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Размерности и другие геометрические критические показатели в теории протекания


Обзор работ, посвященных исследованию размерностных характеристик перколяционных кластеров. Чисто геометрический характер перколяционного фазового перехода и многообразие величин, имеющих критическое поведение, делают такой геометрический подход наглядным и полезным. Помимо фрактальной размерности кластера и его подмножеств (скелета, границ и т. д.) оказывается необходимым ввести дополнительные характеристики. Так, максимальная скорость распространения возбуждений определяется величиной химической размерности кластера, а критическое поведение проводимости, коэффициента диффузии и т. д. — спектральной пли другими, связанными с ней размерностями. Рассмотрены соотношения подобия, связывающие разные размерности, а также связывающие размерности с обычными критическими показателями. Табл. 3. Ил. 16. Библиогр. ссылок 151.

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English fulltext is available at DOI: 10.1070/PU1986v029n10ABEH003526
PACS: 64.60.Ak, 64.60.Fr (все)
DOI: 10.3367/UFNr.0150.198610b.0221
URL: https://ufn.ru/ru/articles/1986/10/b/
Цитата: Соколов И М "Размерности и другие геометрические критические показатели в теории протекания" УФН 150 221–255 (1986)
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English citation: Sokolov I M “Dimensionalities and other geometric critical exponents in percolation theory” Sov. Phys. Usp. 29 924–945 (1986); DOI: 10.1070/PU1986v029n10ABEH003526

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