Математическая модель переключения поляризации, основанная на обобщенном уравнении Ландау – Халатникова – Тани: численная реализация

В статье представлен обзор существующих математических моделей, описывающих динамику изменения поляризации в сегнетоэлектриках на основе термодинамической теории Ландау. Особое внимание уделено обобщённой модели Ландау – Халатникова – Тани, учитывающей инерционные эффекты и позволяющей описывать гистерезисные явления. Модель формализуется в виде начально-краевой задачи для уравнения в частных производных гиперболического типа. Для численного решения задачи построена неявная конечно-разностная схема. Приведены результаты вычислительных экспериментов, демонстрирующих переключение поляризации и построение диэлектрического гистерезиса в сегнетоэлектрических материалах с фазовым переходом первого рода.

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