Abstract
The response of ferrofluids to a high-amplitude AC magnetic field is important for several applications including magnetic hyperthermia and biodetection. In computer simulations of the dynamic susceptibility of a ferrofluid outside the linear response region, there are several problems associated with the fact that an increase in the frequency of the AC field leads to the appearance of additional computational errors, which can even lead to unphysical results. In this article, we study the dependence of the computational error arising in the computer simulation of the dynamic susceptibility on the input parameters of the numerical algorithm: the length of the time step, the total number of computer simulation periods, and averaging period. Computer simulation is carried out using the Langevin dynamics method and takes Brownian rotational relaxation of magnetic particles and interparticle interactions into account. The reference theory [Yoshida T.; Enpuku K. Jap. J. Ap. Phys. 2009] is used to estimate computational error. As a result, we give practical recommendations for choosing the optimal input parameters of the numerical algorithm, which make it possible to obtain reliable results of the dynamic susceptibility of a ferrofluid in a high-amplitude AC field in a wide frequency range.
Highlights
In recent years, there has been growing interest in smart materials that can be controlled by external stimuli such as light, temperature, mechanical force, electrical field, and magnetic field
We have shown that the arising computational errors in the Langevin dynamic (LD) computer simulation of the dynamic susceptibility of a ferrofluid in a high-amplitude alternating magnetic field at high frequencies can be minimized by carefully adjusting the input parameters of the numerical algorithm, namely the time step ht for the solution stochastic Equations (6) and (7), the time step hint for calculation of integrals (9), and the number of calculation periods
Despite the fact that the exact values of input parameters depend on the system under consideration, we have given practical recommendations that make it possible to obtain reliable results of the dynamic susceptibility of a ferrofluid in an AC field of high amplitude 5 ≤ α ≤ 10 in a wide frequency range, at least ωτB ≤ 10−2
Summary
There has been growing interest in smart materials that can be controlled by external stimuli such as light, temperature, mechanical force, electrical field, and magnetic field. There are no studies and practical recommendations about the subject of how to choose the input parameters of the numerical algorithm to minimize computational errors and correctly determine the dynamic susceptibility in a high-frequency region In this regard, obtaining reliable results of computer simulation of the dynamic susceptibility of a ferrofluid under a high-amplitude AC field in a wide frequency range is still a challenge. We analyze the dependence of the time step inputted into the numerical algorithm on the magnitude of the computational error arising in the computer simulation of the dynamic susceptibility for various frequencies and amplitudes of the AC field and give practical recommendations for carrying out the calculations Using these data, the dynamic susceptibility of a ferrofluid with different viscosity, concentration, and intensity of interparticle dipole–dipole interactions is calculated in a wide range of amplitudes and frequencies of the AC field
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