Mean-field theory of strongly nonlinear random composites: Strong power-law nonlinearity and scaling behavior

Wan, Wenhui; Lee, H. C.; Hui, P. M.; Yu, Kin Wah

doi:10.1103/physrevb.54.3946

Cited by 39 publications

(20 citation statements)

References 17 publications

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“…For the static case the results of the last modi"cation of the nonlinear e!ective medium theory [54,55] are in best agreement with comprehensive computer simulations performed for a twodimensional (2D) percolation composite [52,54,55]. The original approach that combines the e!ective medium theory and spectral representation [12,57] has been developed in Refs.…”

Section: Introductionsupporting

confidence: 51%

Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites

2000

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Section: Introductionsupporting

confidence: 51%

Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites

2000

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“…Thus, for extracting the harmonics, a perturbation expansion approach was performed. In the case of strong nonlinearity, this approach is no longer valid, and we might need to resort to a self-consistent method [15,23]. In addition, the dipolar fluid considered here is seen as dispersive.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear alternating current responses of dipolar fluids

Huang

Karttunen

2004

Phys. Rev. E

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The frequency-dependent nonlinear dielectric increment of dipolar fluids in nonpolar fluids is often measured by using a stationary relaxation method in which two electric fields are used: The static direct current (dc) field of high strength causing the dielectric nonlinearity, and the probing alternating current (ac) field of low strength and high frequency. When a nonlinear composite is subjected to a sinusoidal electric field, the electric response in the composite will, in general, consist of ac fields at frequencies of higher-order harmonics. Based on the Fröhlich model, we present a theory to investigate the nonlinear ac responses of dipolar fluids containing both polarizable monomers and dimers. In the case of monomers only, our theory reproduces the known results. We obtain the fundamental, second-, and third-order harmonics of the Fröhlich field by performing a perturbation expansion. The even-order harmonics are induced by the coupling between the ac and dc fields, although the system under consideration has a cubic nonlinearity only. The harmonics of the Fröhlich field can be affected by the field frequency, temperature, dispersion strength, and the characteristic frequency of the dipolar fluid, as well as the dielectric constant of the nonpolar fluid. The results are found to be in agreement with recent experimental observations.

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“…As the local field in the nonlinear component can not be solved exactly, we must resort to the mean-field approximation [18][19][20], which amounts to approximatingẽ e 1 as…”

Section: Formalismmentioning

confidence: 99%

Spectral representation theory for higher order nonlinear responses in random composites with arbitrary nonlinearity

Gao²,

Li³

2004

Physica Status Solidi (b)

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The higher order nonlinear responses of random two-phase composite media are investigated within spectral representation theory. The first component with the volume fraction p is assumed to have the nonlinear displacement (D)-electric field (E) relation of the form, where e 1 is the linear dielectric constant and c 1 is the b þ 1 ð Þth order nonlinear response; the second component is linear with the volume fraction 1 À p and the dielectric constant e 2 . The effective nonlinear responses of the composite media can be defined aswhere e e , c e and h e are the effective linear dielectric constant, the effective b þ 1 ð Þth order nonlinear response and 2b þ 1 ð Þ th order nonlinear response respectively. Based on spectral representation theory and the perturbative expansion method, general expressions for c e and h e are derived as a function of the material parameters and the spectral density function mðxÞ, which are indeed valid for arbitrary b and for any complicated microstructures. For the dilute limit and the Maxwell-Garnett microstructures, our expressions yield the same formulae as those in previous works. Moreover, the theoretical results for Bruggeman effective medium microstructures are compared with numerical simulations, good agreement is found.

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Mean-field theory of strongly nonlinear random composites: Strong power-law nonlinearity and scaling behavior

Cited by 39 publications

References 17 publications

Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites

Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites

Nonlinear alternating current responses of dipolar fluids

Spectral representation theory for higher order nonlinear responses in random composites with arbitrary nonlinearity

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