用分段直线连分数拟合磁化数据，揭示磁畴涨缩机制。
Fitting magnetization data using continued fraction of straight lines
- 将非线性磁化函数建模为分段直线的连分数形式。
- 通过非线性回归估计参数，准确拟合磁化数据变化趋势。
- 适用于研究磁畴在磁场中生长与收缩的微观动力学。
外加磁场下铁磁物质的磁化强度随场强增大而增加，这是由于微观层面内物质某些区域或磁畴中的磁矩逐渐与外场对齐，而错位磁畴数量减少所致。磁畴与外场对齐过程构成了磁化非线性的物理基础。本文将该非线性函数近似为一系列分段直线的连分数形式，所得拟合结果可用于解释磁畴在磁场作用下生长与收缩时的非线性行为。所采用的分段直线连分数是一种代数表达式，可借助非线性回归方法估计模型参数。
原文摘要 · Abstract (English)
Magnetization of a ferromagnetic substance in response to an externally applied magnetic field increases with the strength of the field. This is because at the microscopic level, magnetic moments in certain regions or domains of the substance increasingly align with the applied field, while the amount of misaligned domains decreases. The alignment of such magnetic domains with an applied magnetic field forms the physical basis for the nonlinearity of magnetization. In this paper, the nonlinear function is approximated as a combination of continued fraction of straight lines. The resulting fit is used to interpret the nonlinear behavior in both growing and shrinking magnetic domains. The continued fraction of straight lines used here is an algebraic expression which can be used to estimate parameters using nonlinear regression.
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