The finite - difference time - domain (FDTD) modeling of targets with infinitely thin graphene sheets poses a challenge due to the existence of surface current and the inability of longitudinal discretization. When analyzing the electromagnetic properties of targets via FDTD method, spatial discretization of the target is essential. In the case of macroscopic electromagnetic targets that incorporate ‘infinitely thin’ graphene interfaces, this interface cannot be longitudinally partitioned. Moreover, a surface current exists on the interface, rendering the conventional calculation methods for the tangential electric field on the interface inapplicable. To address this issue, we put forward a novel Equivalent Source Current (ESC) approach. The proposed method enables the graphene sheet to retain a two - dimensional structure and be positioned on the surface of the Yee cell during the spatial discretization of the FDTD method(Fig.2). Subsequently, the surface current on the graphene sheet is approximated as a source volume current. Then, the active Maxwell's equations are discretized at the tangential electric - field nodes on the graphene surface(Fig.2, Fig.3), thereby obtaining a modified formula for the electric - field. By introducing intermediate variables and integrating the Shift Operator (SO) method, which is employed to handle issues related to dispersive media, to process the correction formula, an FDTD iterative formula for calculating the tangential electric field at the graphene interface is deduced. This ultimately enables the FDTD calculations for targets with ‘infinitely thin’ graphene sheets. Excellent agreement between our FDTD results and analytical solutions in several numerical examples validates the proposed method. The methodological framework proposed in this study can be generalized and applied to the ‘zero-thickness’ dispersive interfaces with surface current distributions (such as metallic films and two-dimensional transition metal sulfides). This allows for a convenient numerical analysis of the electromagnetic properties of structures incorporating conductive dispersive interfaces.

Geodesic acoustic modes (GAMs), the high-frequency branch of zonal flows, play a crucial role in regulating turbulence and the associated anomalous transport in tokamaks. Although often treated as electrostatic oscillations, GAMs intrinsically possess an electromagnetic component, manifested as magnetic field perturbations. This component is essential for GAM's interaction with electromagnetic turbulence and for the existence of global GAM eigenmodes. However, a long-standing discrepancy exists between magnetohydrodynamic (MHD) and gyro-kinetic theories regarding the three-dimensional (3D) structure of these perturbations. MHD models consistently predict a full 3D structure, with dominant $m=2$ components in the radial and poloidal magnetic field perturbations and dominant $m=1$ component in the toroidal magnetic field perturbation, where $m$ denotes the poloidal wavenumber. In contrast, most gyro-kinetic studies, adopting the conventional parallel vector potential approximation ($\delta\vec{A} \approx \delta A_\|\vec{b}$), are restricted to describing only the $m=2$ poloidal component while systematically neglecting the radial and parallel (toroidal) components. This limitation has created a theoretical gap, preventing a unified understanding of the electromagnetic nature of GAMs.<br>To address this issue, we employ a self-consistent electromagnetic gyro-kinetic model without invoking the parallel vector potential approximation. Starting from the linear electromagnetic gyro-kinetic equation, we describe the perturbed distribution functions of both ions and electrons. The model is closed with a self-consistent set of field equations—including the quasi-neutrality condition and both the parallel and perpendicular components of Ampère’s law—which determine the evolution of the electrostatic potential $\delta\phi$, the parallel vector potential $\delta A_\|$, and the parallel magnetic perturbation $\delta B_\|$ (associated with the perpendicular vector potential $\delta A_\perp$). By retaining the full perturbed magnetic vector potential $\delta\vec{A}$, the framework naturally incorporates both parallel current perturbations (linked to $\delta A_\|$) and diamagnetic effects (linked to $\delta B_\|$). Analytical solutions are obtained in the long-wavelength limit for a large-aspect-ratio, circular tokamak, including first-order finite-Larmor-radius (FLR) and finite-orbit-width (FOW) effects.<br>For the first time within a gyro-kinetic framework, our analysis yields the complete 3D magnetic perturbation structure of the electromagnetic GAM. The results explicitly demonstrate that the radial ($\delta B_r$) and poloidal ($\delta B_\theta$) perturbations exhibit a dominant $m=2$ standing-wave structure, while the parallel perturbation ($\delta B_\|$) exhibits a dominant $m=1$ structure. This spatial structure is in excellent qualitative agreement with the predictions of ideal MHD theory, thereby resolving the long-standing discrepancy between the two theoretical approaches. Moreover, the gyro-kinetic model provides a refined physical picture beyond the reach of single-fluid MHD. The analytical expressions reveal distinct roles of ions and electrons: the $m=2$ radial and poloidal magnetic field perturbations, associated with parallel currents, are more strongly influenced by the ion thermal pressure, whereas the $m=1$ parallel magnetic field perturbation, linked to diamagnetic effects, receives a relatively larger contribution from the electron thermal pressure. These results not only unify the theoretical description of GAM magnetic perturbations but also advance our understanding of their kinetic physics, offering a more accurate foundation for experimental diagnostics and numerical simulation.

Recent advances in crosstalk simulation using integer-order memristive synapses have shown considerable progress. However, most existing models still employ a single-memristor structure, which constrains synaptic weight modulation and makes it difficult to represent both excitatory and inhibitory synaptic connections in a unified manner. These models also often fail to capture the memory effects and nonlocal dynamic properties inherent in biological neurons. To address these issues, this study introduces a fractional-order memristive bridge synapse model for crosstalk coupling. By combining Hindmarsh–Rose (HR) and FitzHugh–Nagumo (FN) neurons, we construct an 8D heterogeneous coupled neural network based on fractional calculus—designated as the Fractional-Order Memristive Bridge Crosstalk-Coupled Neural Network (FMBCCNN). A major innovation is the incorporation of a fractional-order memristive bridge structure that mimics synaptic connections in a bridge configuration. This design provides both historical memory characteristics and bidirectional synaptic weight regulation, overcoming limitations of traditional coupling forms.<br>Using dynamical analysis tools such as phase portraits, bifurcation diagrams, and Lyapunov exponents, we systematically investigate how synaptic and crosstalk strengths influence system behavior under conventional fractional-order conditions. The results reveal diverse dynamical behaviors, including attractor coexistence, forward and reverse period-doubling bifurcations, and chaotic crises. Further analysis under the more generalized condition of non-uniform fractional orders shows that, compared with the conventional case, the system maintains continuous periodic motion over broader parameter ranges and exhibits clear parameter hysteresis. Although local dynamic patterns remain similar, the corresponding parameter intervals are substantially widened. In addition, the system displays more concentrated and marked alternation between periodic and chaotic behaviors. We also simulate the effect of varying the fractional-order derivative, offering a more general mathematical characterization of neuronal firing activity.<br>Finally, the chaotic sequences generated by the system are applied to an image encryption algorithm incorporating bit-plane decomposition and DNA encoding. Security analysis confirms that the encrypted images have pixel correlation coefficients below 0.01 in horizontal, vertical, and diagonal directions, information entropy greater than 7.999, and a key space of 2<sup>2080</sup>. These results verify the excellent encryption performance and reliability of the proposed scheme and the generated sequences.

The manufacturing process of superconducting quantum processor chips faces unique metal contamination challenges, with significant differences in material systems and process characteristics compared to traditional semiconductor chips. This study focuses on the issue of metal contamination in the fabrication process of quantum chips, systematically analyzing the sources, diffusion mechanisms, and prevention strategies of metal contamination in quantum chips. It particularly emphasizes the bulk diffusion and surface migration behaviors of superconducting materials (such as Ta, Nb, Al, TiN) on sapphire and silicon substrates. The aim is to provide theoretical basis and technical references for process optimization, and to promote the industrialization process of quantum computing technology in our country.<br>The metal contamination in the fabrication of quantum chips is mainly caused by the metal film materials used in the process, the external environment, or the unintended metal impurity atoms introduced during the manufacturing process. Among them, some quantum chip components directly use superconducting metal materials. Unlike semiconductor chips, they cannot achieve front and back stage isolation, resulting in the continuous presence of metal surface migration channels, and there are exposed metal structures on the chip surface. Metal contamination often leads to two fundamental failure problems: circuit short circuits and leakage currents. These problems mainly result from the bulk diffusion of metal impurities in the dielectric layer and the migration behavior on the sample surface. The diffusion and migration rates of metals are affected by temperature, interface reactions, defects, and grain boundaries. The results show that the sapphire substrate, due to its dense lattice structure, exhibits excellent anti-diffusion performance, reducing the risk of contamination and providing a stable interface environment for superconducting quantum chips. For silicon substrates, special attention needs to be paid to the contamination risks posed by high-mobility metals such as Au, In, and Sn. Experimental verification shows that Ti/Au under bump metallization structures on silicon substrates are prone to Au penetration diffusion, and increasing Ti thickness does not significantly improve the blocking effect. The low-temperature process (<250 °C) and ultra-low-temperature operating environment (mK level) of quantum chips effectively suppress metal diffusion, but exposed metal surfaces and material diversity still pose unique challenges.<br>The study recommends establishing a dedicated metal contamination prevention system for quantum chips and proposes future research directions, including evaluation of novel materials, surface state regulation, and long-term reliability studies. This work provides important theoretical support and technical guidance for process optimization and performance enhancement of superconducting quantum chips.

Porous anodic aluminum oxide (AAO) films, due to their excellent dielectric, mechanical, and optical properties, have been widely used in electronic devices, catalytic supports, and optical materials. Anodization is the primary method for fabricating high-quality porous AAO films. The conductive behavior and mechanism of commonly used carbon rod counter electrodes are significant factors influencing the microstructure and properties of the films. In this study, a phosphoric acid solution with a mass fraction of 6% is used as the electrolyte, circular aluminum foil serves as the anode, and carbon rods are used as the counter electrodes spaced 15 cm apart. The oxidation time is fixed at 40 s. The conductive behaviors of the carbon rod under oxidation voltages ranging from 100 to 140 V are experimentally investigated. The results show that the pore depth and diameter of the AAO film symmetrically decrease from the film center toward the edges. When the oxidation voltage is below 110 V, the gradients of pore depth and diameter from the center outward are relatively small, resulting in a macroscopically uniform structural color. At an oxidation voltage of 110 V, the gradients of pore depth and diameter increase significantly, resulting in iridescent concentric ring structural colors. As the voltage increases further, the gradients become more pronounced, the number of structural color rings increases, and the visible color gamut significantly broadens. Electromagnetic and electrochemical theories are utilized to calculate the conductive behaviors of the carbon rod under different oxidation voltages and to analyze its conduction mechanism. The carbon rod is found to exhibit “quasi-point electrode” conductive characteristics, with the selection of point electrode positions on the carbon rod following the principle of minimizing the resistance between the two electrodes. This finding not only enriches the electrochemical theory of anodization but also provides theoretical and experimental support for fabricating multifunctional AAO films.