2025年

研究指出⼿性有機硫催化劑能催化反應合成出⾼立體選擇性的產物，並有相關的研究指出以同族的硒取代⽽成的催化劑也有類似的性質，我們好奇兩者之間催化能⼒的差異處。本研究探討⼿性有機硒催化劑THSeOBn的合成，並將其應用催化形成氮環丙烷化物及環氧化物以探討其性質。本研究發現相較⼿性有機硫催化劑THTOBn催化，其催化形成氮環丙烷反應的dr 值及反應速率皆有顯著的上升，但其催化形成環氧化物的反應儘管反應速率有上升，但是dr值卻下降。最後本研究提出了關於THSeOBn催化形成氮環丙烷及環氧化物的反應機構。

本研究先觀察著名的密克定理（Miquel theorem）與密克點（Miquel point），我們創新給出了新的研究項目，關注密克點𝑃與密克三角形的頂點所構成直線和原三角形𝐴𝐵𝐶三邊直線的其餘六個交點，這是前人沒有觸及的研究項目，從而定義旁接三角形與衍伸三角形。 我們先針對特殊型（直角）的構圖，發現滿足兩個衍伸三角形的有向面積 [𝐴1𝐵1𝐶1]=±[𝐴2𝐵2𝐶2] 時，𝑃 點形成的軌跡為原三角形的 Kiepert hyperbola 與外接圓，這個是有趣且重要發現，我們也進一步給出其幾何必然性。進一步考慮 [𝐴1𝐵1𝐶1]=𝑟[𝐴2𝐵2𝐶2] 時，則刻劃出 𝑃 點軌跡為圓錐曲線系。在前面的基礎下，再針對一般型（任意角）的構圖，若 𝑃 點位於原三角形外接圓及Kiepert hyperbola 與 Steiner circumellipse 的線性組合曲線上，此時兩個衍伸三角形 𝐴1𝐵1𝐶1 與 𝐴2𝐵2𝐶2 的有向面積比值為定值，且兩者恆為相反數。

This paper presents a simplified but mostly accurate model for the acoustic mechanism of Seebeck sirens. We investigate the impact of key parameters, including the number and size of holes, as well as the angular speed of the disk, on the characteristics of the produced sound. The disk is fabricated using fused deposition modelling 3D printing, and we used a brushless motor, an air compressor, and a shotgun microphone to capture the generated sound. An order of magnitude analysis was conducted on the Navier-Stokes equation to formulate a simplified version. These simplifications allowed for a low computational intensity model relating volume flow rate to sound pressure level, which is used to predict the waveform of sound produced. Our findings reveal that the fundamental frequency of the sound can be precisely predicted by only the rotational frequency of the disk and the number of holes, a relationship validated experimentally. Notably, observed asymmetry in the waveform was attributed to skin drag effects, and this hypothesis was experimentally verified. Our model computes a solution in less than half a second on average: far less than the 21h 47min needed for a k−ω turbulent model to compute the same phenomenon. The research presents and verifies a simplified model of acoustic mechanics for the sound generated by rotating systems that require little computational resources, which can prove useful in situations where absolute precision is not required, in exchange for ease of computation. For more precise systems, this model serves as a foundation for quickly generating an initial design, paving the way for subsequent iterations using more comprehensive models. The developed model not only serves as a foundation for efficient preliminary designs but also contributes valuable insights into the intersection of fluid dynamics and sound production.

1.1 Short project summary My project involves the conceptualization and development of an innovative approach to modular self-assembling robotic systems. Through its ability to form any complex configuration, the system is highly adaptable to various scenarios and environments. Before delving deeper into the details of my project, I will provide an overview of my background and motivations. 1.2 Background Ever since I first watched the movie "Big Hero 6", I felt amazed by the applications of the so called “microbots”. From that point on, it made me always wonder what would be possible in the real world. When I did the research, I stumbled upon this field of modular robotics. Initially, I was unsure whether to embark on a project focused on electronics and robotics due to my background in programming. On the other side, this year gave me a chance to see the incredible performances of various projects at different science expos. Besides, I took part in the program of CANSAT LU and learned a lot during it, such as microchips, the control of miniature robotics, and the sensors of it. Finally, at school, I took the option Electronics where we dig into similar topics. With this accumulated knowledge and experience I felt confident enough to start this project.

Carbon capture and storage technology (CCS) has tremendous potential to enable the use of fossil fuels while reducing the emissions of CO2 into the atmosphere, and consequently combating climate change. CCS faces several challenges such as energy consumption, cost, low practical applications and environmentally friendliness. This research presents the first carbon capture device capable of capturing CO2 while generating green energy. By integrating advanced materials science with sustainable energy principles, the device addresses the dual challenges of CO2 mitigation and renewable energy production in a single, cost-effective platform. Beyond its technical innovations, this research highlights the device’s scalability and potential to revolutionize carbon capture deployment. The device can be integrated into industrial emissions systems, transportation systems, urban infrastructure, or even wearable technologies, providing versatile applications across different sectors. Furthermore, the device’s lightweight and flexible form factor ensures accessibility as it improves the applicability of CCS technology in remote or developing regions. This study demonstrated a novel approach to carbon capture by implementing carbon capture into a thin-film moisture electricity generator. The developed thin-film supercapacitor successfully demonstrated the capacity for supercapacitive swing adsorption of CO2, which is a relatively novel approach to CCS that is cheap, environmentally friendly, and efficient while generating green energy from ambient humidity.

Wind energy is one of the most promising and rapidly growing sources of renewable energy, although maximizing its efficiency while minimizing noise remains a challenge and limits its widespread adoption. The emergence of toroidal propellers, which have gained popularity for producing comparable thrust levels to traditional drone propellers while producing less noise, could mitigate this. This study aimed to develop a small-scale toroidal HAWT and compare its power and noise output to a conventional rotor design under similar wind velocity conditions. 15-centimeter diameter models of the toroidal and conventional rotors were created in Fusion 360 and simulated using Ansys Fluent to identify the significant aerodynamic characteristics that positively affect the blades’ power coefficient. The toroidal design with the greatest simulated power output at low tip speed ratios (TSRs) was then 3D printed and physically tested in a wind tunnel against the control rotor. The experimental results confirmed that the toroidal design had greater power coefficients at lower TSRs compared to the control rotor. The toroidal rotor started operating at a wind velocity of 3 m/s compared to the control rotor’s 6 m/s, which indicates superior start-up characteristics. While the toroidal rotor produced half the power output of the control at the highest tested wind speed of 7 m/s, it emitted 18 decibels less noise and showed a reduction in discernible noise between frequencies of two to five kilohertz. The results from this study show its potential in low-noise wind turbines within low-wind velocity environments.

One of the main factors that contribute to fire incidents and the excessive heat people feel during a heat wave is the building materials used, and one such material that possesses durable and heat-resistant properties is sandwich panels. A possible structure that can be used to model sandwich panels is honeycomb structures; however, further research has yet to be conducted on its applications as a heat-resistant urban construction material. This study aims to design a three-dimensional model of a honeycomb sandwich panel and simulate its performance under different thermal and structural stressors. A 3D model of the honeycomb sandwich panel was generated using Autodesk Fusion 360. Then, multiple versions of the panel were generated with varying heat-resistant core materials—namely, aluminum, nickel, nickel-copper alloy 400, and copper—along with polystyrene as the core material for the control model. The following properties of every panel were assessed using finite element analysis (FEA): static deformation, stress distribution, strain distribution, total heat flux, and thermal gradient. Results showed that when subjected to varying structural loads (2 kN, 5 kN, 7 kN), the nickel-core panel demonstrated the best results in terms of static deformation and strain distribution due to its relatively lower deformation and elongation values, respectively. Meanwhile, under the same structural loads, the aluminum-core panel performed better than other core materials in terms of stress distribution due to it having the relatively highest difference between its simulated von Mises stress and its yield strength. The honeycomb sandwich panels have also shown to possess heat-resistivity when subjected to a thermal load of 90°C, with polystyrene being the most promising material overall in terms of heat-resistance due to its relatively lower heat flux and thermal gradient. The results from this study would contribute to future research on honeycomb sandwich panels and may be used in real-life applications.

The equation of an ellipse and quadratic residues are well-known concepts in elementary geometry and number theory, respectively. While the properties of ellipse equations in Euclidean space have been extensively studied, many characteristics of quadratic residues, such as consecutive quadratic residues, have also been explored in past research. In this study, we discovered the characteristic polynomial of the equation of an ellipse over finite fields Fp, a single-variable polynomial that shares the same roots as the ellipse. Furthermore, by examining the parallels between the equation of an ellipse and the pairs of residues and nonresidues, we derived a characteristic polynomial for this concept and demonstrated its connection to the Catalan number, a significant sequence in combinatorics. This research was conducted through the following steps. First, the power sums of the roots of the ellipse in Fp were calculated using the Legendre symbol and Euler’s criterion. Next, the characteristic polynomial of the ellipse was determined using Newton’s identity, generating functions, and Vieta’s theorem. Finally, leveraging the equivalence between the equation of the ellipse and the pairs of residues and nonresidues, we established the main results connecting these two concepts with Catalan numbers.

本研究開發一種新穎孔洞性吸附材料：金屬有機骨架 (MOF)。MOF 在反應溶液中自組裝形成孔洞結構，透過物理吸附有效捕捉氣相乙酸分子。研發出綠色、快速可在常溫常壓下大量合成三種MOF（HKUST-1(Cu)、UTSA-280(Ca) 及 A520(Al)）方法。此外，為提升材料機械強度和應用價值，採用 PVA 聚合技術製備 MOF 複合物，使其造粒型化更易處理，提升商業和環境應用價值。吸附實驗結果顯示，HKUST-1(Cu) 粉末對乙酸移除率高達98%，而HKUST-1(Cu) PVA 複合物達93%，對比活性碳及其PVA複合物（移除率分別為85%和78%）表現更優異。MOF憑藉優異吸附性能和可大量生產低成本優勢，成為極具潛力有機無機氣體吸附劑，可為半導體產業提供一種維持高標準製程環境精密且簡便解決方案。

隨著網路技術不斷的進步，意見和情感分析逐漸成為人們日常生活中的一部分。儘管如此，目前人們缺乏一個方便且快速的情緒分析模型，供廣大大眾使用。 本研究旨在提供人們一個緩解憂鬱情緒的管道——當人們輸入一個需要被安慰的情境時，我們的系統將輸出安慰語句，以緩解該使用者之憂鬱情緒，達到安慰效果。為此，本研究訓練了BERT model以及 LLaMA model。BERT model能判斷使用者輸入的語句是否為需安慰語句。而LLaMA model則作為安慰語句之生成模型，以達到安慰之效果。