The dynamic magnetic susceptibility, $\chi \left(\omega \right)$, of a model ferrofluid at a very low concentration (volume fraction, approximately $0.05\%$), and with a range of dipolar coupling constants ($1\le \lambda \le 8$), is examined using Brownian dynamics simulations. With increasing $\lambda$, the structural motifs in the system change from unclustered particles, through chains, to rings. This gives rise to a nonmonotonic dependence of the static susceptibility $\chi \left(0\right)$ on $\lambda$ and qualitative changes to the frequency spectrum. The behavior of $\chi \left(0\right)$ is already understood, and the simulation results are compared to an existing theory. The single-particle rotational dynamics are characterized by the Brownian time, ${\tau }_B$, which depends on the particle size, carrier-liquid viscosity, and temperature. With $\lambda \le 5.5$, the imaginary part of the spectrum, ${\chi }^{\prime \prime }\left(\omega \right)$, shows a single peak near $\omega \sim {\tau }_B^{-1}$, characteristic of single particles. With $\lambda \ge 5.75$, the spectrum is dominated by the low-frequency response of chains. With $\lambda \ge 7$, new features appear at high frequency, which correspond to intracluster motions of dipoles within chains and rings. The peak frequency corresponding to these intracluster motions can be computed accurately using a simple theory.

中文翻译：

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链和环如何影响高度聚集的铁磁流体的动态磁化率

动态磁化率， $\chi \left(\omega \right)$, 非常低浓度的模型铁磁流体（体积分数，大约 $0.05\%$)，并且具有一定范围的偶极耦合常数 ($1\le \lambda \le 8$)，使用布朗动力学模拟进行检查。随着增加$\lambda$，系统中的结构基序从非簇状粒子，通过链，变为环。这引起了静态磁化率的非单调依赖性$\chi \left(0\right)$ 上 $\lambda$以及频谱的质变。的行为$\chi \left(0\right)$已经理解，并将模拟结果与现有理论进行比较。单粒子旋转动力学以布朗时间为特征，${\tau }_{乙}$，这取决于粒径、载液粘度和温度。和$\lambda \le 5.5$，频谱的虚部， ${\chi }^{\prime \prime }\left(\omega \right)$, 显示附近有一个单峰 $\omega ～{\tau }_{乙}^{-1}$, 单个粒子的特征。和$\lambda \ge 5.75$，频谱以链的低频响应为主。和$\lambda \ge 7$，新特征以高频出现，对应于链和环内偶极子的簇内运动。可以使用简单的理论准确计算与这些簇内运动相对应的峰值频率。