论文标题
关于三个维度弯曲位错的运动：简化的线性弹性
On the motion of curved dislocations in three dimensions: Simplified linearized elasticity
论文作者
论文摘要
结果表明，在核心 - 拉迪乌斯临界值的正则简化弹性中（弹性能量是四方依赖于完整的位移梯度而不是其对称版本的），弹性能的负梯度在脱位曲线上的力无效地接近曲线的平均曲率，因为截止曲线的平均曲率是截止radius deverge to serge converge to sere serge。提供了Hölder空间中的严格错误界限。 作为一种应用，当运动定律通过$ h^1 $ -Type耗散给出时，弹性能的梯度流动到脱位的梯度流动的梯度流动的趋同的收敛性，以及弯曲的趋势缩短流量，以缩短co-Dimension $ 2 $ $ 2 $的平常$ l^2 $ -LISSIPTIPATION $ -DISSIPATION已建立。在第二种情况下，假定存在和规律性，而$ h^1 $ - 级别流的流量将完全普遍处理（短时间内）。 这里开发的方法是用于线性化各向同性弹性的物理设置的蓝图。
It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy depends quadratically on the full displacement gradient rather than its symmetrized version), the force on a dislocation curve by the negative gradient of the elastic energy asymptotically approaches the mean curvature of the curve as the cutoff radius converges to zero. Rigorous error bounds in Hölder spaces are provided. As an application, convergence of dislocations moving by the gradient flow of the elastic energy to dislocations moving by the gradient flow of the arclength functional, when the motion law is given by an $H^1$-type dissipation, and convergence to curve shortening flow in co-dimension $2$ for the usual $L^2$-dissipation is established. In the second scenario, existence and regularity are assumed while the $H^1$-gradient flow is treated in full generality (for short time). The methods developed here are a blueprint for the more physical setting of linearized isotropic elasticity.
