全國中小學科展

2021年

空間中的福特球

本研究旨在探討由法里數列生成的福特圓、以及與其有相似性,但是三維(或更高)的福特球的相關性質,我們分成三個部分來探討。一、首先我們驗證福特圓的衍生方式是否與法里數列相符合,並發想出另一種福特圓的衍生方法;二、以類似福特圓的方式,定義三維中的福特球、推導出以三顆球衍生第四顆球的公式、且限制其衍生的範圍,爾後由同一方向(以最新三顆球作衍生)、固定某一個球(固定某顆球,以最新兩顆球和固定球衍生)等方式衍生,並且利用空間中的索迪公式,對其半徑倒數與配合半徑倒數化繁後的x、y分子的遞迴關係式作探討;三、在高維度中,同樣定義出福特球(並非球體,只是敘述上方便的統稱),利用索迪公式對同一方向衍生的半徑倒數數列的遞迴關係式來探討。

Design and Prototyping of a Low-Cost Ventilator for Rural Hospitals

This report includes the design and prototyping of a portable automatic bag-valve mask (BVM), or commonly known as the Ambu bag. This development is for use in emergency transport, resource-poor environments, and mass casualty cases like the COVID-19 pandemic. This device replaces the need for human operators whose job is to squeeze the BVMs for extended periods of time. The prototype is made from a stainless-steel skeleton, measuring 470 x 240 x 230 mm, with the addition of acrylic coverings. A repurposed motor from a car is used to drive the squeezing arm. The speed of the arm for inspiration and expiration along with the pausing time between each breath can be adjusted with this prototype. It also features an LCD screen to display the arm speed, along with real-time pressure graph displayed on both phones and computer monitors. For future versions, an app is to be developed to enable the control of the automatic bag-valve mask from phones and tablets, further creating ease for users and increasing portability. Additionally, important requirements will be added: alarm system for over pressurization, control for inspiration to expiration ratio, number of breaths per minute, control for tidal volume, pressure relief valve, and assist-control mode. The cost of this prototype is approximately $430. With this design of an automatic BVM, it allows for the production of a ventilator-like technology that will be able to perform main functions of basic ventilators at a fraction of the current cost.

Direct reductive amination of camphor

Terpenoids are an irreplaceable class of natural products. The camphoryl group is an important moiety in the structure of chiral ligands for asymmetric synthesis catalysis or it can be used as an auxiliary group in asymmetric synthesis.[1] The usage of fenchone based molecules for asymmetric catalysis and synthesis is less common because of the difficulty of fenchone modifications due to steric hindrance. Camphor is a readily available starting molecule for the preparation of different compounds with biological activity. For example, camphor diimines demonstrate antiviral activity.[2] Fenchonyl amine-based molecules are potential therapeutic agents for the treatment of Alzheimer’s disease. Amines are a crucial class of organic compounds with multiple academic and industrial applications. There are a plethora of synthetic approaches towards amines synthesis and modifications, reductive amination being one of the most powerful and useful methods. However, the reductive amination of camphor and fenchone remains a challenge. A standard approach to reductive amination with amines other than ammonia and methylamine includes two steps: preparation of azomethines or Schiff bases in the presence of strong Lewis acids and their reduction with more or less conventional reducing agents. The synthesis of fenchonyl amines is even more challenging. There is no universal approach, and almost every manuscript reports some particular protocol different from others. In most cases, the first stage of this process requires quite harsh conditions. For example, the preparation of a Schiff base from camphor and 1-phenylethylamine requires 5-10 days of heating at 150°C.[3] Schiff bases of other primary amines could be prepared under similarly harsh conditions. Preparation of enamines is possible using titanium tetrachloride as a catalyst. The reduction also might be challenging. Sodium borohydride or sodium cyanoborohydride was described as suitable for this goal in several reports.[4] To the best of our knowledge, no papers describe any general approach for the direct reductive amination of camphor or fenchone. There is only one example of camphor direct reductive amination without an external hydrogen source using carbon monoxide as a reducing agent. This protocol is very efficient but its application is limited by the necessity of carbon monoxide and high-pressure equipment for the reaction setup.

往事重「堤」看頭城—突堤效應

突堤效應是指人工建構物突出於海岸,延伸而出,阻擋原先海流和海岸積沙的路徑,造成沙子在上游堆積,而下游原先有沙岸的地區則因為沙子量逐漸減少,侵蝕大於堆積,逐漸出現海岸遭受破壞。突堤效應會造成堤前堆積、堤後侵蝕的情況。因為突堤效應造成的結果,頭城濱海森林公園(原頭城海水浴場),在這十多年中,原本的沙灘現在已完全被海水覆蓋。 本校位於頭城濱海森林公園附近,看到頭城濱海森林公園的海沙在烏石港建後己經流失不見,藉由本實驗瞭解突堤效應確實存在,壩堤長短、角度和洋流速度皆會影響壩堤前後堆積與侵蝕的速度,在實驗後我們對頭城烏石港所造成的突堤效應提出三大改善方案:一、縮短烏石港壩堤的長度100公尺;二、在原壩堤北側加蓋105度的壩堤;三、綜合後的方案會是減緩突堤效應的最佳策略。

Development of a rotor blade with optimized aerodynamics to propel a quadcopter

Sustainable mobility concepts are playing an increasingly important part in today's social developments. As a promising mode of future transportation, quadcopters play a special role, and their further development and optimization is being advanced along many disciplines. Even in my hometown of Zurich this trend has not passed by without leaving its marks. Since 2019, the Swiss National Postal Service has been testing autonomous means of transport together with the Zurich University Hospital as part of a pilot project. However, quadcopters are not exclusively used for transportation purposes. Geologists use them for landscape modeling and the insurance industry utilizes them for damage assessment. Quadcopters have also become an integral part of photography and agriculture, where they are used for pest control, for example [2]. I first became intensively involved with quadcopters in 2017, when I received a hobby model for my birthday in the form of the Mavic Pro from the Chinese company Da-Jiang Innovations Science and Technology Co., Ltd (DJI). In October of the same year, I completed an internship in the biofluid mechanics department of the Institute for ImplantTechnology and Biomaterials e.V., where I studied the aerodynamics of airfoils. With my Mavic Pro in my backpack, I had the idea to develop and prototype my own functional rotor for my quadcopter as part of my upcoming Swiss Matura thesis paper. The rotor would be considered functional if it generates enough lift to keep the quadcopter hovering. The focus of this project was the investigation of aerodynamic properties. The influence of other factors, such as the material used, was not the primary focus of the work and therefore not investigated in detail.

Safety First:分析商場內部貨架擺設

在實體店鋪進行限時搶購活動 (Flash Sale),近年來已逐步在世界各地快速散播。在這樣的閃購活動期間,商場往往會宣傳銷售商品的巨幅折扣,吸引消費者。消費者在閃購的活動期間,爭先恐後的進入商場,過程中,除了可能造成消費者的傷害外,亦有可能造成商品本身的損傷。 本研究發想自第六屆數學建模挑戰賽之國際賽題。首先,本研究分析了商品損壞的各種方式。第二,本研究用虛擬的商品列表,與一個虛擬的商場平面配置圖作為規劃範例。第三,繪製並配對完貨架與商品後,運用賽題中的專家評分、剩餘數量等數據,寫出了每個商品的平均歡迎指數。第四,建立數學函式,計算路徑風險值,並藉由定量分析預測,成功地判斷哪一個以及哪一些商品的受歡迎程度會較高。最後,提出了優化於賽題給予的平面配置圖方式。

Synthesis of Macro Porous Activated Carbon from Waste Polyethylene Terephthalate (PET) Bottles and Investigation of Usability in Dye Removal from Water Sources

Colorants are used in many industries, especially in the textile industry. These substances both cause visual pollution and create an anaerobic environment for aquatic creatures. In this study, it is aimed to examine the usability of activated carbon synthesized from waste polyethylene terephthalate (PET) bottles, which is an important environmental problem, in removing the pollution caused by the colorants caused by industrial activities in water resources.

An In-Depth Patch-Clamp Study of HCN2 Channel (Year II): Discovery of Novel Biomarkers and Therapy for Ih Current Suppression in Autism Spectrum Disorders

The main goal of this study was to address a variety of topics concerning the role of the Ih current in HCN channels of SHANK Wild-Type and Knock-Out Thalamus Neurons (as described further below). This research explored the cellular effects of sedation (like Dexmedetomidine) and laser light stimulations on the Ih current of neurons, as well as discovering novel biomarkers for detecting Autism Spectrum Disorder. This study also showed that methods (like utilizing laser therapy with and without various photosensitizers) have the potential in raising depressed Ih currents of SHANK Knock-Out neurons.

記憶猶新-Scopolamine 對斑馬魚記憶能力與社交行為的影響

東莨菪鹼 (Scopolamine) 是一種乙醯膽鹼受體的拮抗劑,如果服用過量的Scopolamine,可能產生記憶障礙的症狀,所以Scopolamine常作為讓實驗動物記憶能力下降的藥物。近年來全球人口老化速度快,像是阿茲海默症等疾病患者與日俱增,研究記憶的相關機制或能恢復記憶的治療方式成為重要課題。希望本研究能對Scopolamine的作用有更多了解,作為未來以此藥物當作前置實驗藥物的參考。斑馬魚 (Danio rerio) 是一種群居動物,牠們會依據對彼此的熟悉程度而調整未來的社交行為,所以能夠辨識並且記得曾經看過的魚對牠們十分重要。因此本研究選擇斑馬魚作為實驗動物,錄影觀察藥物對牠們記憶和社交行為的影響。 本研究將以斑馬魚的社交記憶 (Social recognition memory) 為主題,探討Scopolamine對斑馬魚學習與記憶能力的影響,以及受藥物影響後的社交行為改變。實驗藉由錄影觀察斑馬魚浸泡Scopolamine 溶液後的行為改變,包括電擊、社交偏好,群游,攻擊性實驗,推測Scopolamine有降低學習能力並在學會的情形下增強記憶的效果,而且能改變斑馬魚的部分社交行為。

利用VAE-pix2pix生成擬真的山脈模型

本研究利用NASA的SRTM 1 Arc-Second資料集來收集全球各地的地形高度圖(heightmap),也利用MapTiler網站收集相對應的衛星空照圖,用這些收集的圖像,訓練我們建構的VAE-pix2pix模型。VAE-pix2pix為Variational Autoencoder (VAE)及pix2pix (為一個Conditional Generative Adversarial Network)結合的模型,能將人工繪製的高度圖加上真實山脈應有的細節(包含尖銳的山脊、山壁上的紋路、連續的河流網路等……),並生成出相對應的擬真衛星空照圖。相較於原pix2pix模型,VAE-pix2pix所生成的高度圖及衛星空照圖會更接近於真實世界的地形高度圖及衛星空照圖,同時VAE-pix2pix模型也能透過改變latent code的數值來生成出不同風格的高度圖及空照圖,如地貌的顏色或雪線的高度等,這些都增加模型生成圖像的多樣性。為了使我們建構的模型能更廣泛的被應用,我們在Unity上開發了Unity客戶端,其生成的mesh可以讓使用者直接應用於遊戲的場景,簡化了遊戲中生成擬真山脈模型的任務。