Singular kernels、微观结构的多尺度分解和位错模型
Singular kernels, multiscale decomposition of microstructure, and dislocation models
摘要：
我们考虑一个模型的位错在晶体中引入Koslowski，Cuitiño和奥尔蒂斯，其中包括弹性相互作用通过一个奇异的内核行为的$H^{1/2}$规范的滑移。在$Γ$ -收敛的框架下，我们得到了模型的一个锐界面极限。从分析的角度来看，我们的功能是一个向量值的推广研究的Alberti，Bouchitté和Seppecher他们的重排参数不再适用。相反，我们表明，微观结构必须是近似一维的最长尺度，并利用这一属性，以获得一个尖锐的下界。
英文摘要：
We consider a model for dislocations in crystals introduced by Koslowski, Cuitiño and Ortiz, which includes elastic interactions via a singular kernel behaving as the $H^{1/2}$ norm of the slip. We obtain a sharp-interface limit of the model within the framework of $Γ$-convergence. From an analytical point of view, our functional is a vector-valued generalization of the one studied by Alberti, Bouchitté and Seppecher to which their rearrangement argument no longer applies. Instead we show that the microstructure must be approximately one-dimensional on most length scales and exploit this property to derive a sharp lower bound.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
