Cole–Davidson equation
The Cole-Davidson equation is a model used to describe dielectric relaxation in glass-forming liquids. The equation for the complex permittivity is

where  is the permittivity at the high frequency limit,  where  is the static, low frequency permittivity, and  is the characteristic relaxation time of the medium. The exponent  represents the exponent of the decay of the high frequency wing of the imaginary part, . The Cole–Davidson equation is a generalization of the Debye relaxation keeping the initial increase of the low frequency wing of the imaginary part, . Because this is also a characteristic feature of the Fourier transform of the stretched exponential function it has been considered as an approximation of the latter, although nowadays an approximation by the Havriliak-Negami function or exact numerical calculation may be preferred. Because the slopes of the peak in  in double-logarithmic representation are different it is considered an asymmetric generalization in contrast to the Cole-Cole equation. The Cole–Davidson equation is the special case of the Havriliak-Negami relaxation with . The real and imaginary parts are

and

See also
 Debye relaxation
 Cole-Cole relaxation
 Havriliak–Negami relaxation
 Curie–von Schweidler law

References

Equations
Glass
Liquids
Electric and magnetic fields in matter