Calibrated shape-only recovery of membrane viscosities
Abstract
Nearby relaxation rates make two membrane viscosities difficult to distinguish from a shape transient. We show how calibrated preparation removes this loss of local sensitivity in a linear Kelvin-Voigt sphere with finite area elasticity and intrinsic membrane dissipation. Two independent releases, with a known signed amplitude ratio and calibrated relative gain and timing, yield normal-displacement records whose fixed linear combination separates the shear and dilatational rates. Their common amplitude remains unknown. For fixed sampling, positive-definite weights, bounded positive rates and nonzero excitation, the amplitude-projected sensitivity has a positive lower bound even at rate coincidence. Without relative calibration, the paired sensitivity decreases linearly with the rate gap; the single tangential-release record decreases quadratically. The calibrated bound is compatible with fixed finite initial energy. A positive local bound also persists with independent ratio calibration of fixed positive precision under a Gaussian error model. Supplied elastic coefficients convert the recovered rates into the two surface viscosities. An unbounded spherical Stokes extension quantifies how bulk dissipation changes the modal patterns and provides a sufficient full-Jacobian criterion for retaining local material sensitivity.
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BibTeX
@misc{olszewski2026calibrated,
title = {{Calibrated shape-only recovery of membrane viscosities}},
author = {Julian Olszewski and Zijian Liu and Jie Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24410},
eprint = {2610.24410},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24410},
}
RIS
TY - UNPB
TI - Calibrated shape-only recovery of membrane viscosities
AU - Julian Olszewski
AU - Zijian Liu
AU - Jie Xu
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24410
UR - https://arxiv.org/abs/2610.24410
AB - Nearby relaxation rates make two membrane viscosities difficult to distinguish from a shape transient. We show how calibrated preparation removes this loss of local sensitivity in a linear Kelvin-Voigt sphere with finite area elasticity and intrinsic membrane dissipation. Two independent releases, with a known signed amplitude ratio and calibrated relative gain and timing, yield normal-displacement records whose fixed linear combination separates the shear and dilatational rates. Their common amplitude remains unknown. For fixed sampling, positive-definite weights, bounded positive rates and nonzero excitation, the amplitude-projected sensitivity has a positive lower bound even at rate coincidence. Without relative calibration, the paired sensitivity decreases linearly with the rate gap; the single tangential-release record decreases quadratically. The calibrated bound is compatible with fixed finite initial energy. A positive local bound also persists with independent ratio calibration of fixed positive precision under a Gaussian error model. Supplied elastic coefficients convert the recovered rates into the two surface viscosities. An unbounded spherical Stokes extension quantifies how bulk dissipation changes the modal patterns and provides a sufficient full-Jacobian criterion for retaining local material sensitivity.
ER -