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Wavelet regularization and the continuous relaxation spectrum

Davies, Arthur Russell and Goulding, Neil 2012. Wavelet regularization and the continuous relaxation spectrum. Journal of Non-Newtonian Fluid Mechanics 189 , pp. 19-30. 10.1016/j.jnnfm.2012.09.002

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The purpose of this paper is to show how continuous wavelet analysis can be used to establish natural models for the continuous relaxation spectrum of a polymeric material. A method of wavelet regularization is proposed for the practical recovery of the continuous spectrum over a limited range of relaxation times. Working with logarithmic variables (log-frequency and log-time), it may be seen that the loss modulus is a scaling function transform of the continuous relaxation spectrum. It is shown how the decomposition formula of Calder´on and Mallat may be used to reconstruct the spectrum from measurements of storage and loss moduli. At practical levels of resolution, the spectrum may be represented as a finite sum of hyperbolic scaling functions. There are two principal regularization mechanisms, namely, sparsity (the number of terms in the sum), and scale (which controls both resolution and smoothness). The method of wavelet regularization is illustrated by recovering spectra from both synthetic and real data.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Elsevier
ISSN: 0377-0257
Date of First Compliant Deposit: 30 March 2016
Last Modified: 04 Jun 2017 04:06

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