Numerical Solution of the Fokker-Planck Equation by Spectral Collocation and Finite-Element Methods for Stochastic Magnetization Dynamics

2021 ◽  
pp. 1-1
Author(s):  
Valentino Scalera ◽  
Patrizio Ansalone ◽  
Salvatore Perna ◽  
Claudio Serpico ◽  
Massimiliano d'Aquino
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Finite Element Methods ◽  
Planck Equation ◽  
Magnetization Dynamics ◽  
Spectral Collocation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Empirical Expression for AC Magnetization Harmonics of Magnetic Nanoparticles under High-Frequency Excitation Field for Thermometry

Nanomaterials ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 2506
Author(s):  
Zhongzhou Du ◽  
Dandan Wang ◽  
Yi Sun ◽  
Yuki Noguchi ◽  
Shi Bai ◽  
...  
Keyword(s):  
Magnetic Nanoparticles ◽  
High Frequency ◽  
Planck Equation ◽  
Magnetization Dynamics ◽  
Excitation Field ◽  
Fokker Planck Equation ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Ac Magnetization ◽  
Fokker Planck

The Fokker–Planck equation accurately describes AC magnetization dynamics of magnetic nanoparticles (MNPs). However, the model for describing AC magnetization dynamics of MNPs based on Fokker-Planck equation is very complicated and the numerical calculation of Fokker-Planck function is time consuming. In the stable stage of AC magnetization response, there are differences in the harmonic phase and amplitude between the stable magnetization response of MNPs described by Langevin and Fokker–Planck equation. Therefore, we proposed an empirical model for AC magnetization harmonics to compensate the attenuation of harmonics amplitude induced by a high frequency excitation field. Simulation and experimental results show that the proposed model accurately describes the AC M–H curve. Moreover, we propose a harmonic amplitude–temperature model of a magnetic nanoparticle thermometer (MNPT) in a high-frequency excitation field. The simulation results show that the temperature error is less than 0.008 K in the temperature range 310–320 K. The proposed empirical model is expected to help improve MNPT performance.

Numerical Solution of the Fokker-Planck Equation for Postharvest Applications

2003 ◽  
Author(s):  
Nico Scheerlinck ◽  
Ann Peirs ◽  
Michèle Desmet ◽  
Sofie Clauwers ◽  
Bart M. Nicolaï
Keyword(s):  
Numerical Solution ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck
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