The rapid evolution of X-ray critical dimension (XCD) metrology demands an accurate and efficient forward model that describes the interaction between incident X-rays and nanostructures under test to support high-throughput experimental data analysis. However, the intricate design of high-aspect-ratio (HAR) nanostructures poses significant computational challenges to the forward model. In this work, we propose a semi-analytical method based on Green's theorem for fast and accurate calculation of small-angle X-ray scattering spectra from HAR nanostructures. Compared with conventional numerical approaches such as the non-uniform fast Fourier transform, the proposed method significantly reduces the number of required sampling points while maintaining high numerical accuracy and stability. Benchmark simulations demonstrate that the method yields a baseline speedup of one to three orders of magnitude over existing techniques, while consistently achieving relative errors below 1%, even for geometrically complex structures. Further acceleration and optimization strategies are also discussed, through which the overall speedup can be extended to two to four orders of magnitude on the current platform. These results highlight the potential of the proposed method as a powerful tool for rapid modeling and large-scale synthetic dataset generation for advanced XCD applications.
Breaking the electric-dipole selection rule in molecular spectroscopy is of great significance for manipulating vibrational state transitions and developing unconventional photofunctions of molecules. In this study, a static plasmonic nanocavity composed of a gold (Au) nanosphere on a silver (Ag) substrate was excited using a radial vector beam with a tunable spatial frequency component. The resulting nanocavity-plasmonic mode has a significantly enhanced electric-field gradient to visualize the electrical-quadrupole transition in the molecule. The static plasmonic nanocavity is tunable by regulating the spatial frequency component of the excitation beam. Thus, the interaction between the electric field/electric-field gradient of the nanocavity-plasmonic mode and the molecular polarizabilities has been accurately identified. This innovative nanospectral platform provides unique opportunities for studying weak physical and chemical processes in molecules.
The deepening processes of globalization and industrialization have given rise to widespread disparities in regional economic development across countries worldwide. As a result, differences in resource endowments, industrial structures, and policy support among regions have led to significant disparities in economic growth rates and development levels. This study investigates the factors behind regional economic disparities and how economic development and population mobility influence each other, highlighting how variations in industrialization, resource distribution, and market-driven economic clustering contribute to the expansion of regional gaps. Through a literature review and comprehensive analysis, the study compares representative regions such as the United States and the European Union to identify the key factors driving regional economic differences and the economic feedback effects of population migration. The results show that differences in industrialization speed, unequal fiscal and financial resource distribution, and market agglomeration effects are the main reasons for the expansion of regional economic disparities. Thus, developed regions, with well-established infrastructure and public services, attract large population inflows, as opposed to less-developed regions, experiencing persistent outflows of capital and talent. At the same time, moderate migration supports resource allocation and industrial change, while excessive inflow strains housing, transport, education, and the environment.
With the frequent occurrence of social emergencies, inflation has become a worldwide concern. To solve this problem, the article analyzed the influence of the policy of raising and lowering interest rates. The most important thing is finding the best method to reduce the inflation problem. The article selected and analyzed the impact of two monetary policies on domestic and foreign countries, and it was supported by Keynesian theory and Fisher's equation. The result showed whether hiking or cutting interest rates alone influences the economy. To maintain the stability of the money supply, it is necessary to alternate interest rate hikes and interest rate cuts to ensure the balance of the money supply. The method is significant to maintain the healthy development of the global economy, As the economic landscape continues to evolve in complexity, ongoing research and adaptive policymaking will prove indispensable in navigating these challenges effectively and continued exploration and refinement of these strategies also will be key to fostering resilient global economies.
The environmental impact of civil aircraft noise has increased, adversely affecting airport operations and the health of nearby residents, and representing a major barrier to the aviation industrys green development. This paper aims to systematically explore the main noise sources and their variation characteristics of civil aircraft during different flight stages such as takeoff, cruise and landing, and to clarify the evolution mechanism of typical sound sources. By reviewing recent research, this paper explores three mainstream noise reduction methods, including airframe noise reduction with passive damping and multi-layer sound absorption, engine noise control via bypass ratio optimization and acoustic liners, and active control systems for cabin and external areas. The results show that, despite success in some frequency ranges, current technologies still face issues with cost, structural integration, and operational energy use. As such, it further explores future development paths like additive manufacturing, intelligent control systems and alternative fuels, and points out that civil aviation noise control will tend towards the integrated evolution direction of multi-system coordination and structural intelligence integration, providing technical references for the design of low-noise green aircraft.
