论文标题
从PEIERLS-NABARRO模型的1-D Groma-Balogh方程推导
Derivation of the 1-D Groma-Balogh equations from the Peierls-Nabarro model
论文作者
论文摘要
我们考虑了与半线性的尺寸中的半线性突出方程，该方程与半laplacian相关的溶液代表晶体中的原子位错。该方程包括经典的Peierls-Nabarro模型的进化版本。我们表明，对于大量的位错，正确重新缩放的溶液会收敛到完全非线性的非线性差异方程的溶液，这是宏观晶体可塑性具有脱位密度的模型。这导致了1-D Groma-Balogh方程的形式推导\ cite {groma}，这是一个流行的模型，描述了阳性和负向平行直的直脱位线密度的演变。本文完成了\ cite {patsan}的工作。这里的主要新颖性是我们允许位错具有不同的方向，因此我们必须处理它们的冲突。
We consider a semi-linear integro-differential equation in dimension one associated to the half Laplacian whose solution represents the atom dislocation in a crystal. The equation comprises the evolutive version of the classical Peierls-Nabarro model. We show that for a large number of dislocations, the solution, properly rescaled, converges to the solution of a fully nonlinear integro-differential equation which is a model for the macroscopic crystal plasticity with density of dislocations. This leads to the formal derivation of the 1-D Groma-Balogh equations \cite{groma}, a popular model describing the evolution of the density of positive and negative oriented parallel straight dislocation lines. This paper completes the work of \cite{patsan}. The main novelty here is that we allow dislocations to have different orientation and so we have to deal with collisions of them.
