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Havriliak–Negami relaxation
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Havriliak–Negami relaxation : ウィキペディア英語版
Havriliak–Negami relaxation
Havriliak–Negami relaxation is an empirical modification of the Debye relaxation model, accounting for the asymmetry and broadness of the dielectric dispersion curve. The model was first used to describe the dielectric relaxation of some polymers,〔
〕 by adding two exponential parameters to the Debye equation:
:
\hat(\omega) = \varepsilon_ + \frac},

where \varepsilon_ is the permittivity at the high frequency limit, \Delta\varepsilon = \varepsilon_-\varepsilon_ where \varepsilon_ is the static, low frequency permittivity, and \tau is the characteristic relaxation time of the medium. The exponents \alpha and \beta describe the asymmetry and broadness of the corresponding spectra.
Depending on application, the Fourier transform of the stretched exponential function can be a viable alternative that has one parameter less.
For \beta = 1 the Havriliak–Negami equation reduces to the Cole–Cole equation, for \alpha=1 to the Cole–Davidson equation.
== Mathematical properties ==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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