Abstract

The paper is devoted to the development and implementation of a hybrid stochastic fractal-based approach for modeling electron-induced kinetics of polarization switching in ferroelectrics as the self-similar memory physical systems. The mathematical model of fractal dynamic system includes the initial value problem for the fractional order differential equation. Computational schemes for solving fractional differential problem are constructed using the Adams–Bashforth–Moulton type predictor-corrector methods. The stochastic algorithm based on the Monte Carlo method is proposed to simulate the domain nucleation process during restructuring the domain structure in ferroelectrics. The polarization switching current of ferroelectrics in the electron injection mode is evaluated to demonstrate the computational experiment results with a comparison of the experimental data.

中文翻译：

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基于混合分形的混合方法在注入模式下铁电开关动力学建模

摘要

本文致力于基于混合随机分形的方法的开发和实现，该方法用于模拟铁电介质中电子感应的极化转换动力学作为自相似存储物理系统。分形动力系统的数学模型包括分数阶微分方程的初值问题。使用Adams–Bashforth–Moulton型预测器-校正器方法构造了解决分数阶微分问题的计算方案。提出了一种基于蒙特卡洛方法的随机算法，以模拟铁电体结构重构过程中的晶核形成过程。