Diaz Adrian, Davydov Denis, Chen Youping
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA.
Chair of Applied Mechanics, University of Erlangen-Nuremberg, Erlangen, Germany.
Proc Math Phys Eng Sci. 2019 Mar;475(2223):20180688. doi: 10.1098/rspa.2018.0688. Epub 2019 Mar 20.
Although there are numerous formulae for atomic-level fluxes, they are expressed either in terms of a singlet density, resulting from Irving and Kirkwood's statistical mechanics formulation of hydrodynamical equations, or a pair density, proposed in kinetic theories of transport processes. Flux formulae using singlet density have been further developed and widely implemented in molecular dynamics (MD) simulations by either replacing the Dirac delta with a volumetric averaging function or performing a surface average of the flux operators. Pair density-based flux formulae have also been further developed by using spatial-averaging kernels; these formulae, however, have rarely been implemented or used in modern MD. In this work, distributional calculus is used to reformulate the fluxes in momentum and energy transport processes. The formulation results demonstrate that these two types of existing flux formulae are mathematically equivalent when expressed with the Dirac delta. The lasting confusion regarding these two different types of flux formulae from two different formalisms is thus resolved.
尽管有许多用于原子级通量的公式，但它们要么是根据由欧文和柯克伍德对流体动力学方程的统计力学公式推导得出的单重态密度来表示，要么是根据输运过程动力学理论中提出的对密度来表示。使用单重态密度的通量公式已得到进一步发展，并通过用体积平均函数替代狄拉克δ函数或对通量算符进行表面积分，在分子动力学（MD）模拟中得到广泛应用。基于对密度的通量公式也通过使用空间平均核得到了进一步发展；然而，这些公式在现代MD中很少被应用或使用。在这项工作中，分布微积分被用于重新表述动量和能量输运过程中的通量。公式推导结果表明，当用狄拉克δ函数表示时，这两种现有的通量公式在数学上是等价的。因此，解决了长期以来关于这两种源自不同形式体系的不同类型通量公式的困惑。
