Maoqin Yuan

We develop an energy-stable variable-step BDF2-based scalar auxiliary variable (SAV) finite element scheme for a droplet thin-film coarsening model with a Lennard–Jones singular potential. The method uses continuous piecewise linear finite elements in space and retains the original linear SAV update. We prove discrete mass conservation, modified-energy decay under an admissible step-ratio condition, and solvability of the coupled algebraic system. A Sherman–Morrison realization exploits the rank-one coupling and reduces each accepted time step to two solves with the same sparse base matrix. Numerical experiments assess temporal and spatial convergence, SAV-shift sensitivity, two-droplet mesh dependence, long-time coarsening, and solver efficiency. The film-height variable exhibits second-order temporal convergence and the expected spatial rates, whereas the auxiliary variable is first-order accurate; the consistency audit shows no hidden cancellation. The computations also verify mass conservation, modified-energy decay, positive film heights in the reported runs, and the efficiency of the sparse solver.

Designing structure-preserving numerical schemes for the generalized Poisson-Nernst-Planck (PNP) system is challenging due to its inherent strong nonlinearity and coupling. In this paper, we propose a class of efficient, unconditional energy-stable schemes based on the Stabilized Scalar Auxiliary Variable (S-SAV) framework combined with the finite element method. We construct both first-order (BE-S-SAV) and second-order (BDF2-S-SAV) fully discrete schemes. A distinguishing feature of our approach is the use of a linear decomposition strategy, which decouples the complex nonlinear system into a sequence of linear, constant-coefficient elliptic equations at each time step. This significantly reduces computational complexity by avoiding expensive nonlinear iterations. We provide rigorous theoretical proofs demonstrating that the proposed schemes are unconditionally energy stable and strictly preserve mass conservation. Numerical experiments satisfy the theoretical analysis, confirming optimal convergence rates and demonstrating robust preservation of mass conservation and modified energy stability in the tested regimes.

This study investigates the potential impact of "LK-99," a novel material developed by a Korean research team, on the power equipment industry. Using evolutionary game theory, the interactions between governmental subsidies and technology adoption by power companies are modeled. A key innovation of this research is the introduction of sensitivity analyses concerning time delays and initial subsidy amounts, which significantly influence the strategic decisions of both government and corporate entities. The findings indicate that these factors are critical in determining the rate of technology adoption and the efficiency of the market as a whole. Due to existing data limitations, the study offers a broad overview of likely trends and recommends the inclusion of real-world data for more precise modeling once the material demonstrates room-temperature superconducting characteristics. The research contributes foundational insights valuable for future policy design and has significant implications for advancing the understanding of technology adoption and market dynamics.

A stabilized finite element method is considered for the Stokes eigenvalue problem based on the lowest equal-order element pair, which does not need to choose stabilization parameter. Stabilization terms of the stabilized finite element method include not only the term related to the momentum equation but also the continuity equation. Furthermore, combined the approximation of compact operator with the analysis of Stokes source problem, error estimates of the present method are deduced. Finally, numerical tests are made to confirm effectively.

This study discusses a new method combining image steganography technology with Natural Language Processing (NLP) large models, aimed at improving the accuracy and robustness of extracting steganographic text. Traditional Least Significant Bit (LSB) steganography techniques face challenges in accuracy and robustness of information extraction when dealing with complex character encoding, such as Chinese characters. To address this issue, this study proposes an innovative LSB-NLP hybrid framework. This framework integrates the advanced capabilities of NLP large models, such as error detection, correction, and semantic consistency analysis, as well as information reconstruction techniques, thereby significantly enhancing the robustness of steganographic text extraction. Experimental results show that the LSB-NLP hybrid framework excels in improving the extraction accuracy of steganographic text, especially in handling Chinese characters. The findings of this study not only confirm the effectiveness of combining image steganography technology and NLP large models but also propose new ideas for research and application in the field of information hiding. The successful implementation of this interdisciplinary approach demonstrates the great potential of integrating image steganography technology with natural language processing technology in solving complex information processing problems.