arXiv subjects

Julian Olszewski

Publications and source records attributed to Julian Olszewski.

3 recordsLinked to original sources

arXiv2026

Structural identifiability and stress reconstruction from incomplete optical maps with velocimetry

Reconstructing the stress field of a planar viscoelastic flow from optical measurements loses its direct evidence wherever optical coverage is interrupted, and no improvement in optical precision restores an observation that was never made. We characterize what a second, velocity channel adds, and what neither channel can supply. Two calibrated optical components determine the local deviatoric stress pointwise, while velocity constrains spatial stress variation through momentum balance, so the two channels are complementary rather than redundant. The isotropic part of the stress is unobservable to both: the divergence of an isotropic field is a pure gradient, which the Leray projection annihilates, so every representable isotropic mode lies in the joint null space. That accounts for the null space exactly when the optical field is complete, and bounds it from below otherwise, since finite incomplete sampling and aperture zeros can remove further directions. We verify the count directly on three discretizations. In paired synthetic tests with finite measurement apertures, spatially correlated noise and optical stripe dropout, adding velocity reduces the mean whole-domain deviatoric error from 50.40% to 27.82% at 3% reference noise, and the improvement survives shared gaps, inverse-grid refinement at fixed physical sampling, and a constitutively generated stress field. The improvement does not rest on how the regularization parameter is chosen: it holds under both the expected-norm discrepancy rule and generalized cross-validation, and we report each selection with its position in the search interval, which is where the two rules differ.

physics.flu-dyn↗

arXiv2026

A closed-form solution for streaming and Lagrangian transport in a deforming circular cavity

Streaming from a deforming cavity wall serves micromixing, pumping and particle handling. We solve it in closed form in a two-dimensional circular cavity, for any azimuthal wall mode $m$, in the viscous-dominated limit $\mathrm{Wo}^2 \to 0$, where the Stokes layer spans the cavity. A biharmonic inversion against the Reynolds-stress forcing, corrected by the second-order slip a moving wall imposes, gives the Lagrangian mean a tracer follows as an elementary streamfunction for a deforming no-slip wall, $ψ_L = -[m(5m+4)a_m^2/(128(m+2)(2m+1))]\,r^{2m}(r^2-1)^2\sin 2mθ$, and a second for a shear-free interface. The factor $(5m+4)/(m+2)$ relating it to the auxiliary reference-boundary solution $ψ_2$ is universal across the prescribed-velocity family; at $m=2$ the physical Eulerian mean peaks an order of magnitude above $ψ_2$ and with opposite sign. At every $m$ the no-slip cell centers lie at $r^2 = m/(m+2)$, and at large $m$ the peak streamfunction falls as $m^{-2}$ and the peak speed as $m^{-1}$. The ranking over $m$ is set by the wall kinematics: an externally driven wall is largest at $m=1$, where rigidly translating the same circle drives nothing; an inextensible shell peaks at $m=3$. The inversion extends to mode superpositions without degenerating. At finite $\mathrm{Wo}$ the first order stays closed form in Bessel functions and the second reduces to quadrature; the construction recovers Rayleigh's coefficient $-3m/8$ on a separate tangentially driven boundary problem. An independent finite-element solver, written with the closed form withheld, reproduces $ψ_2$ with second-order convergence.

physics.flu-dyn↗

arXiv2026

Design of a combined polarimetric and velocimetric measurement for viscoelastic stress, and its constitutive resolving power

A polarimeter does not report stress. It reports a retardance and an azimuth, and converting those to a stress pair fixes both the calibration that is required and the covariance that the subsequent inference must carry. We set out that observation chain for planar viscoelastic flow, combine it with velocimetry, and ask what the combined measurement can resolve. The calibration constant is fixed by three separately measurable quantities: path length, stress-optic coefficient and wavelength, rather than being fitted. Propagating the polarimetric errors to first order gives a stress covariance that is anisotropic and site dependent even for independent homoscedastic inputs, and whose conditioning degrades as the retardance approaches zero, where the linearization itself stops describing the measurement. Wrapping imposes a separate design bound. Holding the total scalar count fixed and varying the split between velocimetric and optical sites, an unequal allocation favoring optical sites outperforms either pure configuration. We then ask what the measurement resolves between constitutive models compatible with the same velocity data. In self-consistent pressure-driven flow of the finitely extensible nonlinear elastic Peterlin model, at extensibility L^2=50 and 3% noise, the optical channel rejects the velocity-compatible Oldroyd-B family in 78.1% of realizations at the Deborah number De=2, the ratio of the relaxation time to the flow timescale, and in 100% at De=4, while rejecting only about 5% below De=0.3. The resolving power of a design is therefore a strong function of Deborah number and must be quoted with it. Both numerical studies use ideal calibrated stress coordinates under a prescribed covariance; propagating the polarimetric covariance into them is the next step.

physics.flu-dyn↗