Searcharxiv⌕ Search

arXiv subjects

Jooyeon Park

Publications and source records attributed to Jooyeon Park.

4 recordsLinked to original sources
arXiv2026

Conformal structures and rigidity of complete stable minimal hypersurfaces

We study complete stable minimal hypersurfaces in Riemannian manifolds under various curvature assumptions. In an $(n+1)$-dimensional complete oriented manifold with nonnegative scalar curvature, we prove that no complete oriented noncompact stable minimal hypersurface can be conformally equivalent to a bounded domain in an $n$-dimensional manifold with nonpositive scalar curvature. As a consequence, there exists no complete stable minimal hypersurface in $\mathbb{R}^{n+1}$ that is conformally equivalent to a bounded domain in $\mathbb{R}^n$. We also show that compact stable minimal hypersurfaces in manifolds with nonnegative scalar curvature have nonnegative smooth Yamabe invariant and we characterize the equality case. Next, we consider complete two-sided stable minimal hypersurfaces in ambient manifolds with pinched sectional curvature. Under an additional curvature condition that makes the second fundamental form a Codazzi tensor, we obtain a rigidity result under an $L^2$-condition on the second fundamental form and derive an upper bound for the first eigenvalue of the Laplacian. Finally, we establish that any complete noncompact two-sided minimal hypersurface immersed in a warped product manifold is stable, provided that the angle function is positive and the second derivative of the warping function is nonnegative.

math.DG↗
arXiv2026

Impact of viscoelastic polymer solution droplets on a granular bed

The impact of polymer solution droplets on granular beds is relevant to powder processing, binder jetting additive manufacturing, and environmental applications involving erosion control or spray deposition, yet most controlled studies of drop--grain interactions have focused on Newtonian liquids. In this study, we experimentally investigate the impact of viscoelastic polyethylene oxide (PEO) droplets on a dry granular bed and compare the resulting cratering dynamics with those of Newtonian liquids over a wide range of impact energies and Ohnesorge numbers. Crater morphology changes with impact energy, and this evolution occurs at lower energies for drops of polymer solution, consistent with their distinct liquid--grain interactions during impact. The crater diameter exhibits two distinct regimes: a low-energy plateau and a power-law growth at higher impact energies. We identify the transition between these regimes and show that, although the plateau size and the power law remain nearly unchanged, viscoelastic droplets reach the transition at lower impact energy than Newtonian droplets. This suggests that viscoelasticity modifies how the impact energy is partitioned between droplet deformation and dissipation in the granular bed.

cond-mat.soft↗
arXiv2026

Axial forces in capillary liquid bridges of polymer solutions

Liquid bridges form between particles during wet mixing with binders or by condensation due to ambient humidity. The consequences of capillary bridges can be quite drastic, creating macroscopic cohesion, as seen in sandcastles and in the formation of particulate agglomerates. Bulk effects in cohesive particles arise from forces generated by capillary bridges, so particle-scale measurements are needed to develop predictive models. Most existing studies at the particle scale assume Newtonian liquids. Yet many binders in industry and in the environment can exhibit viscoelastic behavior. In this study, we measure the axial force generated by liquid bridges of viscoelastic polymer solutions between two spherical beads during controlled uniaxial separation. We vary the polymer concentration, separation velocity, and particle size, and track the force as the bridge thins and ruptures. At quasi-static rates, the axial force remains dominated by capillarity and is not significantly affected by polymer rheology. However, increasing the stretching rate increases the peak force through viscous dissipation and promotes the formation of a viscoelastic filament, thereby delaying rupture. The peak axial forces collapse when rescaled by a capillary number and particle size, while the effective rupture distance collapses with a Weissenberg number. These results provide a simple first-order particle-scale force law for polymeric binders.

cond-mat.soft↗