Sampling Localization in Determining the Relaxation Spectrum

Research Report MRR97-013

Sampling Localization in Determining the Relaxation Spectrum

A. R. Davies and R. S. Anderssen

Abstract: It is widely believed that the storage and loss moduli over the frequency range $\omega _{\min }<\omega <\omega _{\max }$ yield information about the relaxation spectrum over the range of relaxation times $(\omega _{\max })^{-1}<\tau <(\omega _{\min })^{-1}$ ; i.e., the reciprocal frequency range. This rule-of-thumb is often used to discard estimates of the relaxation spectrum provided by indirect methods outside the reciprocal frequency range of the data. We will show, however, that this rule is imprecise, and that the relaxation spectrum is determined on a shorter interval of relaxation times than the reciprocal frequency range. This is formalized in the paper as sampling localization.

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