Subordination scenario of the Cole-Davidson relaxation

The non-exponential relaxation is shown to result from the temporal subordination of an initial, exponentially decaying state by inverse tempered α-stable processes. In contrast to the ordinary α-stable processes the tempered α-stable ones are characterized by the finiteness of their moments. This approach establishes a direct link between the Cole-Cole and the Cole-Davidson relaxation laws.     

Structural ion-sound plasma turbulence as a self-similar random process

It is shown that the experimentally investigated structural ion-sound plasma turbulence is a self-similar stationary random process. The self-similarity parameter is determined by two temporal laws: the nonrandom character of the appearance of nonlinear structures (nonlinear ion-sound solitons) in the plasma, and the nonlinear interaction between them. As the distance from the threshold of the ion-sound current instability increases, the self-similar random process approaches a Gaussian random process, but this limit has not been attained experimentally. The possibility of recording superlong time series of the fluctuations of the signal of the plasma process and processing of the time series by the R/S analysis method has made it possible to prove self-similarity of the plasma structural turbulence. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 203–208 (10 August 1999)     

Williams-watts dielectric relaxation: A fractal time stochastic process

Dielectric relaxation in amorphous materials is treated in a defect-diffusion model where relaxation occurs when a mobile defect, such as a vacancy, reaches a frozen-in dipole. The random motion of the defect is assumed to be governed by a fractal time stochastic process where the mean duration between defect movements is infinite. When there are many more defects than dipoles, the Williams-Watts decaying fractional exponential relaxation law is derived. The argument of the exponential is related to the number of distinct sites visited by the random walk of the defect. For the same reaction dynamics but with more traps than walkers, an algebraically decaying relaxation is found.     

Dielectric relaxation of the cowle-cowle type and self-similar relaxation processes

In order to describe relaxation processes not obeying an exponential law a model of a self-similar relaxation process is proposed which is described by an equation containing fractional differentiation operators. It turns out that the complex susceptibility corresponding to such a model system has a form which agrees with the known empirical Cowle—Cowle expression. Kazan State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 6–11, April, 1997.     

Conductivity and dielectric relaxation of gelatin films with glycerol as plasticizer

Gelatin films complexed with ionic salts are of current interest as potential solid polymer electrolytes. However, even without salt, gelatin films are found to have quite high ionic conductivity at room temperature (around 30 °C), when plasticized with an adequate fraction of glycerol. In the present work, the admittance and dielectric properties of gelatin are studied as a function of glycerol content and temperature. An enhancement in the ionic conductivity by four orders of magnitude to ～9.13?×?10^?3 S/m at room temperature is obtained by adding 35.71 wt% of glycerol. This enhancement appears to be correlated with the changes in the local microstructure on plasticizer addition. Admittance and dielectric relaxation have been studied to understand the dynamics of the charge carriers. Differential scanning calorimetry, X-ray diffraction and scanning electron microscopy are also done.     

Conflicting theories of dielectric relaxation

Differences in theories of dielectric relaxation in polar liquids are shown, by thermodynamic analysis, to arise from artificial internal surface states associated with physical discontinuities in cavity model calculations.     

On the theory of dielectric relaxation

The Kirkwood expression for the static dielectric constant of a polar substance is extended to non-zero frequencies by a means which avoids the introduction of spherical specimens and the connection between the dipoledipole correlation functions of distinct spatial regions. The procedure is based on a previously derived relation between the dynamic dielectric constant and the current-current susceptibility and on the use of the Callen-Welton theorem to relate the susceptibility to fluctuations. Surface effects are eliminated at the outset by consideration of media which are infinite in extent. A general relation between the long-range dipole-dipole correlations (which fall off as the inverse cube of the distance) and short-range correlations in a specimen composed of non-polarizable molecules is found from a consistency relation. It is shown that the two microscopic relaxation times which result from the existence of but one relaxation time in the dielectric constant correspond to the transverse and longitudinal relaxation times with the longitudinal time being screened relative to the transverse time by the static dielectric constant.     

High frequency dielectric relaxation of chlorobenzene

Low and high frequency data on dielectric relaxation of chlorobenzene are used to test an extended Nee-Zwanzig formula including inertial effects. Although this formula fits very well the low frequency data and reproduces the general features of the observed absorption curve, it is shown that neither this formula, nor the formula of Lobo, Robinson and Rodriguez can represent both the low and high frequency behaviour of this polar liquid with the same set of parameters.     

Memory effect in dielectric relaxation I

Dielectric relaxation theory is formulated taking into account the effect of inertia and the memory effect. With the use of the damping theoretical expansion formula, a rigorous equation for the probability density is derived and solved exactly in terms of the Jacobi theta function. Dielectric absorption, dispersion and fluctuation of the dipole moment are determined. For higher frequencies (i.e. short time behavior), deviation from the Debye result is found and the relevance to experiments is discussed.     

Effect of tunneling on dielectric relaxation

An analytic solution is derived for the kinetic equation of dielectric relaxation taking into account tunneling in a quasiclassical approximation for a symmetric two-well model. Analysis of the general formula for the relaxation time in the limit cases of high and low temperatures shows it to be consistent with earlier approximate solutions and allows determining more precisely the region of non-Arrhenius relaxation.Translated from Izvestiya Vysshikh Uchebynkh Zavedenii, Fizika, No. 2, pp. 36–41, February, 1987.     

Isothermal relaxation current in a dielectric with partially blocking contacts

The continuity and Poisson's equations are solved numerically for a dielectric with partially blocking electrodes in the nonsteady case. The distribution of the mobile-charge-carrier concentration and the electric field strength inside the dielectric is obtained at various times after the potential source is switched on. The time dependence of the isothermal current and the emf of high-voltage polarization of the dielectric with a single type of mobile charge carriers at different values of the contact current is calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 12–16, September, 1985.     

Local field and radiative relaxation rate in a dielectric medium

The effect of macroscopic parameters of a substance on the optical characteristics of impurity particles is investigated. A generalized control equation is derived for two-level emitters forming an ensemble of optical centers in a transparent dielectric medium. In this equation, the effective values of the acting pump field and the radiative relaxation rate of an optical center are taken into account. The formalism developed here is a completely microscopic approach based on the chain of the Bogoliubov-Born-Green-Kirkwood-Yvon equations for reduced density matrices and correlation operators for material particles and modes of a quantized radiation field. The method used here makes it possible to take into account the effects of individual and collective behavior of emitters, which are associated with the presence of an intermediate medium, consistently without using phenomenological procedures. It is shown that the resultant analytic expression for the effective lifetime of the excited state of an optical center conforms with experimental data.     

Frequency control of the dielectric temperature coefficient of resistance in the process of relaxation polarization

It is shown that the dielectric temperature coefficient of resistance (TCR) can be changed in the process of relaxation polarization. The TCR frequency dependences are calculated using the Debye model of polarization. When the signal frequency is altered, both the value and the sign of the TCR change. The effect of the change in the value and sign of the TCR when the frequency is altered is discovered experimentally in doped semiconductor barium titanate.     

Hierarchical description for a non-Markoff relaxation process

A phenomenal model is proposed in this paper to describe a non-Markoff relaxation process. The main feature of the model is the fractal time concept introduced to take account of the coupling of a relaxation mode with a heat bath. The theoretical investigation indicates that a weakly non-Markoff relaxation process can be related to a set of hierarchically distributed Markoff relaxation processes and the fractal exponential law exp [?(t/τ)^1?σ] is the character of a non-Markoff relaxation process. Calculations about the temperature and time scale dependence of the exponent σ have been made, and comparison with recent experiments is also given.     

Choice of a dielectric relaxation model of a substance by hypothesis testing

A procedure for processing of measured complex permittivity spectra of a substance for the main Debye, Cole-Cole, Cole-Davidson, and Havriliak-Negami relaxation models is described. The most probable model is chosen by hypothesis testing. The results of processing of experimental permittivity spectra for methyl alcohol and water mixtures are presented. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 15–22, November, 1999.     

Derivation of the dielectric loss formula (a theory of dielectric relaxation in glassy systems)

The derivation is given of the empirical formula tan $\text{σ = A(ω)[}\text{1}\text{B}\text{(T?T}{}_{\mathrm{c}}\text{)]}{}^2\text{sech}{}^2\text{[}\text{1}\text{B}\text{(T?T}{}_{\mathrm{c}}\text{)]}$, where A (ω), B and T_c are constants of the dipolar material at constant applied frequency ω, which has been shown to be in excellent agreement with experimental dielectric loss data on polymers and other amorphous glasses. The derivation is based on the dynamics of a two-level model. The energy splitting, Δ, of the system is derived and determined experimentally for polymers.