Compact group method in the theory of permittivity of heterogeneous systems

Sushko, M. Ya.; Kris’kiv, S. K.

doi:10.1134/s1063784209030165

Cited by 27 publications

(14 citation statements)

References 2 publications

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“…The CGA allows one to find these averages in the long-wavelength limit. For macroscopically homogeneous and isotropic systems [28][29][30]…”

Section: General Theoretical Backgroundmentioning

confidence: 99%

“…In order to find ε, one should sum up the series in (2), (3). For (4), this gives the following equation for ε [29]:…”

Section: General Theoretical Backgroundmentioning

confidence: 99%

“…The working model is based on the compact groups approach (CGA) [5,[28][29][30]. The 'compact groups' are macroscopic regions in a system with typical linear sizes L that are much smaller than the wavelength of probing field λ in the system: L = λ.…”

Section: Introductionmentioning

confidence: 99%

“…For these reasons, it was chosen as a basis for achieving the stated goals. The in-depth analysis of the CGA for the model under consideration can be found in [28][29][30]34].…”

Section: Introductionmentioning

confidence: 99%

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On applicability of differential mixing rules for statistically homogeneous and isotropic dispersions

Semenov

2018

J. Phys. Commun.

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The classical differential mixing rules are assumed to be independent effective-medium approaches, applicable to certain classes of systems. In the present work, the inconsistency of differential models for macroscopically homogeneous and isotropic systems is illustrated with a model for the effective permittivity of simple dielectric systems of impenetrable balls. The analysis is carried out in terms of the compact group approach reformulated in a way that allows one to analyze the role of different contributions to the permittivity distribution in the system. It is shown that the asymmetrical Bruggeman model (ABM) is physically inconsistent since the electromagnetic interaction between previously added constituents and those being added is replaced by the interaction of the latter with recursively formed effective medium. The overall changes in the effective permittivity due to addition of one constituent include the contributions from both constituents and depend on the system structure before the addition. Ignoring the contribution from one of the constituents, we obtain generalized versions of the original ABM mixing rules. They still remain applicable only in a certain concentration ranges, as is shown with the Hashin-Shtrikman bounds. The results obtained can be generalized to macroscopically homogeneous and isotropic systems with complex permittivities of constituents.

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“…The CGA allows one to find these averages in the long-wavelength limit. For macroscopically homogeneous and isotropic systems [28][29][30]…”

Section: General Theoretical Backgroundmentioning

confidence: 99%

“…In order to find ε, one should sum up the series in (2), (3). For (4), this gives the following equation for ε [29]:…”

Section: General Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…For these reasons, it was chosen as a basis for achieving the stated goals. The in-depth analysis of the CGA for the model under consideration can be found in [28][29][30]34].…”

Section: Introductionmentioning

confidence: 99%

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On applicability of differential mixing rules for statistically homogeneous and isotropic dispersions

Semenov

2018

J. Phys. Commun.

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“…Для уточнения вычислений необходимо рассмотреть теорию эффективной среды. На сегодняшний день существует несколько методов описания эффективной среды нанокомпозита [21]. Основным приближением в случае малой концентрации металлической компоненты является метод эффективной среды Максвелла-Гарнетта, который описывает структуру через эффективную диэлектрическую проницаемость ε eff .…”

Section: теория эффективной среды как инструмент анализа оптических сunclassified

Теория Эффективной Среды Как Инструмент Анализа Оптических Свойств Нанокомпозитов

Юрасов¹,

университет²,

Яшин³

et al. 2018

Российский технологический журнал

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Analysing the impact of temperature on polarisation in the microlayer of magnetic nanofluid in an electric field

Demin,

Morozova

2023

Pramana - J Phys

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Compact group method in the theory of permittivity of heterogeneous systems

Cited by 27 publications

References 2 publications

On applicability of differential mixing rules for statistically homogeneous and isotropic dispersions

On applicability of differential mixing rules for statistically homogeneous and isotropic dispersions

Теория Эффективной Среды Как Инструмент Анализа Оптических Свойств Нанокомпозитов

Analysing the impact of temperature on polarisation in the microlayer of magnetic nanofluid in an electric field

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