Liqun Cao

Chupeng Ma, Liqun Cao, Yanping Lin

In this paper we study the numerical method and the convergence for solving the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge. An alternating Crank-Nicolson finite element method for solving the problem is presented and the optimal error estimate for the numerical algorithm is obtained by a mathematical inductive method. Numerical examples are then carried out to confirm the theoretical results.

Chupeng Ma, Liqun Cao, Jizu Huang et al.

In this paper, we consider the initial-boundary value problem for the time-dependent Maxwell--Schrödinger equations in the Coulomb gauge. We first prove the global existence of weak solutions to the equations. Next we propose an energy-conserving fully discrete finite element scheme for the system and prove the existence and uniqueness of solutions to the discrete system. The optimal error estimates for the numerical scheme without any time-step restrictions are then derived. Numerical results are provided to support our theoretical analysis.

Chupeng Ma, Liqun Cao

In this paper we consider the initial-boundary value problem for the time-dependent Maxwell-Schrödinger equations, which arises in the interaction between the matter and the electromagnetic field for the semiconductor quantum devices. A Crank-Nicolson finite element method for solving the problem is presented. The optimal energy-norm error estimates for the numerical algorithm without any time-step restrictions are derived. Numerical tests are then carried out to confirm the theoretical results.

Chenxing Meng, Wuzhou Quan, Yingjie Cai et al.

Cloud occlusion severely degrades the semantic integrity of optical remote sensing imagery. While incorporating Synthetic Aperture Radar (SAR) provides complementary observations, achieving efficient global modeling and reliable cross-modal fusion under cloud interference remains challenging. Existing methods rely on dense global attention to capture long-range dependencies, yet such aggregation indiscriminately propagates cloud-induced noise. Improving robustness typically entails enlarging model capacity, which further increases computational overhead. Given the large-scale and high-resolution nature of remote sensing applications, such computational demands hinder practical deployment, leading to an efficiency-reliability trade-off. To address this dilemma, we propose EDC, an efficiency-oriented and discrepancy-conditioned optical-SAR semantic segmentation framework. A tri-stream encoder with Carrier Tokens enables compact global context modeling with reduced complexity. To prevent noise contamination, we introduce a Discrepancy-Conditioned Hybrid Fusion (DCHF) mechanism that selectively suppresses unreliable regions during global aggregation. In addition, an auxiliary cloud removal branch with teacher-guided distillation enhances semantic consistency under occlusion. Extensive experiments demonstrate that EDC achieves superior accuracy and efficiency, improving mIoU by 0.56\% and 0.88\% on M3M-CR and WHU-OPT-SAR, respectively, while reducing the number of parameters by 46.7\% and accelerating inference by 1.98$\times$. Our implementation is available at https://github.com/mengcx0209/EDC.

Liqun Cao, Chupeng Ma, Jianlan Luo et al.

This paper discusses the multiscale approach and the convergence of the time-dependent Maxwell-Schrödinger system with rapidly oscillating discontinuous coefficients arising from the modeling of a heterogeneous nanostructure with a periodic microstructure. The homogenization method and the multiscale asymptotic method for the nonlinear coupled equations are presented. The efficient numerical algorithms based on the above methods are proposed. Numerical simulations are then carried out to validate the method presented in this paper.

Jinzhe Zeng, Liqun Cao, Mingyuan Xu et al.

Understanding and prediction of the chemical reactions are fundamental demanding in the study of many complex chemical systems. Reactive molecular dynamics (MD) simulation has been widely used for this purpose as it can offer atomic details and can help us better interpret chemical reaction mechanisms. In this study, two reference datasets were constructed and corresponding neural network (NN) potentials were trained based on them. For given large-scale reaction systems, the NN potentials can predict the potential energy and atomic forces of DFT precision, while it is orders of magnitude faster than the conventional DFT calculation. With these two models, reactive MD simulations were performed to explore the combustion mechanisms of hydrogen and methane. Benefit from the high efficiency of the NN model, nanosecond MD trajectories for large-scale systems containing hundreds of atoms were produced and detailed combustion mechanism was obtained. Through further development, the algorithms in this study can be used to explore and discovery reaction mechanisms of many complex reaction systems, such as combustion, synthesis, and heterogeneous catalysis without any predefined reaction coordinates and elementary reaction steps.