AI 中文总结
本文验证了原子位错模型分析中线性化力平衡条件，阐明了其对远场衰减的作用，并指出一般物理相容预测器下该条件不成立会导致更慢衰减。
AI 中文摘要
研究了原子位错模型分析中出现的一个技术条件。Ehrlacher、Ortner和Shapeev（2016）证明的远场应变行为的关键估计依赖于线性化力的分部求和论证，该论证需在无限系统中满足充分衰减和净力为零的条件。特别是，后一条件是将该理论应用于标准远场位错预测器所必需的，但相关力总和的消失尚未被完全证明。本文提供了该条件的缺失验证，并阐明了其在确定校正子远场衰减中的作用。此外，研究表明，对于更一般的物理相容预测器，线性化力总和不一定为零，从而导致更慢的衰减和可能发散的有限域近似。
英文摘要
A technical condition arising in the analysis of atomistic models for dislocations is studied. Key estimates for the far-field strain behaviour proved in Ehrlacher, Ortner, Shapeev (2016) rely on a summation-by-parts argument for linearised forces, under conditions of sufficient decay and of vanishing net force in an infinite system. In particular, the latter condition is required for an application of this theory to the standard far-field dislocation predictor, but the vanishing of the associated force sum has not been fully justified. Here, the missing verification of this condition is provided and its role in determining the far-field decay of the corrector is clarified. It is moreover shown that for more general physically compatible predictors, the linearised force sum need not vanish, leading to slower decay and potentially divergent finite-domain approximations.
