A formal hierarchy of exact evolution equations are derived for physically relevant space-time averages of state functions of microscopic dislocation dynamics. While such hierarchies are undoubtedly of some value, a primary goal here is to expose the intractable complexity of such systems of nonlinear partial differential equations that, furthermore, remain `non-closed' and therefore subject to phenomenological assumptions to be useful. It is instead suggested that such hierarchies be terminated at the earliest stage possible and effort be expended to derive closure relations for the `non-closed' terms that arise from the formal averaging by taking into account the full-stress-coupled microscopic dislocation dynamics, a matter on which these formal hierarchies, whether of kinetic theory type or as pursued here, are silent.

中文翻译：

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正式的层次结构有多大用处？平均位错动力学定义细观宏观可塑性的案例研究

对于微观位错动力学状态函数的物理相关时空平均值，推导出了精确演化方程的正式层次结构。虽然这样的层次结构无疑具有一定的价值，但这里的主要目标是揭示这种非线性偏微分方程系统难以处理的复杂性，而且这些系统仍然是“非封闭的”，因此服从于现象学假设是有用的。相反，建议在尽可能早的阶段终止这种层次结构，并通过考虑全应力耦合的微观位错动力学，努力为正式平均产生的“非封闭”项推导出封闭关系，这些正式的等级制度，无论是动力学理论类型的还是这里所追求的，都保持沉默。