非Debye弛豫的非线性模型

摘要：

我们提出了一个简单的非线性弛豫方程，其中包含德拜方程作为一个特殊情况。建议的松弛方程的结果在幂律衰减的波动。该方程包含定义介电常数的频率依赖性的参数，类似于众所周知的Cole-Cole、Davidson-Cole和Kohlrausch-Williams-Watts的单参数唯象方程。与这些模型不同，所获得的介电常数（i）服从Kramers-Kronig关系;（ii）在大频率下具有适当的行为;（iii）其虚部，电导率，显示出幂律频率依赖性σ~ ω^n，其中n<1对应于经验Jonscher的普遍弛豫定律，而n>1也在几个实验中观察到。所提出的非线性方程可用于弛豫理论的各个领域。

英文摘要：

We present a simple nonlinear relaxation equation which contains the Debye equation as a particular case. The suggested relaxation equation results in power-law decay of fluctuations. This equation contains a parameter defining the frequency dependence of the dielectric permittivity similarly to the well-known one-parameter phenomenological equations of Cole-Cole, Davidson-Cole and Kohlrausch-Williams-Watts. Unlike these models, the obtained dielectric permittivity (i) obeys to the Kramers-Kronig relation; (ii) has proper behaviour at large frequency; (iii) its imaginary part, conductivity, shows a power-law frequency dependence σ~ ω^n where n<1 corresponds to empirical Jonscher's universal relaxation law while n>1 is also observed in several experiments. The nonlinear equation proposed may be useful in various fields of relaxation theory.

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