论文标题
平面脱节的离散到范围限制
Discrete-to-continuum limits of planar disclinations
论文作者
论文摘要
在材料科学中，楔形脱节是由晶体学晶格中的角不匹配引起的缺陷。为了描述这种脱节，我们在平面域中引入了一个原子模型。该模型由原子债券的最接近邻居型能量给出，并具有额外的术语以惩罚数量变化。我们通过特殊的边界条件强制执行脱节的外观。 我们的主要结果是由于晶格尺寸趋于零，因此该能量的离散到范围极限。我们的证明方法是放松能量。我们证明的主要数学新颖性是特殊边界条件的密度定理。除了我们的极限定理外，我们还构建了平面脱节的示例作为模型数值最小化的解决方案，并表明我们的分析可以恢复楔形脱节的经典结果。
In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a nearest-neighbor-type energy for the atomic bonds with an additional term to penalize change in volume. We enforce the appearance of disclinations by means of a special boundary condition. Our main result is the discrete-to-continuum limit of this energy as the lattice size tends to zero. Our proof method is relaxation of the energy. The main mathematical novelty of our proof is a density theorem for the special boundary condition. In addition to our limit theorem, we construct examples of planar disclinations as solutions to numerical minimization of the model and show that classical results for wedge disclinations are recovered by our analysis.
