Revealing the Mechanism of Magnetic Domain Formation by Topological Data Analysis
Revealing the Mechanism of Magnetic Domain Formation by Topological Data Analysis
复制标题
DOI：
--
复制
发表时间：
2022-04
期刊：
影响因子：
--
通讯作者：
Yoh-ichi Mototake;M. Mizumaki;K. Kudo;K. Fukumizu
中科院分区：
文献类型：
--
作者：
Yoh-ichi Mototake;M. Mizumaki;K. Kudo;K. Fukumizu
摘要了解长程相互作用导致非均匀和非周期性结构的图案形成过程对于揭示自然界中广泛观察到的复杂系统的物理特性非常重要。在许多情况下，图案形成过程是基于最小元素的空间粗粒度特征（即，灰度图像的像素空间）来测量的。通过使用公共阈值对数据进行二值化，可以使用诸如域的数量（贝蒂数）或域大小的几何特征来分析这样的灰度图像数据。由于这种拓扑特征是统一评价所有区域的指标，因此很难确定非均匀结构中每个区域的性质。此外，二值化导致有价值的信息的丢失，例如域中的波动。在这里，我们表明，基于持久同源性的分析方法提供了有效的知识来理解这种模式的形成过程。具体来说，我们分析了图案形成过程中的铁磁材料下快速扫描的外部磁场，发现不仅现有类型的图案形成动力学，但也新颖的。在拓扑数据分析结果的基础上，我们还发现了一个候选的简化模型来描述这些新的磁畴形成的机制。本文提出的具有持久同源性的分析过程提供了一种适用于从具有长程相互作用的广泛模式形成过程中提取科学知识的格式。
Abstract Understanding pattern formation processes with long-range interactions that result in nonuniform and nonperiodic structures is important for revealing the physical properties of widely observed complex systems in nature. In many cases, pattern formation processes are measured on the basis of spatially coarse-grained features of the smallest elements, that is, the pixel space of a grayscale image. By binarizing the data using a common threshold, one can analyze such grayscale image data using geometrical features, such as the number of domains (Betti number) or domain size. Because such topological features are indicators for evaluating all regions uniformly, it is difficult to determine the nature of each region in a nonuniform structure. Moreover, binarization leads to loss of valuable information such as fluctuations in the domain. Here, we show that the analysis method based on persistent homology provides effective knowledge to understand such pattern formation processes. Specifically, we analyze the pattern formation process in ferromagnetic materials under a rapidly sweeping external magnetic field and discover not only existing types of pattern formation dynamics but also novel ones. On the basis of results of topological data analysis, we also found a candidate reduction model to describe the mechanics of these novel magnetic domain formations. The analysis procedure with persistent homology presented in this paper provides one format applicable to extracting scientific knowledge from a wide range of pattern formation processes with long-range interactions.