Zhiping Li

Chunmei Su, Zhiping Li

The approximation properties of a quadratic iso-parametric finite element method for a typical cavitation problem in nonlinear elasticity are analyzed. More precisely, (1) the finite element interpolation errors are established in terms of the mesh parameters; (2) a mesh distribution strategy based on an error equi-distribution principle is given; (3) the convergence of finite element cavity solutions is proved. Numerical experiments show that, in fact, the optimal convergence rate can be achieved by the numerical cavity solutions.

Weijie Huang, Zhiping Li

A mixed finite element method combining an iso-parametric $Q_2$-$P_1$ element and an iso-parametric $P_2^+$-$P_1$ element is developed for the computation of multiple cavities in incompressible nonlinear elasticity. The method is analytically proved to be locking-free and convergent, and it is also shown to be numerically accurate and efficient by numerical experiments. Furthermore, the newly developed accurate method enables us to find an interesting new bifurcation phenomenon in multi-cavity growth.

Liang Wei, Zhiping Li

A Fourier-Chebyshev spectral method is proposed in this paper for solving the cavitation problem in nonlinear elasticity. The interpolation error for the cavitation solution is analyzed, the elastic energy error estimate for the discrete cavitation solution is obtained, and the convergence of the method is proved. An algorithm combined a gradient type method with a damped quasi-Newton method is applied to solve the discretized nonlinear equilibrium equations. Numerical experiments show that the Fourier-Chebyshev spectral method is efficient and capable of producing accurate numerical cavitation solutions.

Xiaohan Wang, Nan Zhang, Sulene Han et al.

The pharmaceutical industry is facing challenges with quality management such as high costs of compliance, slow responses and disjointed knowledge. This paper presents GMPilot, a domain-specific AI agent that is designed to support FDA cGMP compliance. GMPilot is based on a curated knowledge base of regulations and historical inspection observations and uses Retrieval-Augmented Generation (RAG) and Reasoning-Acting (ReAct) frameworks to provide real-time and traceable decision support to the quality professionals. In a simulated inspection scenario, GMPilot shows how it can improve the responsiveness and professionalism of quality professionals by providing structured knowledge retrieval and verifiable regulatory and case-based support. Although GMPilot lacks in the aspect of regulatory scope and model interpretability, it is a viable avenue of improving quality management decision-making in the pharmaceutical sector using intelligent approaches and an example of specialized application of AI in highly regulated sectors.

Hengzhu Tang, Zefeng Zhang, Zhiping Li et al.

Video Quality Assessment (VQA) is vital for large-scale video retrieval systems, aimed at identifying quality issues to prioritize high-quality videos. In industrial systems, low-quality video characteristics fall into four categories: visual-related issues like mosaics and black boxes, textual issues from video titles and OCR content, and semantic issues like frame incoherence and frame-text mismatch from AI-generated videos. Despite their prevalence in industrial settings, these low-quality videos have been largely overlooked in academic research, posing a challenge for accurate identification. To address this, we introduce the Multi-Branch Collaborative Network (MBCN) tailored for industrial video retrieval systems. MBCN features four branches, each designed to tackle one of the aforementioned quality issues. After each branch independently scores videos, we aggregate these scores using a weighted approach and a squeeze-and-excitation mechanism to dynamically address quality issues across different scenarios. We implement point-wise and pair-wise optimization objectives to ensure score stability and reasonableness. Extensive offline and online experiments on a world-level video search engine demonstrate MBCN's effectiveness in identifying video quality issues, significantly enhancing the retrieval system's ranking performance. Detailed experimental analyses confirm the positive contribution of all four evaluation branches. Furthermore, MBCN significantly improves recognition accuracy for low-quality AI-generated videos compared to the baseline.

Weijie Huang, Zhiping Li

A mixed finite element method (MFEM), using dual-parametric piecewise bi-quadratic and affine (DP-Q2-P1) finite element approximations for the deformation and the pressure like Lagrange multiplier respectively, is developed and analyzed for the numerical computation of incompressible nonlinear elasticity problems with large deformation gradient, and a damped Newton method is applied to solve the resulted discrete problem. The method is proved to be locking free and stable. The accuracy and efficiency of the method are illustrated by numerical experiments on some typical cavitation problems.

Chunmei Su, Zhiping Li

The orientation-preservation condition, i.e., the Jacobian determinant of the deformation gradient $\det \nabla u$ is required to be positive, is a natural physical constraint in elasticity as well as in many other fields. It is well known that the constraint can often cause serious difficulties in both theoretical analysis and numerical computation, especially when the material is subject to large deformations. In this paper, we derive a set of sufficient and necessary conditions for the quadratic iso-parametric finite element interpolation functions of cavity solutions to be orientation preserving on a class of radially symmetric large expansion accommodating triangulations. The result provides a practical quantitative guide for meshing in the neighborhood of a cavity and shows that the orientation-preservation can be achieved with a reasonable number of total degrees of freedom by the quadratic iso-parametric finite element method.