Fitting magnetization data using continued fraction of straight lines

TL;DR

This paper introduces a novel method for fitting magnetization data using continued fractions of straight lines, enabling better interpretation of nonlinear magnetic behaviors in ferromagnetic materials.

Contribution

It proposes a new algebraic approach employing continued fractions of straight lines for nonlinear regression in magnetization data analysis.

Findings

Effective approximation of nonlinear magnetization curves.

Parameter estimation through nonlinear regression.

Enhanced interpretation of magnetic domain behavior.

Abstract

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.