Use of the vibrational approach to determine bounds for the effective permittivity in random media

Beran, Mark J.

doi:10.1007/bf02748596

Cited by 243 publications

(117 citation statements)

References 3 publications

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“…The local thermal conductivity for a two-phase particulate composite is defined as 9) where the subscripts p and m denote the particle and matrix phases, respectively. Using variational principles, Beran [23] derived third-order bounds for the effective thermal conductivity, κ L ≤ κ e ≤ κ U , of homogeneous and isotropic heterogeneous materials. The superscripts L and U denote the lower and upper bounds, respectively.…”

Section: (I) Thermal Conductivitymentioning

confidence: 99%

Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics

et al. 2015

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Section: (I) Thermal Conductivitymentioning

confidence: 99%

Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics

et al. 2015

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“…(The term nth order bounds refers to the fact that the bounds are exact to O(σ 1 − σ 2 ) n ). The Beran [4] bounds were derived using variational principles and were subsequently simplified by Milton [7]. Following the notation of Milton we define < a >= pa 1 + qa 2 , <ã >= qa 1 + pa 2 (interchanging p and q) and < a > ζ = ζ 1 a 1 + ζ 2 a 2 .…”

Section: Bounds On the Effective Properties Of Composite Materialsmentioning

confidence: 99%

Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and simulation

1995

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We investigate the effective conductivity (σe) of a class of amorphous media defined by the levelcut of a Gaussian random field. The three point solid-solid correlation function is derived and utilised in the evaluation of the Beran-Milton bounds. Simulations are used to calculate σe for a variety of fields and volume fractions at several different conductivity contrasts. Relatively large differences in σe are observed between the Gaussian media and the identical overlapping sphere model used previously as a 'model' amorphous medium. In contrast σe shows little variability between different Gaussian media. 05.40.+j, 72.15.Cz

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“…11,12 The threepoint upper bound is much more tedious to compute. Expressions given by Prager 13 and Beran 14 were later simplified: it was shown that the three-point bound can be written using a threefold integral of the three-point correlation function of the metal. 15,16 This functional is often denoted by f 2 0; 1 ½ .…”

Section: Theories For the Effective Conductivitymentioning

confidence: 99%

Backbone of conductivity in two-dimensional metal-insulator composites

Reuteler

Hütter

Gauckler

2011

Journal of Applied Physics

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In percolation theory, the backbone is defined by chopping off dangling ends from the percolating cluster. For structures with high degree of spatial correlation, as they are typical for porous thin films, trimming of the full structure to reveal the part determining the electrical conductivity is more subtle than the classic definition of the backbone. To expand the applicability of the concept, we present a purely geometric definition for the backbone of a two-dimensional percolating cluster. It is based on a sequence of image analysis operations defining the backbone in terms of an image filter. The change of both area fraction and effective conductivity induced by applying the backbone filter to various binary images and a two-parameter family of sets is assessed by numerical means. It is found that the backbone filter simplifies the geometry of complex microstructures significantly and at the same time preserves their electrical DC behavior. We conclude that the backbone will be useful as a first ingredient for a geometric estimator of the effective conductivity of metal-insulator composites.

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Use of the vibrational approach to determine bounds for the effective permittivity in random media

Cited by 243 publications

References 3 publications

Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics

Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics

Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and simulation

Backbone of conductivity in two-dimensional metal-insulator composites

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