TrepoGroup of Magnetism and Simulation G+, Institute of Physics, University of
TrepoGroup of Magnetism and Simulation G+, Institute of Physics, University of Antioquia, Medell A. A. 1226, Colombia; [email protected] Correspondence: [email protected]: A C2 Ceramide manufacturer normal canonical Markov Chain Monte Carlo method implemented having a singlemacrospin movement Metropolis dynamics was carried out to study the hysteretic properties of an ensemble of independent and non-interacting magnetic nanoparticles with uniaxial magnetocrystalline anisotropy randomly distributed. In our model, the acceptance-rate algorithm enables accepting new updates at a continual rate by suggests of a self-adaptive mechanism from the amplitude of N l rotation of magnetic moments. The influence of this proposal upon the magnetic properties of our system is explored by analyzing the behavior in the magnetization versus field isotherms for a wide range of acceptance rates. Our outcomes Etiocholanolone Neuronal Signaling permits reproduction of your occurrence of both blocked and superparamagnetic states for high and low acceptance-rate values respectively, from which a link with all the measurement time is inferred. Finally, the interplay involving acceptance rate with temperature in hysteresis curves as well as the time evolution of the saturation processes is also presented and discussed. Search phrases: Markov chain Monte Carlo; Metropolis astings algorithm; acceptance price; magnetic nanoparticle; uniaxial magnetic-crystalline anisotropy; hysteresis loops; superparamagnetismCitation: Zapata, J.C.; Restrepo, J. Self-Adaptive Acceptance Rate-Driven Chain Monte Carlo Strategy Algorithm Applied to the Study of Magnetic Nanoparticles. Computation 2021, 9, 124. https:// doi.org/10.3390/computation9110124 Academic Editor: Claudio Amovilli Received: 9 September 2021 Accepted: 13 October 2021 Published: 19 November1. Introduction The theoretical study of magnetic nanoparticle systems dates to the pioneering work of E. C. Stoner and E. P. Wohlfarth. (1948) [1], L. N l (1949) [2] and W. J. Brown (1963) [3]. These works set the starting point for existing developments and applications in the field of magnetic fluids, which consist of magnetic resonance imaging, magnetic hyperthermia for cancer therapy, among other folks. [4]. Due to the mathematical complexity of systems composed of many particles, it is essential to implement numerical simulations carried out by personal computer, through algorithms and simulation approaches to recreate their behaviors. For magnetic nanoparticle systems, the stochastic differential Landau ifshitz ilbert (LLG) [8,9] equation or the respective Fokker lanck (FP) [10] equation, are often integrated to reproduce the movement of magnetic moments and also the appropriate probability distribution. However, some authors prefer to use Monte Carlo (MC) simulations based on Metropolis astings (MH) dynamics for this objective [11,12]. Monte Carlo techniques, as is well established, is usually primarily based on sampling of discrete events or on Markov chains. This latter is referred to as Markov chain Monte Carlo (MCMC), from which the MH algorithm would be the most preferred MCMC approach to create Markov chains based on a specific proposal probability distribution. In a classical physical method of magnetic moments in contact with a thermal reservoir, such a distribution is given by the Maxwell-Boltzmann statistics. The MCMC approach, which uses the Bayesian inversion strategy, has been demonstrated to be a strong tool to estimate unknown observables in line with a prior expertise since it may be discovered in various reported perform.
