论文标题
在概率模型上，用于结合机械兼容性的马氏体雪崩
On a probabilistic model for martensitic avalanches incorporating mechanical compatibility
论文作者
论文摘要
在\ cite {BCH15，CH18，TIVP17}中的作品的基础上，在本文中，我们提出和研究了一种简单，几何约束的，概率的算法，用于捕获形状 - 内存合金中核的某些方面。作为\ cite {bch15，ch18，tivp17}中的算法的主要新颖性，我们包括\ emph {机械兼容性}。通过在成核步骤中使用\ emph {convex Integration buildration bloce}来保证此处的机械兼容性。我们通过分析研究算法的收敛性和解决方案的规律性，将后者视为衡量所得微结构分形的量度。我们通过对方案的数值插入进行补充，并将其与\ cite {BCH15，CH18，TIVP17}中的数值结果进行比较。
Building on the work in \cite{BCH15,CH18,TIVP17}, in this article we propose and study a simple, geometrically constrained, probabilistic algorithm geared towards capturing some aspects of the nucleation in shape-memory alloys. As a main novelty with respect to the algorithms in \cite{BCH15,CH18,TIVP17} we include \emph{mechanical compatibility}. The mechanical compatibility here is guaranteed by using \emph{convex integration building blocks} in the nucleation steps. We analytically investigate the algorithm's convergence and the solutions' regularity, viewing the latter as a measure for the fractality of the resulting microstructure. We complement our analysis with a numerical implemenation of the scheme and compare it to the numerical results in \cite{BCH15,CH18,TIVP17}.
