Summary
In this paper a modification of the method of moments is used to obtain a first-order approximation to the electric field in a random medium subjected to 1) a constant electric field and 2) a constant electric-displacement vector. The results are then used in two classical variational principles to obtain bounds on the effective permittivity of the medium. These bounds are seen to involve integrals of three-point correlation functions involving both the permittivity and the natural logarithm of the permittivity. The paper concludes with a simplification of these bounds for a special mathematically defined material termed a two-phase cell material.
Riassunto
In questo articolo si usa una modificazione del metodo degli impulsi per ottenere un’approssimazione del primo ordine al campo elettrico in un mezzo disordinato soggetto 1) a un campo elettrico costante e 2) a un vettore di spostamento elettrico costante. Si usano poi i risultati in due principi variazionali classici per ottenere i limiti della permissività effettiva del mezzo. Si vede che questi limiti coinvolgono integrali di funzioni di correlazione di tre punti che interessano sia la permissività che il suo logaritmo naturale. Si conclude con una semplificazione di questi limiti per un materiale specifico definito matematicamente, chiamato materiale cellulare a due fasi.
Реэюме
В зтой статье испольэуется модификация метода моментов для получения первого приближения по злектрическому полю в случайной среде, которая находится 1) в постоянном злектрическом поле и 2) при постоянном векторе злектрического смешения. Затем зти реэультаты испольэуются для получения границ зффективной дизлектрической постоянной среды в двух классических вариационных принципах. Покаэывается, что зти границы содержат интегралы от трех-частичных корреляционных функций, включаюших и дизлектрическую постоянную и ее натуральный логарифм. Статья эаканчивается упрошением зтих границ для специального математически определенного материала, представляюшего двух-фаэовый ячеистый материал.
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References
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This work was done while the author was visiting Pahlavi University, Shiraz.
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McCoy, J.J. A new set of bounds for the effective permittivity of a random medium. Nuovo Cimento B (1965-1970) 57, 139–153 (1968). https://doi.org/10.1007/BF02710322
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DOI: https://doi.org/10.1007/BF02710322