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arXiv · 2610.24410

Calibrated shape-only recovery of membrane viscosities

Julian Olszewski·Zijian Liu·Jie Xu
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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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Julian Olszewski, Zijian Liu, Jie Xu. 2026-10-17. Calibrated shape-only recovery of membrane viscosities. https://arxiv.org/abs/2610.24410

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