The efficient development and utilisation of magnetic nanoparticles (MNPs) for applications in enhanced biosensing relies on the use of magnetisation dynamics, which are primarily governed by the time-dependent motion of the magnetisation due to externally applied magnetic fields. An accurate description of the physics involved is complex and not yet fully understood, especially in the frequency range where Néel and Brownian relaxation processes compete. However, even though it is well known that non-zero, non-static local fields significantly influence these magnetisation dynamics, the modelling of magnetic dynamics for MNPs often uses zero-field dynamics or a static Langevin approach. In this paper, we developed an approximation to model and evaluate its performance for MNPs exposed to a magnetic field with varying amplitude and frequency. This model was initially developed to predict superparamagnetic nanoparticle behaviour in differential magnetometry applications but it can also be applied to similar techniques such as magnetic particle imaging and frequency mixing. Our model was based upon the Fokker–Planck equations for the two relaxation mechanisms. The equations were solved through numerical approximation and they were then combined, while taking into account the particle size distribution and the respective anisotropy distribution. Our model was evaluated for Synomag®-D70, Synomag®-D50 and SHP-15, which resulted in an overall good agreement between measurement and simulation.
Corrigendum to “Numerical approximation of the data-rate limit for state estimation under communication constraints” [J. Math. Anal. Appl. 473 (2) (2019) 1280–1304]