Fractional relaxation and wave equations for dielectrics characterized by the Havriliak-Negami response function

Details Fractional relaxation and wave equations for dielectrics characterized by the Havriliak-Negami response function Fractional relaxation and wave equations for dielectrics characterized by the Havriliak-Negami response function

2010-08-24

arxiv.org/abs/1008.3972v1

Physics

Condensed Matter

Other Condensed Matter

5 pages, 4 figures, presented at Int. Conf. "New Trends in Nanotechnology and Dynamical Systems - 2010" (Turkey, Ankara)

Scientific paper

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 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.

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