论文标题
从Peierls-Nabarro模型到位错连续性运动方程
From the Peierls-Nabarro model to the equation of motion of the dislocation continuum
论文作者
论文摘要
我们考虑一个半线性突出方程在维度上，该方程与半拉普拉斯％相关的一个模型描述了与位错相关的相变的演变。其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于head \ cite {h}称为“位错连续元素运动方程”的溶液。极限方程是宏观晶体可塑性具有脱位密度的模型。特别是，我们恢复了所谓的Orowan定律，该定律指出，位错的速度与有效压力成正比。
We consider a semi-linear integro-differential equation in dimension one associated to the half Laplacian %This model describes the evolution of phase transitions associated to dislocations. 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 well known equation called by Head \cite{H} "the equation of motion of the dislocation continuum". The limit equation is a model for the macroscopic crystal plasticity with density of dislocations. In particular, we recover the so called Orowan's law which states that dislocations move at a velocity proportional to the effective stress.
