Fractional Wave Equation for Dielectric Medium with Havriliak–Negami Response

Abstract

A fractional relaxation equation in dielectrics with response function of the Havriliak-Negami type is derived. An explicit expression for the fractional operator in this equation is obtained and Monte Carlo algorithm for calculation of action of this operator and is constructed. Relaxation functions calculated numerically according to this scheme coincide with analytical functions obtained earlier by other authors. The algorithm represents a numerical way of calculation in relaxation problems with arbitrary initial and boundary conditions. A fractional equation for electromagnetic waves in such dielectric media is obtained. Numerical results are in a good agreement with experimental data.

Fractional Relaxation Equations and Brownian Crossing Probabilities of a Random Boundary

“…to study the electromagnetic properties of a wide range of materials (which display a long-memory, instead of exponential, decay-see [30] and [31]) as well as the rheological models for the description of some viscoelastic materials (see [10], [21], [22], and [29]). to study the electromagnetic properties of a wide range of materials (which display a long-memory, instead of exponential, decay-see [30] and [31]) as well as the rheological models for the description of some viscoelastic materials (see [10], [21], [22], and [29]).…”

Two-dimensional finite-difference time-domain formulation for sound propagation in a temperature-dependent elastomer-fluid medium

“…5 A number of empirical models including Maxwell, Cole-Cole (C-C) and Havriliak-Negami (H-N) relations have been proposed to fit the dynamic mechanical spectra. [6][7][8][9][10] In particular, H-N relation provides an extensible frequency-domain model to parametrize the mechanical response of dispersive media and a better description for the asymmetric relaxation loss peak, especially under acoustic pulse excitation. Effects of temperature on dynamic mechanical parameters can be considered by H-N relations.…”

Dielectric response of BaZrO3/BaTiO3 superlattice

“…15,16 In relaxors, the slow dynamics results in the complex low-frequency part in the dielectric responses. Different formulas, such as the Cole-Cole, 17 HavriliakNegami equations, 18 and other models 19 have been proposed to model the relaxation process, as polarization in such systems adopts complex dynamics due to various interactions.…”