Related papers: Analytical representations for relaxation function…
The extensions of the classical Debye model of susceptibility of dielectric materials to the well-known Cole-Cole, Davidson- Cole, or the Havriliak-Negami models is done by introducing non-integer power parameters to the frequency-domain…
The relaxation properties of dielectric materials are described, in the frequency domain, according to one of the several models proposed over the years: Kohlrausch-Williams-Watts, Cole-Cole, Cole-Davidson, Havriliak-Negami (with its…
The introduction of a fractional differential operator defined in terms of the Riemann-Liouville derivative makes it possible to generalize the kinetic equations used to model relaxation in dielectrics. In this context such fractional…
Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching…
An improved approximation via Havriliak-Negami (HN) functions to the Fourier Transform (FT) of certain Weibull distributions, -\psi_{\beta}, (the time derivative of the Kohlrausch-Williams-Watts function), is given for a large interval of…
The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in…
X-ray photon correlation is used to probe the slow dynamics of the glass-former B2O3 across the glass transition. In the undercooled liquid phase the decay times of the measured correlation functions are consistent with visible light…
A multi-time extension of a density correlation function is introduced to reveal temporal information about dynamical heterogeneity in glass-forming liquids. We utilize a multi-time correlation function that is analogous to the higher-order…
We investigate the relaxation process and the dynamical heterogeneities of the kinetically constrained Kob--Anderson lattice glass model, and show that these are characterized by different timescales. The dynamics is well described within…
The suitability of a double Havriliak-Negami (HN) approximant to represent the Fourier Transform of the time derivative of Kohlrausch-Williams-Watts function, -\psi_{\beta}, has been discussed in the first part of this work. There, it is…
We study theoretically and numerically a family of multi-point dynamic susceptibilities that quantify the strength and characteristic lengthscales of dynamic heterogeneities in glass-forming materials. We use general theoretical arguments…
We derive a general pattern of the nonexponential, two-power-law relaxation from the compound subordination theory of random processes applied to anomalous diffusion. The subordination approach is based on a coupling between the very large…
Molecular-dynamics simulations are presented for two correlation functions formed with the partial density fluctuations of binary hard-sphere mixtures in order to explore the effects of mixing on the evolution of glassy dynamics upon…
We provide a review of theoretical results concerning the Havriliak-Negami (HN) and the Jurlewicz-Weron-Stanislavsky (JWS) dielectric relaxation models. We derive explicit forms of functions characterizing relaxation phenomena in the time…
Time-dependent density functional theory, proposed recently in the context of atomic diffusion and non-equilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the…
The time-dependent susceptibility for the finite-size mean-field Random Orthogonal model (ROM) is studied numerically for temperatures above the mode-coupling temperature. The results show that the imaginary part of the susceptibility…
The relaxation functions introduced empirically by Debye, Cole-Cole, Cole-Davidson and Havriliak-Negami are, each of them, solutions to their respective kinetic equations. In this work, we propose a generalization of such equations by…
We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural…
We study functions related to the experimentally observed Havriliak-Negami dielectric relaxation pattern in the frequency domain $\sim[1+(i\omega\tau_{0})^{\alpha}]^{-\beta}$ with $\tau_{0}$ being some characteristic time. For $\alpha =…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…