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Julian Olszewski

Publications and source records attributed to Julian Olszewski.

7 recordsLinked to original sources
arXiv2026

Physics-informed neural network (PINN) approximations of capillary menisci in polygonal channels

In a zero-gravity cylindrical container, a meniscus can span a square or equilateral-triangular cross-section only at contact angles at or above the respective Concus-Finn critical angles of 45 degrees and 60 degrees. We study strong-form physics-informed neural networks (PINNs) across these thresholds under fixed collocation and optimization budgets. Classical capillary flux balance yields a lower bound on the combined interior and wall residual loss for arbitrary positive sampling densities. In the tested nonexistence regime, several degrees below the critical angles, independently evaluated network losses are 1.6-1.9 times this bound. A polynomial least-squares comparison supports the same geometric interpretation. The PINNs still return smooth graphs with finite axial extent, even though the prescribed equilibrium problem has no spanning graph solution. Their small interior residuals coexist with wall-flux deficits near corners, where adjoining contact-angle conditions demand more flux than a finite-slope graph can supply. Residuals vary on both sides of the critical angle, while the bound tends uniformly to zero at threshold for fixed wall weight. These results give a geometric scale for interpreting the computed loss and locate the incompatibility that a small interior residual can conceal.

physics.flu-dyn↗
arXiv2026

Three-body corrections to Brownian hard-sphere viscosity

For Brownian hard spheres without hydrodynamic interactions, we obtain a conditional enclosure between 1.8266948 and 1.8267157 for the third-order zero-shear Brownian viscosity coefficient. It applies when the physical three-body correction coincides with the finite-energy weak solution and the remote remainder in the pair adjoint identity vanishes. Kirkwood superposition gives zero because three nonzero pair contributions cancel exactly. An elementary radial identity exposes this cancellation, and a common contact-stress convention allows direct comparison of closure predictions. Although superposition solves the bulk equation, it leaves a shared-contact flux error. Correcting this error defines a unique weak response with positive Dirichlet energy. Explicit symmetric trials yield a variational lower bound and a residual upper bound using the rotational structure of shear and three-sphere geometry. Exact integration and outward interval evaluation enclose the fixed-trial functionals. Under the stated physical conditions, the resulting interval excludes all closure coefficients compared here and supplies a quantitative benchmark for dilute three-body Brownian stress.

cond-mat.soft↗
arXiv2026

Resonant-pair energy return beyond the early Green-Kubo plateau in a quartic chain

Distinguishing rapid local energy exchange from sustained transport matters when thermal conductivity is inferred from finite simulations. In a weakly coupled chain of separable quartic oscillators, we identify a quantitative mechanism that changes an early Green--Kubo plateau: resonant neighbors exchange energy and coherently return it. The pair heat-current integral maps to the classical pendulum trapping response. Quartic homogeneity gives an energy-independent reference period $T_{\rm lib}=7.77ε^{-1/2}$, where $ε$ is the coupling. Without fitted parameters, the leading response predicts a negative first minimum at $0.952T_{\rm lib}$ with depth $-0.74$ times the independent-cell exchange coefficient. Isolated-pair simulations test this reference and resolve finite-coupling corrections. The chain reaches its first minimum on the same time scale, with a shallower minimum and a small later residual. Comparisons with chaotic cells and energy-conserving noise show regimes in which coherent return is absent or interrupted over the measured windows. These finite-time results provide a quantitative reference for separating the early exchange plateau from subsequent correlated dynamics.

cond-mat.stat-mech↗
arXiv2026

Calibrated shape-only recovery of membrane viscosities

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.

cond-mat.soft↗
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. Two numerical studies follow, both in ideal calibrated stress coordinates under a prescribed covariance rather than the propagated polarimetric one. 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.

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 $m$, as $\mathrm{Wo}^2 \to 0$. A biharmonic inversion against the Reynolds stress, corrected by the second-order slip a moving wall imposes, gives the Lagrangian mean a tracer follows for a deforming no-slip wall, $ψ_L = -[m(5m+4)a_m^2/(128(m+2)(2m+1))]\,r^{2m}(r^2-1)^2\sin 2mθ$, with a companion form for a shear-free interface. For a single mode the factor $(5m+4)/(m+2)$ relating it to the auxiliary solution $ψ_2$ is the same for every member of the co-phased prescribed-velocity family; at $m=2$ the physical Eulerian mean peaks an order of magnitude above $ψ_2$, with opposite sign. The no-slip cell centers lie at $r^2 = m/(m+2)$, and at large $m$ the peak streamfunction falls as $m^{-2}$, the peak speed as $m^{-1}$. At fixed radial wall-velocity amplitude the ranking over $m$ follows the wall kinematics: an externally driven wall peaks at $m=1$, a wall with zero first-order surface strain at $m=3$. Mode superpositions invert without degenerating, each harmonic carrying its own correction. At finite $\mathrm{Wo}$ the first-order field stays closed form in Bessel functions and the mean flow reduces to quadrature; the construction approaches the $m=2$ Rayleigh limit on a separate tangentially driven boundary problem. An independent finite-element solver, with the closed form withheld, reproduces $ψ_2$ with quadratic mesh convergence.

physics.flu-dyn↗
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↗