Abstract
In this paper, we illustrate a method of reconstructing the size distribution of magnetic nano-particles (MNP) using a magnetization curve that was measured on a water-based MNP. The objective was to find solutions to the ill-posed problem in the matrix equation Ax=b, which was obtained from the numerical model on magnetization. Prior the use of Singular Value Decomposition (SVD), a method utilizing a total of 60 sample points of magnetization curves was obtained from Superconducting QUantum Interface Devices (SQUID) in attempts to achieve a favorable solution. However, eliminating oscillation in this manner was proven difficult. Therefore, the Tikhonov regulation (A T A-aI) was offered in the solution to overcome the above-mentioned ill-posed problem. Size distributions from Tikhonov SVD (TSVD) were found stable. As predicted in previous theoretical analyses, a lognormal-like distribution of the MNP could be observed in single-origin MNP EMG1111.
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