Дробно-дифференциальный подход для численного моделирования электронно-индуцированной зарядки сегнетоэлектриков

Дробно-дифференциальный подход для численного моделирования электронно-индуцированной зарядки сегнетоэлектриков

Мороз Л. И., Масловская А. Г.
Сибирский журнал индустриальной математики, 27, 1(97), 55–71 (2024)
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УДК 519.63 
DOI: 10.33048/SIBJIM.2024.27.105

Аннотация:

В работе предложена дробно-дифференциальная модификация математической модели процесса нестационарной зарядки полярных диэлектрических материалов в условиях облучения электронными пучками средних энергий. В основе математической формализации лежит сферически-симметричное диффузионно-дрейфовое уравнение с производной дробного порядка по времени. С использованием аппроксимации производной Капуто построена неявная конечно-разностная схема. В ППП Matlab разработана прикладная программа, реализующая сконструированный вычислительный алгоритм. Верификация приближенного решения задачи продемонстрирована на тест-примере. Представлены результаты вычислительных экспериментов по оценке характеристик полевых эффектов инжектированных зарядов в сегнетоэлектриках при вариации порядка дробного дифференцирования в субдиффузионных режимах.

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Работа выполнена при финансовой поддержке Минобрнауки РФ (проект 122082400001-8). Других источников финансирования проведения или руководства данным конкретным исследованием не было.

Л. И. Мороз
  1. Амурский государственный университет, 
    Игнатьевское шоссе, 21, г. Благовещенск 675027, Россия

E-mail: lubovep@mail.ru

А. Г. Масловская
  1. Амурский государственный университет, 
    Игнатьевское шоссе, 21, г. Благовещенск 675027, Россия

E-mail: maslovskayaag@mail.ru

Статья поступила 04.09.2023 г. 
После доработки 01.02.2024 г.
Принята к публикации 07.02.2024 г.

Abstract:

The paper proposes a fractional-differential modification of the mathematical model of the process of nonstationary charging of polar dielectric materials under conditions of irradiation with medium-energy electron beams. The mathematical formalization is based on a spherically symmetric diffusion-drift equation with a fractional time derivative. An implicit finite-difference scheme is constructed using the Caputo derivative approximation. An application program has been developed in Matlab software that implements the designed computational algorithm. Verification of an approximate solution of the problem is demonstrated using a test example. The results of computational experiments to evaluate the characteristics of field effects of injected charges in ferroelectrics when varying the order of fractional differentiation in subdiffusion regimes are presented.

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