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Main Authors: Ramírez, Jorge, Tassieri, Manlio
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.09708
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author Ramírez, Jorge
Tassieri, Manlio
author_facet Ramírez, Jorge
Tassieri, Manlio
contents Reliable transformation between frequency- and time-domain material functions remains a central challenge in linear viscoelasticity due to finite bandwidth, discrete sampling, and experimental noise. We introduce \emph{i\text{-}Rheo-Tempo}, a quadrature-free method that reconstructs the shear relaxation modulus directly from dynamic measurements through an exact second-derivative representation of the complex viscosity. When the spectrum is approximated as piecewise linear, the inversion reduces to a compact interval-slope formulation based solely on local spectral properties, avoiding numerical quadrature, parametric fitting, and predefined relaxation spectra. The method is validated against a set of complex fluids including synthetic models, polymer melts, industrial elastomers, comb polymers, and broadband microrheology datasets spanning nearly nine decades in frequency. In all cases, the reconstructed relaxation modulus is in quantitative agreement with independent time-domain measurements. These results demonstrate that \emph{i\text{-}Rheo-Tempo} provides a robust, model-free solution to the frequency-to-time inverse problem and, more generally, establishes a framework for recovering time-domain responses from experimentally measured complex spectra.
format Preprint
id arxiv_https___arxiv_org_abs_2604_09708
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle i-Rheo-Tempo: A Model-Free, Quadrature-Free Reconstruction of the Shear Relaxation Modulus from Complex Viscosity
Ramírez, Jorge
Tassieri, Manlio
Soft Condensed Matter
Complex Variables
Reliable transformation between frequency- and time-domain material functions remains a central challenge in linear viscoelasticity due to finite bandwidth, discrete sampling, and experimental noise. We introduce \emph{i\text{-}Rheo-Tempo}, a quadrature-free method that reconstructs the shear relaxation modulus directly from dynamic measurements through an exact second-derivative representation of the complex viscosity. When the spectrum is approximated as piecewise linear, the inversion reduces to a compact interval-slope formulation based solely on local spectral properties, avoiding numerical quadrature, parametric fitting, and predefined relaxation spectra. The method is validated against a set of complex fluids including synthetic models, polymer melts, industrial elastomers, comb polymers, and broadband microrheology datasets spanning nearly nine decades in frequency. In all cases, the reconstructed relaxation modulus is in quantitative agreement with independent time-domain measurements. These results demonstrate that \emph{i\text{-}Rheo-Tempo} provides a robust, model-free solution to the frequency-to-time inverse problem and, more generally, establishes a framework for recovering time-domain responses from experimentally measured complex spectra.
title i-Rheo-Tempo: A Model-Free, Quadrature-Free Reconstruction of the Shear Relaxation Modulus from Complex Viscosity
topic Soft Condensed Matter
Complex Variables
url https://arxiv.org/abs/2604.09708