论文标题
在没有仪表不可分割的多孔成核问题的缩放定律上
On Scaling Laws for Multi-Well Nucleation Problems without Gauge Invariances
论文作者
论文摘要
在本文中，我们研究了简化的缩放定律，用于简化的多孔成核问题，而没有量规数的量表，这些数字是由形状 - 记忆合金模型动机的。为了探索层压层在成核过程的能量缩放方面的作用，我们为两个和三个维度的各种模型问题提供了缩放定律。特别是，我们讨论（最佳）缩放会导致体积和奇异扰动参数的设置，其中周围父相位是成核阶段井中的第一个和三阶层压层凸壳。此外，我们为在牙垢正方形的背景下产生的无限顺序层压板的设置提供了相应的结果。特别是，我们的结果在存在强大的非局部各向异性的情况下提供了等等估计值。
In this article we study scaling laws for simplified multi-well nucleation problems without gauge invariances which are motivated by models for shape-memory alloys. Seeking to explore the role of the order of lamination on the energy scaling for nucleation processes, we provide scaling laws for various model problems in two and three dimensions. In particular, we discuss (optimal) scaling results in the volume and the singular perturbation parameter for settings in which the surrounding parent phase is in the first, the second and the third order lamination convex hull of the wells of the nucleating phase. Furthermore, we provide a corresponding result for the setting of an infinite order laminate which arises in the context of the Tartar square. In particular, our results provide isoperimetric estimates in situations in which strong nonlocal anisotropies are present.
