使离散螺旋位错沿滑移方向的运动最小化
Minimising movements for the motion of discrete screw dislocations along glide directions
摘要：
文献[3]提出了一个简单的离散方案，计算螺位错向低能组态的运动。在那里，一个正式的限制，这样的计划，作为晶格间距和时间步长趋于零，已被描述。极限动力学与[8]中引入的最大耗散准则一致，并预测了沿晶体滑移方向的运动。本文对文[3]中的结果，特别是从离散动力学到连续动力学的过渡，提供了严格的证明。证明是基于$Γ$ -收敛技术。
英文摘要：
In [3] a simple discrete scheme for the motion of screw dislocations toward low energy configurations has been proposed. There, a formal limit of such a scheme, as the lattice spacing and the time step tend to zero, has been described. The limiting dynamics agrees with the maximal dissipation criterion introduced in [8] and predicts motion along the glide directions of the crystal. In this paper, we provide rigorous proofs of the results in [3], and in particular of the passage from the discrete to the continuous dynamics. The proofs are based on $Γ$-convergence techniques.
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