论文标题
通过虚拟工作方法的单一刚性哑铃的压力张量
Stress Tensor of Single Rigid Dumbbell by Virtual Work Method
论文作者
论文摘要
我们使用虚拟工作方法得出了刚性哑铃的应力张量。在虚拟工作方法中，我们实际上对系统应用了一个小的变形，并将能量的变化与压力张量进行的工作相关联。刚性哑铃由两个粒子组成，该粒子由长度为恒定的刚性键（刚性约束）组成。刚性哑铃的能量仅由动能组成。同样，只有不违反刚性约束的变形。因此，我们需要与刚性约束一致的动态方程式以应用虚拟变形。我们将不足的SLLOD型动态方程式的动态方程重写为与刚性约束一致的形式。然后，我们根据获得的动态方程将虚拟变形应用于刚性哑铃。我们从动能的变化中得出了刚性哑铃模型的应力张量。最后，我们采用过度阻尼的极限，并得出过度阻尼刚性哑铃的应力张量和动态方程。我们表明，可以通过将应力张量和动态方程组合在过度阻尼极限的情况下来重现绿色kubo型线性响应公式。
We derive the stress tensor of a rigid dumbbell by using the virtual work method. In the virtual work method, we virtually apply a small deformation to the system, and relate the change of the energy to the work done by the stress tensor. A rigid dumbbell consists of two particles connected by a rigid bond of which length is constant (the rigid constraint). The energy of the rigid dumbbell consists only on the kinetic energy. Also, only the deformations which do not violate the rigid constraint are allowed. Thus we need the dynamic equations which is consistent with the rigid constraint to apply the virtual deformation. We rewrite the dynamic equations for the underdamped SLLOD-type dynamic equations into the forms which are consistent with the rigid constraint. Then we apply the virtual deformation to a rigid dumbbell based on the obtained dynamic equations. We derive the stress tensor for the rigid dumbbell model from the change of the kinetic energy. Finally, we take the overdamped limit and derive the stress tensor and the dynamic equation for the overdamped rigid dumbbell. We show that the Green-Kubo type linear response formula can be reproduced by combining the stress tensor and the dynamic equation at the overdamped limit.
