Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/76054
Title: Frequency domain description of Kohlrausch response through a pair of Havriliak-Negami-type functions: An analysis of functional proximity
Authors: Medina, J. S.
Prosmiti, R.
Villarreal, P.
Delgado-Barrio, G.
Alemán, J. V.
UNESCO Clasification: 23 Química
Keywords: Dielectric Relaxation Behaviour
Empirical Decay Function
Williams-Watts Function
Underlying Distributions
Mathematical Functions, et al
Issue Date: 2011
Journal: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 
Abstract: An approximation to the Fourier transform (FT) of the Kohlrausch function (stretched exponential) with shape parameter 0 < beta <= 1 is presented by using Havriliak-Negami-like functions. Mathematical expressions to fit their parameters alpha, gamma, and tau, as functions of beta (0 < beta <= 1 and 1 < beta < 2) are given, which allows a quick identification in the frequency domain of the corresponding shape factor beta. Reconstruction via fast Fourier transform of frequency approximants to time domain are shown as good substitutes in short times though biased in long ones (increasing discrepancies as beta -> 1). The method is proposed as a template to commute time and frequency domains when analyzing complex data. Such a strategy facilitates intensive algorithmic search of parameters while adjusting the data of one or several Kohlrausch-Williams-Watts relaxations.
URI: http://hdl.handle.net/10553/76054
ISSN: 1539-3755
DOI: 10.1103/PhysRevE.84.066703
Source: Physical Review E [ISSN 1539-3755], v. 84 (6), 066703, (Diciembre 2011)
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