arXiv 1701.040362017-01math-phmath.MP

扩展Hamilton动力学的连续统平衡

Continuum balances from extended Hamiltonian dynamics

Giulio G. Giusteri, Paolo Podio-Guidugli, Eliot Fried

发表信息：: J. Chem. Phys., 146 (2017), 224102
DOI：: 10.1063/1.4984823

摘要：

欧文和柯克伍德在1950年设计的经典程序，稍后由诺尔完成，从物质点系统动力学的普通哈密顿描述开始，产生标准连续介质力学基本平衡定律的对应物。1980年后的分子动力学模拟中，这些系统的时间演化使用了扩展的哈密顿量，例如Andersen、Nosé、Parrinello和Rahman所引入的哈密顿量。在这些扩展中存在的附加项影响系统的统计特性，以便捕获某些目标现象，否则将无法达到。在这里，我们提出了一个物理上一致的应用程序的欧文-柯克伍德-诺尔程序扩展的哈密顿系统的物质点。我们的程序产生的平衡方程在连续水平具有非标准项，因为辅助自由度的存在会产生额外的通量和源，影响的热力学和输运性质的连续模型。意识到额外的贡献可能是至关重要的，在设计多尺度计算方案，其中信息是原子级和连续级之间的交换。

英文摘要：

The classical procedure devised by Irving and Kirkwood in 1950 and completed slightly later by Noll produces counterparts of the basic balance laws of standard continuum mechanics starting from an ordinary Hamiltonian description of the dynamics of a system of material points. Post-1980 molecular dynamics simulations of the time evolution of such systems use extended Hamiltonians such as those introduced by Andersen, Nosé, and Parrinello and Rahman. The additional terms present in these extensions affect the statistical properties of the system so as to capture certain target phenomenologies that would otherwise be beyond reach. We here propose a physically consistent application of the Irving-Kirkwood-Noll procedure to extended Hamiltonian systems of material points. Our procedure produces balance equations at the continuum level featuring non-standard terms, because the presence of auxiliary degrees of freedom gives rise to additional fluxes and sources that influence the thermodynamic and transport properties of the continuum model. Being aware of the additional contributions may prove crucial when designing multiscale computational schemes in which information is exchanged between the atomistic and continuum levels.

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