Institute of Mathematics and Physics, UTP University of Science and Technology, 85-796 Bydgoszcz, Poland.
Sensors (Basel). 2021 Jul 22;21(15):4974. doi: 10.3390/s21154974.
A novel, two-parameter modification of a Drude model, based on fractional time derivatives, is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing good agreement between theoretical description and numerical results. The absorption coefficient and wave vector are shown to follow a power law in the frequency domain, which is a common phenomenon in electromagnetic and acoustic wave propagation in complex media such as biological tissues. The main novelty of the proposal is the introduction of two separate parameters that provide a more flexible model than most other approaches found in the literature. Moreover, an efficient numerical implementation of the model is presented and its accuracy and stability are examined. Finally, the model is applied to an exemplary soft tissue, confirming its flexibility and usefulness in the context of medical biosensors.
提出了一种基于分数阶时间导数的德拜模型的双参数修正新方法。解析计算了介电常数,并进行了数值模拟,理论描述与数值结果吻合良好。结果表明,吸收系数和波矢在频域中遵循幂律关系,这是复杂介质中电磁和声波传播的常见现象,如生物组织。该建议的主要新颖之处在于引入了两个独立的参数,与文献中大多数其他方法相比,该模型提供了更灵活的模型。此外,还提出了该模型的有效数值实现,并检验了其准确性和稳定性。最后,将模型应用于示例软组织,证实了其在医学生物传感器中的灵活性和实用性。