用于在平衡分子动力学 (MD) 模拟中获得模型液体的剪切粘度，通常需要较长的模拟时间才能获得可接受的统计结果。本研究将 GK 方法推广到包含空间相关性。GK 表达式中的总剪切应力被分解为连续体积中其分量的网格。通过这样做，系统总应力的自相关可以重写为子体积应力的互相关。这为液体结构提供了新的实空间洞察，而此前液体态理论仅在傅里叶空间中处理这一问题。研究发现了一种新颖的类行波结构，该结构可由一个领先的高斯脉冲加上第二个负高斯脉冲（用于回弹）很好地拟合。拟合参数包括波的位置、幅度和宽度，这些参数对液体性质提供了深刻的见解。该波在短时间内以声速传播，随后速度随时间的平方根而减小，而波包也随时间的平方根展宽。幅度以 $t^{-3/2}$ 的形式减小，这一结果在 MD 模拟的历史中具有重要意义。这些拟合形式意味着液体的整个时空响应可以通过拟合数据以闭合形式建模，短期需要 MD，而长时间和大距离则由高斯形式近似。通过将相关性限制在局部相互作用，可以消除长程贡献（这些贡献本质上仅增加噪声）。这看起来是一种很有前景的方法，通过进行短 MD 运行并拟合长时间行为来模拟粘度。
英文摘要
The Green-Kubo (GK) method which is used to obtain the shear viscosity of a model liquid in equilibrium molecular dynamics (MD) often requires long simulation times to obtain acceptable statistics. This work extends the GK approach to include spatial correlations. The total shear stress in the GK expression is split into a grid of its components in contiguous volumes. In doing this, the autocorrelation of the total system stress can be rewritten as the cross-correlation of the subvolume stresses. This provides a novel real-space insight into the liquid structure, something previously only treated in Fourier space by liquid-state theory. A novel travelling wave like structure is exposed that is shown to be well fitted by a leading Gaussian pulse added to a second negative Gaussian for the bounce back. The fitting parameters include the wave position, magnitude and width which show deep insights into the liquid property. The wave moves at the speed of sound over short times before decreasing in speed with the square root of time, while the wave packet spreads out also as the square root of time. The magnitude is decreasing with form $t^{-3/2}$, a result with strong significance in the history of MD simulation. These fitted forms mean the entire spatial temporal response of the liquid can be modelled in closed form by fitting to data, with short term requiring MD and the long time and distances approximated by the Gaussian form. By limiting the correlation to localized interactions the longer range contribution, which essentially only contribute to the noise, can be eliminated. This looks like a promising approach to model viscosity by taking short MD runs and fitting the long time behaviour.
Comments41 pages (double spaced), 14 Figures, pre-final checks draft
