晶体缺陷弹性远场的渐近展开
Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect
摘要：
晶体材料中的晶格缺陷产生长程弹性场，其可以使用离散非线性力平衡方程的无限系统在原子尺度上建模。从这些方程开始，这项工作严格推导出一种新的远场扩展这些领域：扩展是可计算的，并表示为连续校正和离散多极项的总和，随着代数率的增加而衰减作为扩展的顺序增加。截断的扩展留下一个剩余的描述缺陷的核心结构，这是本地化的意义上说，它的衰减与代数率对应的顺序发生截断。
英文摘要：
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work rigorously derives a novel far-field expansion of these fields: The expansion is computable and is expressed as a sum of continuum correctors and discrete multipole terms which decay with increasing algebraic rate as the order of the expansion increases. Truncating the expansion leaves a remainder describing the defect core structure, which is localised in the sense that it decays with an algebraic rate corresponding to the order at which the truncation occurred.
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