全國中小學科展

四等獎

正多角柱內皂膜的形狀與對稱性破缺

本研究旨在探討正多角柱內所產生之肥皂泡膜形狀,以及改變正多角柱邊長與高度比例時,所發生的對稱破缺的現象。在初步研究中我們發現,正五角柱內的肥皂泡膜確實存在對稱破缺的現象,因此我們希望進一步確認並理解箇中奧秘。我們的研究將以實驗觀測做基礎,然後在理論上配合最小曲面的面積近似解來分析,為了將實驗與理論作結合,我們透過免費的數學軟體GeoGebra來進行數值模擬計算以及圖形展示,並使用薄膜干涉測量討論皂膜的厚度,對皂膜受力的影響。

球形浮體於液面弧度微動力研究

不同於歷屆科展使用如浮沉子(2)、硬幣(3)、試管(5)等”沉體”在”凹”水面上對表面張力做研究,我們使用乒乓球作為”浮體” 並且於”凸”水面上做實驗,過去研究cheerios effect(6)的實驗多使用簡化的模型,忽略了沉體兩側的作用力只考慮沉體與容器邊壁的作用力,因此,我們強調的是,討論浮體兩側液面上因接觸角的差異所產生的水平側向力,並使用電流天平直接量測水平側向力的大小,我們釋放浮體使用影格分析法研究浮體的運動,最後我們得知浮體於液面上運動的機制。

滄海桑田-草漯砂丘沉積、侵蝕探討

草漯砂丘位於臺灣西北部沿海,為風成砂丘。本研究選擇此區高度最高的沙丘,藉由長期砂丘地形監測、砂丘表層及垂直方向沉積物取樣進行粒度及磁鐵礦砂含量分析,試圖了解草漯砂丘沉積及侵蝕狀況。監測砂丘自2011年9月中至2012年1月底間發現受風力侵蝕可達3公尺,侵蝕速率平均達8公分/天以上,2011年10月30日此沙丘進行固砂工程前後砂丘外形、侵蝕速率發生明顯變化,足見固砂工程對砂丘環境影響。垂直採樣分析9管沉積物粒度及磁鐵礦砂含量,發現四個特殊層,繪製成立體層面圖,發現類似沙丘滑落面地形,且藉由粒度及磁鐵礦砂分析也間接證明沙丘滑落面沉積現象。最後利用沉積物各層粗顆粒、磁鐵礦砂含量與中央氣象局提供之日均風速進行對比,推測9管沉積物應為2011年5月至9月間堆積。

伍拾元語音辨識系統

探討在低成本下,完成非特定人中文語音辨識的可行性,作品的特色如下: 1. 語音辨識系統:8K ROM、2.5K RAM、辨識率 80%、成本 50 元以下 2. 音節簡化:發音去掉聲音調後,再將同類聲音進行整併,整理出133 個音節→資料量是繁體13060 字數的 1 / 100 3. 資料庫化簡:使用整數的指數取代符點運算→資料量為傳統的語音特徵的 1 / 20 4. 語音辨識演算法:使用梅爾倒頻譜係數、隱藏馬可夫模型 5. 處理器:使用16位元的整數運算,可在低價的處理器上執行 6. 訓練用的語音:向中華民國計算語言學學會(MAT)購買純語音的資料庫

挑動心弦-弦長,圖心與新的圖形辨識

本文所探討的是建立一新的幾何描述模型,以過圖形內一點之弦長來描述圖形的特徵值,而其中牽涉到一客觀並方便求得的觀察點(我們稱之為圖心),即弦長標準差最小點,過此點所得弦長集合就是圖形的特徵值集合。我們先研究圓與橢圓的弦長標準差,利用過圓內一點之弦長函數的反函數求出累積分配與機率密度函數,再求得子樣本的期望值與標準差,並以聯合機率密度函數求出母體的分佈。關於不規則圖形的研究,本文先集中在不規則凸圖形。我們發現不規則凸圖形中弦長標準差大小竟然有規則性,而這規則性讓我們可以發展出『篩法』,利用層層篩子逼近弦長標準差最小點。本文最後以此模型比較蛋形、蛋圓、圓形三個圖形的相似性,得到令人滿意的結果。

"turn" -on (free food and renewable energy )

Nowadays Electric energy is the most useful in the world because we use it every day for lightening, work, entertainment ext … but electric energy also can be expensive and it will pollute the air plus we all know that the air pollution is getting worse. Our world consumes a huge amount of electric energy . Also we know that the homelessness is getting higher all around the globe and it reached a high percentage. The high price and the sudden cut of the electric energy and with it the air pollution makes a big problem. That’s why we created this project named TURN ON which is a friend of the environment and a friend of the humans. Our product will help us to produce and create strong, clean and renewable energy plus it will help the homeless to have free food and free transport tickets. After doing a lot of researches we found that our new method of producing energy gives a great electric energy and limit pollution. The kinetic energy is produced using rotations. That’s why we used the rotations of motorbikes, bicycles, cars wheels and turn that mechanical energy (wm) into electrical energy (we) that we can easily use in our daily life plus we can help homeless by giving them food widgets… in exchange with the electrical energy that they produced while using bicycles…After performing several tests and taking notes, we are able to conclude that our apparatus is indeed efficient as it is able to convert the rotation into electronic energy that we can store and use in emergencies to solve this big problem and in the same time to limit air pollution with using bicycles and reducing hunger regarding homeless. This machine should be easy to implement, cheap, does not depend on any other parameters such as the wind. Any rotation in any place can be a source of Electrical Energy. To facilitate the use of this new device, A START UP will be launched to rent electric bikes for “free”, distribute free food, snacks, tickets to homeless regarding to the energy production.

Robotic Search and Rescue

I built a robot that is able to improve safety in mines. The robot takes a series of sensor readings, do 3D mapping to compare deteriorating physical conditions in time, detect CO and CH4 levels and record video footage. All of this information is then sent back to the user. The project aims to build a robot that could decrease the amount of casualties in mines due to gas or instability. A strict engineering process, which comprised researching different features on a robot, was followed. A prototype robot was built, tested and improvements made. Some of the challenges faced, while building the prototype robot, included manoeuvrability over any type of terrain, even rough and rocky terrain. Choosing the correct driving mechanism (wheels, tracks, suspension and steering) also proved to be a very important feature that had to be kept in mind. The sensors used included, a temperature, humidity, carbon monoxide gas, as well as a methane gas sensor. A Gyro, Accelerometer and compass for easier navigation were also used. Two cameras which included a front camera for navigation and 3D mapping as well as a back camera for navigation were installed. The robot was tested over various terrains, it was able to retrieve sensor data and all of the engineering goals were reached. After the robot was built it was tested on various terrains. The robot achieved all of the engineering goals. The sensors was able to give readings, the robot 3D mapped an area and was also able to manoeuvre over rough terrain.

介面活性劑對電流變現象的影響

本研究在探討介面活性劑對二氧化矽電流變液在外加電場下黏度的影響。主要是用沉降法測試溶液的黏度。經甘油以及90%甘油水黏度的測量後,確定此方法可行。 測量二氧化矽電流變液的黏度後,發現黏度和電場的平方成正比。在電流變液中加入不同體積的介面活性劑triton X-100,發現介面活性劑體積百分濃度為3.75%、二氧化矽體積百分濃度20%和介面活性劑體積百分濃度為1.875%、二氧化矽體積百分濃度10%的流變效果最佳。研讀介面活性劑橋理論後,我推測造成上述差異是介於兩二氧化矽粒子間介面活性劑的量。當介面和法向量的夾角接近90度時其作用力為最大;而介面活性劑的量稍微多或少時,因為角度的改變,使其作用力減少而黏度減少。觀察電流變液中氧化鐵粒子在低電壓和高電壓的運動,發現粒徑較大的粒子在高電壓下無法運動,推測為高電場下鍊與鍊之間距離縮小造成。

多邊形的內接母子相似作圖與相關問題的研究

文獻上,要尋找任意多邊形的內接母子相似圖形,尚未有好的辦法可解決此問題,本研究,藉由多邊形的旋轉與伸縮觀念產生相似形的定理,作出多邊形內接母子相似圖形,並找到相關性質。 利用相關性質,我們得到: (1) 一般化的「內接母子相似作圖」法:可輕易過邊上一點、或過形內一點作出內接母子相似圖形。並找出最小內接母子相似及過形內一點三角形內接相似圖形的最多數量。 (2) 若 邊形存在內接母子相似圖形,則此 邊形必有「旋心」。反之,亦成立。 (3) 特殊四邊形(長方形、菱形、平行四邊形、等腰梯形、梯形、鳶形)存在內接母子相似形的條件。 (4) 探討多邊形具有內接母子相似圖形的條件。 (5) 建構出具有內接母子相似圖形的多邊形

一步合成碳奈米複合材料與奈米碳管應用於超級電容電極修飾

本研究以高溫鍛燒的褐藻酸鈉鹽與亞硫酸銨混合粉末作為電極修飾材料,並與多層奈米碳管(CNT)混合後,附著於碳紙極電板上。修飾材料中推測含有碳奈米纖維與碳量子點,其表面具親水性的含氧官能基,可提高CNT在水相中的分散性;而碳奈米纖維則推測可增加材料的機械強度,提升電極可撓度。研究藉由調整鍛燒溫度和氮材合成比例,探討不同變因下製造的電極修飾材料對電容效能的影響。 得知最佳鍛燒條件為:褐藻酸鈉鹽與亞硫酸銨1:1(重量比)、鍛燒溫度為160℃。利用此條件下製作出來的電極修飾材料,可以使實驗材料達到最高的比電容值324F/g。此製程大幅提升了奈米碳管的比電容值(對照組128F/g),期待未來能實際運用於電能儲存裝置上,或搭配電池應用於可撓式電子裝置。