In this study, the coupled ordinary differential equations for the galloping of the first two modes in iced bundled conductors, including in-plane, out-of-plane, and torsional directions, are derived. Furthermore, through numerical analysis, the critical conditions of this modal galloping are determined in the range of wind speed–sag parameters, and the galloping patterns and variation laws in different parameter spaces are analyzed. The parameter space is then divided into five regions according to the different galloping modes. Under the multimodal coupling mechanism of galloping, the impact of single and two kinds of coupled mode galloping on the spatial nonlinear behavior is explored. The results reveal that the system exhibits an elliptical orbit motion during single mode galloping, while an “8” motion pattern emerges during coupled mode galloping. Moreover, two patterns of “8” motion are displayed under different parameter spaces. This research provides a theoretical foundation for the design of transmission lines.

An aircraft that has been carefully optimized for a single flight condition will tend to perform poorly at other flight conditions. For aircraft such as long-haul airliners, this is not necessarily a problem, since the cruise condition so heavily dominates a typical mission. However, other aircraft, such as Unmanned Aerial Vehicles (UAVs), may be expected to perform well at a wide range of flight conditions. Morphing systems may be a solution to this problem, as they allow the aircraft to adapt its shape to produce optimum performance at each flight condition. This study proposes an aerodynamic optimization framework for morphing airfoils by integrating Principal Component Analysis (PCA) for geometric dimensionality reduction and deep learning (DL) for surrogate modeling, alongside an optimization-guided data augmentation strategy. By employing PCA, the geometric dimensionality of airfoil surfaces is reduced from 24 to 18 design variables while preserving 100% shape fidelity, thus establishing a compressed morphing parameterization space. A Multi-Island Genetic Algorithm (MIGA) efficiently explores the reduced design space, while iterative retraining of the surrogate model enhances prediction accuracy, particularly in high-performance regions. Additionally, Shapley Additive Explanation (SHAP) analysis reveals interpretable correlations between principal component modes and aerodynamic performances. Experimental results show that the optimized airfoil achieves a 54.66% increase in low-speed cruise lift-to-drag ratio and 10.90% higher climb lift compared to the baseline. Overall, the proposed framework not only enhances the adaptability of morphing airfoils across various low-speed flight conditions but also facilitates targeted surrogate refinement and efficient data acquisition in high-performance regions.

Carbon-based nanomaterials with excellent electrical and optical properties are highly sought after for a plethora of hybrid applications, ranging from advanced sustainable energy storage devices to opto-electronic components. In this contribution, we examine in detail the dependence of electrical conductivity and the ultrafast optical nonlinearity of graphene oxide (GO) films on their degrees of reduction, as well as the link between the two properties. The GO films were first synthesized through the vacuum filtration method and then reduced partially and controllably by way of femtosecond laser direct writing with varying power doses. Subsequently, the four-point probe measurements of the reduced-GO (r-GO) films were demonstrated to exhibit superior resistivity and electrical conductivity compared with the pristine-GO counterpart. It was found that the conductivity of the film increases and then decreases with increasing ablation laser power (P), and GO was completely reduced at P = 100 mW, with a resistivity and electrical conductivity of 1.09 × 10⁻³ Ω·m and 9.19 × 10² S/m, respectively. GO was over-reduced at P = 120 mW, with its resistivity and electrical conductivity being 3.72 × 10⁻³ Ω·m and 2.69 × 10² S/m, respectively. We further tested the ultrafast optical nonlinearity (ONL) of the as-prepared pristine and reduced GO with the femtosecond Z-scan technique. The results show that the behavior of ONL is reversed whenever GO is reduced in a controlled manner. More interestingly, the higher the ablation laser power is, the stronger the optical nonlinearity of r-GO is. In particular, the nonlinear absorption and refraction coefficients of the r-GO films reach up to 3.26 × 10⁻⁸ m/W and −1.12 × 10⁻¹³ m²/W when P = 120 mW. The nonlinear absorption and refraction coefficients reach 1.9 × 10⁻⁸ m/W and −3 × 10⁻¹³ m²/W, respectively, for P = 70 mW. GO/r-GO thin films with tunable photovoltaic response properties have potential for a wide range of applications in microelectronic circuits, energy, and environmental sustainability.