Yanxiang Zhao

Wangbo Luo, Zhonghua Qiao, Yanxiang Zhao

In this paper, we develop and analyze exponential time differencing (ETD) schemes for a phase-field model of multicomponent membranes proposed in our previous work \cite{luo2025ohta}, in which membrane deformation is governed by a force-balance phase-field equation and protein segregation is described by a membrane-associated Ohta-Kawasaki (OK) dynamics. For a fixed phase-field membrane, we introduce a geometry-adapted operator splitting method based on the localization function, which reformulates the surface OK dynamics into a form suitable for ETD integration. The resulting first- and second-order ETD schemes, combined with finite-difference spatial discretization, are rigorously proved to satisfy a discrete maximum-bound principle and unconditional energy stability. For the coupled system, we construct stabilized ETD schemes in an FFT-based spectral framework, treating stiff linear terms exactly and nonlinear mechanochemical couplings explicitly. A narrow-band implementation further reduces the computational cost by restricting surface calculations to the diffuse membrane region. Numerical experiments confirm the predicted temporal accuracy, maximum-bound preservation, and energy decay for the fixed-membrane OK problem, and demonstrate stable and efficient three-dimensional simulations of protein-driven pattern formation and membrane deformation.

Yanxiang Zhao, Yanping Ma, Hui Sun et al.

We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and electrostatic interaction energy that is described by the Coulomb-field approximation, all coupled together self-consistently through a phase field. By introducing a new phase-field term in the description of the solute-solvent van der Waals and electrostatic interactions, we can keep the phase-field values closer to those describing the solute and solvent regions, respectively, making it more accurate in the free-energy estimate. We first prove that our phase-field functionals $Γ$-converge to the corresponding sharp-interface limit. We then develop and implement an efficient and stable numerical method to solve the resulting gradient-flow equation to obtain equilibrium conformations and their associated free energies of the underlying charged molecular system. Our numerical method combines a linear splitting scheme, spectral discretization, and exponential time differencing Runge-Kutta approximations. Applications to the solvation of single ions and a two-plate system demonstrate that our new phase-field implementation improves the previous ones by achieving the localization of the system forces near the solute-solvent interface and maintaining more robustly the desirable hyperbolic tangent profile for even larger interfacial width. This work provides a scheme to resolve the possible unphysical feature of negative values in the phase-field function found in the previous phase-field modeling (cf. H. Sun, et al. J. Chem. Phys., 2015) of charged molecules with the Poisson--Boltzmann equation for the electrostatic interaction.

Chong Wang, Xiaofeng Ren, Yanxiang Zhao

A nonlocal diffuse interface model is used to study bubble assemblies in ternary systems. As model parameters vary, a large number of morphological phases appear as stable stationary states. One open question related to the polarity direction of double bubble assemblies is answered numerically. Moreover, the average size of bubbles in a single bubble assembly depends on the sum of the minority constituent areas and the long range interaction coefficients. One identifies the ranges for area fractions and the long range interaction coefficients for double bubble assemblies.

Xiang Xu, Yanxiang Zhao

In this paper, we propose a first order energy stable linear semi-implicit method for solving the Allen-Cahn-Ohta-Kawasaki equation. By introducing a new nonlinear term in the Ohta-Kawasaki free energy functional, all the system forces in the dynamics are localized near the interfaces which results in the desire hyperbolic tangent profile. In our numerical method, the time discretization is done by some stabilization technique in which some extra nonlocal but linear term is introduced and treated explicitly together with other linear terms, while other nonlinear and nonlocal terms are treated implicitly. The spatial discretization is performed by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are proved for this method in both semi-discretization and full discretization levels. Numerical experiments indicate the force localization and desire hyperbolic tangent profile due to the new nonlinear term. We test the first order temporal convergence rate of the proposed scheme. We also present hexagonal bubble assembly as one type of equilibrium for the Ohta-Kawasaki model. Additionally, the two-third law between the number of bubbles and the strength of long-range interaction is verified which agrees with the theoretical studies.

Zhongyuan Zhang, Yi Qian, Yanxiang Zhao et al.

Unlike ordinary computer vision tasks that focus more on the semantic content of images, the image manipulation detection task pays more attention to the subtle information of image manipulation. In this paper, the noise image extracted by the improved constrained convolution is used as the input of the model instead of the original image to obtain more subtle traces of manipulation. Meanwhile, the dual-branch network, consisting of a high-resolution branch and a context branch, is used to capture the traces of artifacts as much as possible. In general, most manipulation leaves manipulation artifacts on the manipulation edge. A specially designed manipulation edge detection module is constructed based on the dual-branch network to identify these artifacts better. The correlation between pixels in an image is closely related to their distance. The farther the two pixels are, the weaker the correlation. We add a distance factor to the self-attention module to better describe the correlation between pixels. Experimental results on four publicly available image manipulation datasets demonstrate the effectiveness of our model.

Yuhang Zhou, Yanxiang Zhao, Zhongyun Hua et al.

Person re-identification (ReID) is a fundamental task in many real-world applications such as pedestrian trajectory tracking. However, advanced deep learning-based ReID models are highly susceptible to adversarial attacks, where imperceptible perturbations to pedestrian images can cause entirely incorrect predictions, posing significant security threats. Although numerous adversarial defense strategies have been proposed for classification tasks, their extension to metric learning tasks such as person ReID remains relatively unexplored. Moreover, the several existing defenses for person ReID fail to address the inherent unique challenges of adversarially robust ReID. In this paper, we systematically identify the challenges of adversarial defense in person ReID into two key issues: model bias and composite generalization requirements. To address them, we propose a debiased dual-invariant defense framework composed of two main phases. In the data balancing phase, we mitigate model bias using a diffusion-model-based data resampling strategy that promotes fairness and diversity in training data. In the bi-adversarial self-meta defense phase, we introduce a novel metric adversarial training approach incorporating farthest negative extension softening to overcome the robustness degradation caused by the absence of classifier. Additionally, we introduce an adversarially-enhanced self-meta mechanism to achieve dual-generalization for both unseen identities and unseen attack types. Experiments demonstrate that our method significantly outperforms existing state-of-the-art defenses.