arXiv subjects

Siqi Ren

Publications and source records attributed to Siqi Ren.

5 recordsLinked to original sources

arXiv2026

Asymptotic linear stability of columnar vortices driven by Coriolis force

In this paper, we establish the asymptotic linear stability of a class of Coriolis-driven columnar vortices for the 3-D axisymmetric Euler equations. This result represents a critical step toward proving the nonlinear asymptotic stability of such vortices. The key and widely applicable strategy is to construct a distorted Fourier basis, which is achieved by solving a two-parameter $(c, \xi)$-dependent Schr\"odinger equation associated with the linearized operator of the system. To capture the precise asymptotic behavior of the solution, we decompose the $c-\xi$ plane into distinct regions, with the partitioning guided by the leading-order profiles of the Schr\"odinger equation across different parameter regimes.

math.AP↗

arXiv2026

Instability of shear flows with neutral embedded eigenvalues

We study the linear stability of a class of monotone shear flows. When the associated Rayleigh operator possesses a neutral embedded eigenvalue, we show that solutions of the linearized system may exhibit arbitrarily large growth in both the $L^\infty$ and $L^2$ norms. Moreover, when the embedded eigenvalue is multiple, we prove that the instability becomes stronger and explicitly construct solutions that grow linearly in time. This instability originates from the non-normality of the Rayleigh operator.

math.AP↗

arXiv2025

On the asymptotic limit for the dynamic isotropic-nematic phase transition with anisotropic elasticity

We consider the isotropic--nematic phase transition dynamics for liquid crystals based on the Landau--de Gennes $Q$-tensor theory. When the anisotropic elastic constant $L_2$ is negative, we rigorously justify the limit from the Landau--de Gennes flow to a sharp interface system: the interface which separates the two bulk regions evolves by mean curvature flow; in the isotropic region, the limit alignment tensor $Q(x,t)\equiv 0$; in the nematic region, the limit $Q(x,t)$ can be characterized by the gradient flow of the Oseen--Frank energy with a strong normal anchoring condition on the interface. This result rigorously verifies a claim by de Gennes [Mol. Cryst. Liq. Cryst. 1971] regarding the surface tension strength of isotropic--nematic interfaces in dynamical settings.

math.AP↗

arXiv2024

Linear inviscid damping in the presence of an embedding eigenvalue

In this paper, we investigate the long-time dynamics of the linearized 2-D Euler equations around a hyperbolic tangent flow $(\tanh y,0)$. A key difference compared to previous results is that the linearized operator has an embedding eigenvalue, which has a significant impact on the dynamics of the linearized system. For the first mode, the dynamics consists of there parts: non-decay part related to the eigenspace associated with the embedding eigenvalue, slow decay part due to the resolvent singularity, and fast decay part related to the inviscid damping. For higher modes, the dynamics is similar to the inviscid damping phenomena in the case without embedding eigenvalues.

math.AP↗

arXiv2021

Minority Oversampling for Imbalanced Time Series Classification

Many important real-world applications involve time-series data with skewed distribution. Compared to conventional imbalance learning problems, the classification of imbalanced time-series data is more challenging due to high dimensionality and high inter-variable correlation. This paper proposes a structure preserving Oversampling method to combat the High-dimensional Imbalanced Time-series classification (OHIT). OHIT first leverages a density-ratio based shared nearest neighbor clustering algorithm to capture the modes of minority class in high-dimensional space. It then for each mode applies the shrinkage technique of large-dimensional covariance matrix to obtain accurate and reliable covariance structure. Finally, OHIT generates the structure-preserving synthetic samples based on multivariate Gaussian distribution by using the estimated covariance matrices. Experimental results on several publicly available time-series datasets (including unimodal and multimodal) demonstrate the superiority of OHIT against the state-of-the-art oversampling algorithms in terms of F1, G-mean, and AUC.

cs.LG↗