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Research Report MRR98-017
Sampling localization, duality algorithms and the Kramers-Kronig relations
A.R. Davies and R.S. Anderssen
Abstract:
In a recent paper, Anderssen and Davies have derived moving-average
formulae which can be applied to oscillatory shear data to recover
estimates of the relaxation spectrum of the viscoelastic material
tested. These moving-average formulae represent an improvement
over commercial packages currently available, for two reasons.
First, they take the limits imposed by sampling localization in
determining the relaxation spectrum fully into account. Secondly,
to within finite resolution, these formulae yield accurate
relaxation spectra in a fraction of a second on a PC. Anderssen
and Davies have also indicated that their formulae are best
employed within an iterative algorithm which exploits the natural
duality between storage and loss moduli. The purpose of this paper
is to pursue this natural duality further, and present a class of
fast algorithms accessible to the experimentalist. Their
performance when applied to noisy data is described. Their success
is attributed to the implicit duality constraints imposed through
sampling localization and the Kramers-Kronig relations.
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