arXiv subjects

Lingling Xie

Publications and source records attributed to Lingling Xie.

5 recordsLinked to original sources

arXiv2026

Asymptotic behavior of generic Riemann solutions to one-dimensional full compressible Navier-Stokes-Poisson equations

This paper investigates the time-asymptotic stability of the one-dimensional full compressible Navier-Stokes-Poisson equations, assuming that the corresponding quasi-neutral Euler equations admit a generic Riemann solution consisting of a shock, a contact discontinuity, and a rarefaction wave. It is proved that there exists a unique global-in-time solution, which converges in $L^\infty$ norm, as time goes to infinity, to the ansatz composed of a viscous shock with a time-dependent shift, a viscous contact wave, and an inviscid rarefaction wave. The main difficulty arises from the non-conservative lower-order source terms induced by the electric potential in the momentum and energy equations, which significantly complicates the proof of the existence of individual waves (especially the viscous shock) and the derivation of the relative entropy estimates. To overcome this, we make full use of the Poisson equation satisfied by the electric potential, and combine the weighted relative entropy method with the $a$-contraction method with shifts to close the estimates within the $H^2$-perturbation framework.

math.AP↗

arXiv2026

Splashing-regime transitions and secondary-droplet scaling in oblique drop impacts on a deep pool

Oblique drop impact onto a deep liquid pool produces asymmetric crowns, directional jetting, and splashing transitions that cannot be characterized by the total impact inertia alone. We numerically investigate water drops impacting a quiescent deep pool over $41\leq We\leq1790$ and $10^\circ\leqθ\leq90^\circ$. The simulations reproduce the principal features observed experimentally and identify five post-impact regimes in the $We$--$θ$ plane: deposition, front splashing, side splashing, side-front splashing, and crown splashing. The deposition--front-splashing transition is described by the tangential-inertial parameter $K_s=We\cosθ$, with $K_s^c\approx120$. This criterion follows from the competition between downstream crown-rim inertia and capillary retraction at the Taylor--Culick velocity. The transition from front to side-front splashing is instead governed primarily by normal impact inertia, with a critical normal Weber number $We_N^c\approx318$. Beyond these regime transitions, the secondary-droplet statistics reveal fragmentation behavior common to the different splashing regimes. The droplet-size distributions are positively skewed, and the median diameter follows $d_{s,\mathrm{med}}/D\sim We^{-3/5}$. Second-order velocity structure functions support a scale-dependent capillary--inertial description of rim and ligament breakup. Combined with mass conservation, this scaling gives $N_s\sim We^{9/5}$, providing a numerical explanation for the secondary-droplet-number scaling observed experimentally. Thus, directional impact inertia governs the macroscopic selection of splashing regimes, whereas the secondary-droplet populations across these regimes exhibit a common capillary--inertial fragmentation scaling.

physics.flu-dyn↗

arXiv2026

Lagrange multiplier expressions for matrix polynomial optimization and tight relaxations

This paper studies matrix constrained polynomial optimization. We investigate how to get explicit expressions for Lagrange multiplier matrices from the first order optimality conditions. The existence of these expressions can be shown under the nondegeneracy condition. Using Lagrange multiplier matrix expressions, we propose a strengthened Moment-SOS hierarchy for solving matrix polynomial optimization. Under some general assumptions, we show that this strengthened hierarchy is tight, or equivalently, it has finite convergence. We also study how to detect tightness and how to extract optimizers. Numerical experiments are provided to show the efficiency of the strengthened hierarchy.

math.OC↗

arXiv2026

A finite-termination algorithm for testing copositivity over the positive semidefinite cone

This paper proposes an efficient algorithm for testing copositivity of homogeneous polynomials over the positive semidefinite cone. The algorithm is based on a novel matrix optimization reformulation and requires solving a hierarchy of semidefinite programs. Notably, it always terminates in finitely many iterations. If a homogeneous polynomial is copositive over the positive semidefinite cone, the algorithm provides a certificate; otherwise, it returns a vector that refutes copositivity. Building on a similar idea, we further propose an algorithm to test copositivity over the direct product of the positive semidefinite cone and the nonnegative orthant. Preliminary numerical experiments demonstrate the effectiveness of the proposed methods.

math.OC↗

arXiv2023

Stabilization of Ferroelectric Hf0.5Zr0.5O2 Epitaxial Films via Monolayer Reconstruction Driven by Interfacial Redox Reaction

The binary fluorite oxide Hf0.5Zr0.5O2 tends to grab a significant amount of notice due to the distinct and superior ferroelectricity found in its metastable phase. Stabilizing the metastable ferroelectric phase and delineating the underlying growth mechanism, however, are still challenging. Recent discoveries of metastable ferroelectric Hf0.5Zr0.5O2 epitaxially grown on structurally dissimilar perovskite oxides have triggered intensive investigations on the ferroelectricity in materials that are nonpolar in bulk form. Nonetheless, the growth mechanism for the unique fluorite/perovskite heterostructures has yet to be fully explored. Here we show that the metastable ferroelectric Hf0.5Zr0.5O2 films can be stabilized even on a one-unit-cell-thick perovskite La0.67Sr0.33MnO3 buffer layer. In collaboration with scanning transmittance electron microscopy (STEM) based characterizations, we show that monolayer reconstruction driven by interfacial redox reactions plays a vital role in the formation of a unique heterointerface between the two structurally dissimilar oxides, providing the template monolayer that facilitates the epitaxial growth of the metastable HZO films. Our findings offer significant insights into the stabilization mechanism of the ferroelectric Hf0.5Zr0.5O2, and this mechanism could be extended for exploring functional metastable phases of various metal oxides.

cond-mat.mtrl-sci↗