In this project, I investigated the aerodynamic load acting on an igloo structure when it is subjected to different wind angles. By using Computational Fluid Dynamics (CFD) simulations on COMSOL Multiphysics, I first analyzed a simple 2D cylinder case as a way to learn the software. After that, I studied a sample CFD case of a NACA 0012 airfoil that is published under the COMSOL website. Finally, I moved on to create my own igloo CFD case to study its aerodynamic load under varying wind angles (0-30 degrees in 3-degree increments). Understanding the aerodynamic load of this sample igloo can be useful in learning how igloos behave in extreme weather conditions and fast wind velocities. It is also beneficial to know when will the igloo experience the least force when built under a non-level surface and the wind is hitting the structure at an angle.

Maritime Cruises Mini-Submarines (MCMS), a company based in Greece, aims to offer safe and deep-sea exploratory experiences to tourists. This paper discusses the primary challenges involved in ensuring tourist safety, particularly focusing on maintaining security in scenarios of mechanical failures or lost communication with the main vessel. We propose comprehensive safety protocols and technological solutions tailored for deep-sea tourist submersibles. The analysis begins with a detailed study of the forces acting on a submersible, considering both operational modes and the impact of ocean currents, utilizing a rigid-body coordinate system and Eulerian angular coordinate transformations to describe the submersible’s motion comprehensively. We derive motion and safety parameters by solving the force differential equations, allowing the host ship to predict the submersible’s position accurately. In addressing the recovery of lost submersibles, our approach evaluates power loss scenarios and search efficiency, recommending an optimal combination of hydroacoustic and frequency-hopping communication technologies for reliable, low-loss data transmission. We further enhance search methodologies by integrating motion parameters and ocean current dynamics to pinpoint probable locations, adjusting search strategies dynamically based on real-time data, and employing probabilistic models to optimize resource allocation during search operations. A case study in the Caribbean Sea exemplifies applying these methodologies, incorporating localized flow regimes and cooperative communication strategies among multiple submersibles to improve operational efficiency and safety.

This paper delves into three fundamental numerical methods and computational techniques in financial mathematics: Finite Difference Methods (FDM), Monte Carlo Simulations (MCS), and Machine Learning (ML) applications. Finite Difference Methods are widely utilized for solving partial differential equations (PDEs) in option pricing, with various schemes offering different stability and convergence properties. Monte Carlo Simulations provide a powerful approach for pricing complex derivatives and risk management, addressing the challenges of high-dimensionality and computational complexity. Machine Learning has revolutionized predictive modeling in finance, enabling sophisticated analysis of large datasets to uncover hidden patterns and enhance trading strategies. Through a detailed examination of these methods, including specific examples and data, this paper highlights their theoretical foundations, practical implementations, and the advancements they bring to computational finance. By bridging theoretical approaches with practical applications, we aim to offer insights into the future directions and challenges in financial mathematics.

Innovation drives modern industry and enhances enterprise competitiveness. Despite China's progress, evident by its 14th position in the Global Innovation Index 2020, a gap remains compared to Western developed nations. Enterprises are key to national innovation, especially in the rapidly evolving tech landscape. Big data presents new opportunities and challenges for innovation. This study explores how enterprises can leverage big data to improve innovation outcomes, identifying factors that influence this process. Grounded in resource-based and social network theories, the research employs questionnaires to assess big data analytic capabilities, external network relationships, and innovation performance. Using hierarchical regression analysis and reliability tests, findings reveal that foundational and management capabilities of big data significantly impact innovation, while technical capabilities do not. External network relationships partially mediate this effect. The results offer insights for managers on utilizing big data and strengthening external ties to drive innovation and competitive advantage.

With the promotion and application of big data, mathematical models are also more widely referenced in the research and development of different professions. In this paper, the relationship between mathematical modeling and social sciences will be explored by examining the application of mathematical modeling in social sciences through quantitative analysis. In addition, the author is willing to learn about different models related to economics, psychology, and sociology. Based on the analysis, this paper provides relevant suggestions for solving potential problems in the application of models, including, that attention should be paid to the description of contextual details, that the results of the study should take into account motivational factors, and that the data involved must be valid and not too superficial.

Tackling the complexity of particle interactions, this investigation introduces a unified computational methodology employing Moldy, Gnuplot, and Visual Molecular Dynamics (VMD). Inspired by the n-body problem's persistent intrigue, specifically the three-body dynamics within molecular systems, we leverage Molecular Dynamics (MD) simulations to forecast and scrutinize the nuanced behavior of atomic and molecular entities. Moldy, a flexible MD software, facilitated the simulation of particle trajectories and interactions across diverse scenarios, with meticulous documentation of the resulting data. For visual analytics and insight extraction, Gnuplot crafted detailed plots depicting kinetic and potential energies alongside other thermodynamic metrics over temporal scales. The integration of VMD culminated in our analysis by vividly portraying the molecular motions, enhancing comprehension of emergent patterns. This study not only endorses Moldy's precision in MD simulations but also highlights the potent alliance among simulation, analysis, and visualization in elucidating intricate particle interactions. In summary, our work underscores the efficacy of the Moldy-Gnuplot-VMD triad as a formidable resource for scientists engaged in molecular motion prediction and analysis, paving fresh paths in computational physics and chemistry research.

This review provides a comparative analysis of atmospheric circulation across four planets in our solar system: Venus, Mars, Jupiter, and Earth. By examining the unique characteristics of each planet, including atmospheric composition, rotation rates, axial tilt, and solar radiation, the study explores how these factors influence the dynamics of their respective atmospheres. Venus, with its dense CO₂ atmosphere and slow retrograde rotation, exhibits a super-rotating atmosphere leading to extreme and uniform climate conditions. Mars’s thin atmosphere and significant seasonal variations, combined with global dust storms, result in highly variable and dynamic atmospheric patterns. Jupiter’s rapid rotation and internal heat contribute to complex and powerful atmospheric dynamics, including strong jet streams and long-lasting storms like the Great Red Spot. In contrast, Earth's atmospheric circulation is driven by a combination of solar radiation, rotation, and the presence of oceans and continents, resulting in relatively stable and predictable weather patterns. The study highlights the diversity of atmospheric processes within our solar system, providing insights that are crucial for understanding planetary climates and assessing the potential habitability of exoplanets.

Mathematics is a fundamental science and a problem-solving method that plays an important role in revealing the essential laws of the development of certain things. It has rigorous logic, high abstractness, and wide applicability. This brings great difficulties to enterprises, especially high school mathematics because it involves a wide range of knowledge points and complex calculations. Among them, the formation of financial mathematics has greatly promoted the development of China's financial industry. Moreover, in solving financial problems, relevant knowledge and theories of mathematics can be used to analyze and explore financial laws, and the application effect is significant, for example, using deterministic mathematical method and nondeterministic mathematical method to solving question about financial investment and returns; building securities investment portfolio model or asset valuation model to calculating and expressing some economic models. Based on this, this article discusses the application of mathematical knowledge to several financial problems, analyzes the current problems, and looks forward to the future of financial mathematics.

In high-speed ground racing cars, the aerodynamics of the tail wing are crucial as they directly affect the overall performance and results of the car. In the aerodynamic performance of the tail wing, down force and drag are the two most important parameters. In order to study the specific effects of factors such as racing speed, tail wing profile, and tail angle of attack on the aerodynamic performance of the tail wing, fluid dynamics numerical simulation methods were used for research.The research results indicate that within the parameter range of 160km/h to 240 km/h, both resistance and down force continuously increase with the increase of speed, and show a typical linear variation pattern. Within the range of 0 ° to 35 ° angle of attack, both drag and down force increase, but within 20 °, the increase in down force is faster, and once it exceeds 20 °, the increase in drag becomes more pronounced.At the same time, four different airfoil structures were compared and analyzed, and it was concluded that the NACA airfoil is more suitable for low-speed operating conditions, as it can generate higher down force at lower speeds. The research results of this article provide certain reference value for the design and finalization of racing tail fins.

High-fidelity audio signal processing plays an important role in modern audio technology. With the increasing demand for this technology in various audio application scenarios, the optimization of adaptive filters has emerged as a significant challenge in this field. This paper focuses on improving the performance of adaptive filters in high-fidelity audio signal processing which aims to improve the adaptability and efficiency of filters in complex audio environments by improving algorithms. In this study, the adaptive filtering algorithm based on wavelet transform and particle swarm optimization is used to verify the audio data processing by simulation and real data processing. The research data was collected using the standard audio signal database and the actual collected high-fidelity audio samples. The results show that the improved adaptive filter can significantly improve the performance of complex audio environments, improve the clarity and fidelity of audio signals and reduce the computational complexity. It is also suitable for real-time processing scenarios with limited resources. The conclusion shows that this method provides an efficient solution for high-fidelity audio signal processing and has a wide application prospect.