全國中小學科展

2018年

利用都卜勒效應探討美濃地震的破裂方向性

本研究使用一規模較小的地震做為參考地震並得出其頻譜,將測站測得的美濃地震頻譜與之比較得出頻譜比,消除場址效應等非震源效應產生的影響,以探究美濃地震的破裂方向性。就每一對對震央方位角相差 180 度的地震而言,如果兩測站收到的頻譜比差距愈大,就表示地震的破裂方向越可能是該對測站的方向。 本研究的研究結果顯示測站距離對測站測得的頻譜比影響可忽略,且該方法用於尋找地震的破裂方向性確實可行。本研究得出美濃地震的破裂方向約在300到320度(即西偏北30~50度),且隨時間無明顯變化,與其他研究得出的結果相符。

A Modular Comprehensive Assessment Platform for Aircraft Maintenance

We were very curious about whether the aircraft will suffer lightning damages during flight, so we tried to search the answer on the internet. According to the searching results, we realized that during flight departure, passenger planes can suffer lightning damage. As a result, there will be lightning strike points, which needs immediate solutions for safety concerns. Besides, we found out that the exterior aircraft components, such as aircraft body, wings, tail, turbine engine and other areas, are vulnerable to corrosion, which also needs immediate solutions. Luckily, we came across a chance to chat with the engineer who works in the airport. Through that meeting, we knew that the maintenance of the aircraft is very important. However, the maintenance of the components depends on professional technicians, weather, the surrounding noise level, and other environmental effects. As a result, we think that it is initial for us to develop a device that can automatically complete the missions of aircraft maintenance. Below are two objectives that we need to complete: 1. Complete a non-destructive testing for aircraft damage, including corrosion and lightning strike points. Assessment areas include: Aircraft body, airplane wings, tail of the aircraft and the turbine engine 2. Engage in scanning results to analyze and predict for flight readiness. The collected results will proceed to the aviation company for inspection and maintenance. Based on these two objectives, we designed an automatic platform for aircraft maintenance. Below are four innovations of this platform: 1. we developed a method to replace the current stage based on the manual operation of the aircraft maintenance, the use of AGV (Automated guided vehicle) and the robotic arm combination. 2. Design a modular platform based on this method, including telescopic four-wheel independent rotating chassis and locking mechanism, scissors lifting mechanism, double sided synchronous belt forward detection telescopic mechanism, etc. The platform can shrink at the minimum height of A320, convenient access to the machine abdomen. 3. The positioning algorithm of the platform relative to the aircraft is proposed.

費馬多邊形數定理之延伸探討

本研究旨在研究費馬多邊形數定理(任意非負整數必可表成k個k邊形數的和)的一般化情況,也就是說,任意非負整數是否能表成給定的二次多項式數列中所選取的γ項和。以數學模型敘述,就是探討對一個已知的二次多項式an2+bn+c,是否可找到一正整數γ,滿足∀x∈N∪{0},∃α1,α2,…αγ,使得x=∑γi=1(aαi2+bαi+c)。 本作品主要探討若此探究模型存在,那麼數列〈an 〉的一般式an2+bn+c與γ值之間會存在什麼關係,並期望能運用一個簡潔明瞭又一般化的數學式表示。本文亦提供另一個數學模型,探討γ值與某些特殊係數a,b,c之間的關聯性。而本文探尋[a/2]n2+[b/2]n+1,a∈N,b∈Z,a+b≡0(mod 2)(此為本文主要探討的二次式),求得此二次式所對應之γ值的方法為先令p=[2a/(a+b)]+2,再藉由所建立的模型二,求出[(p-2)/2] n2+[(4-p)/2] n的γ值,接著再用所建立的模型一來求得[a/2]n2+[b/2]n+1的γ值,進而依循此方法最後得出任意形如[a/2]n2+[b/2]n+1的二次式之γ值。

Gannet Investigation: Survivng an Unnatural Disaster

For a unique marine bird, so magnificent and accessible to the public, the Australasian Gannet (Morus serrator) colony found at Cape Kidnappers, 紐西蘭, significantly lacks research. Knowledge of gannet behaviour and how humans could best sustain a relationship with them remains unstudied. M. serrator are colonial monogamous breeders and produce a single chick each breeding season (Ismar, S.M.H. 2013). With the same mate over breeding seasons, pairs work cooperatively sharing the energy input into a single chick. Such parental care leads to highly territorial behaviour (McMeekan, C. P. & Wodzicki, K. A. 1946). This suggests more dominant gannets would claim larger territories to have a greater distance between nests of other birds, to increase the survival of their offspring. With a land-based colony this means the gannets are at risk from land and airborne predators, suggesting more dominant birds will claim territories in the central area as it offers greater safety from predator pressures (Minias, P. 2014). It was hypothesised that birds in the centre will have a greater distance between their nests and have a smaller height compared to those around the periphery of the Plateau Colony. The distances between nests and the heights of nests were recorded in the centre and around the periphery of the colony to determine if there was a correlation between the variables. It was found that centre nests had a greater distance between them and were of a smaller nest height when compared to those around the periphery. Anthropogenic influences from tourism and conservation has the potential to change the evolutionary trajectory of managed populations. This colony is protected by predator control programs. Altering this significant selection pressure has the potential to change the nesting behaviour of this species. Monitoring annual nesting distribution patterns and colony numbers over time, may enable informed development of more sustainable ecotourism and protection of the colony. This investigation provides baseline data to support further research on this colony.

積少成多—以階差級數計算填數字方法數並推導其生成函數

本研究主要解決的問題為:在任意多邊形上填入特定範圍的正整數,使得相鄰兩邊上的數差1,求符合以上條件的填數字方法數。 為了解決問題,本研究做了兩項突破。第一項是題目的轉變,將問題轉變成路徑問題。第二項則是將路徑數計算的方式(加法原理)之逆運算,求出從原點前往含直線y=-x及其右半平面上的任意格子點之捷徑數,並搭配巴斯卡三角形中的組合數列,成功地推導、證明此問題方法數的公式。 接著本研究將原題延伸,推廣至討論任相鄰兩邊上的數之差為固定某一正整數的情形,也成功地推導、證明其方法數公式。最後,本研究討論原題目的生成函數並成功導出。

A Novel Spectroscopic-Chemical Sensor Using Photonic Crystals

Detection of harmful chemicals used in industrial complexes is crucial in order to create a safer environment for the workers. Presently, most chemical detectors used in workplaces are expensive, inefficient, and cumbersome. In order to address these deficiencies, a novel sensor was fabricated to produce a unique spectroscopic fingerprint for various toxic chemicals. The sensor was fabricated by depositing several layers of silica spheres (diameter ~250 nm) on a glass substrate using evaporation-based self assembly. As the spheres assemble to form a photonic crystal, they also create void (i.e., air) spaces in between them. Once the spheres assemble as a photonic crystal, a spectrometer was used to monitor the reflectivity. The spectrum had a high reflectivity at a specific wavelength, which is governed by the average index of refraction between the spheres and the void spaces. As a foreign chemical infiltrates into the photonic crystal, it occupies the void space, which results in an increase of the average index of refraction of the structure. Consequently, the peak wavelength of the reflectivity spectrum red-shifts, which then confirms the presence of a foreign substance. While the as-grown photonic crystal is able to detect chemicals, it is unable to differentiate between chemicals that have similar indices of refraction, such as ethanol and methanol. In order to detect chemicals with similar indices of refraction, five pieces of a single photonic crystal (i.e. five pixel device) were exposed to different silanes, which changed the surface chemistry of the silica spheres in the photonic crystal. In turn, the five pixel device was able to produce a unique chemical fingerprint for several chemicals, which can be calibrated to detect toxins in the workplace.

Studies of Hydrogen Evolution Reactions from Aluminum Foil using Waste Materials and Their Reaction Mechanism

Nowadays, the most of waste materials are incinerated and generated the toxic gases in 日本. On the other hand, the Hydrogen gas (H2) has attracted attention as clean energy due to no emissions of toxic gases. In this work, we investigated that the new hydrogen evolution system using waste materials, such as aluminum (Al) foil and lime desiccant, and also investigated their reaction mechanism. The grinded desiccant was added to Erlenmeyer flask containing 300 mL of water. After dissolution the desiccant, the Al foil was added to the solution to begin the reaction. Generated gas was determined by water displacement method. The gas components are identified by gas chromatography. We found that the waste material reaction combined with waste lime desiccant and Al foil could be used for one of the hydrogen evolution system. This reaction is depended on solubility of lime desiccant, thus mean solubility of CaO in water. The Al foil is reacted with the desiccant more than 20 times of reaction stoichiometry. The calcium ion or calcium complex ions are involved with the excess reaction of Al foil.

在酵母菌中被熱休克蛋白90所保護的遺傳變異之探討

基因型的改變會導致表現型的改變,然而,有一種稱為遺傳緩衝的效應,能隱蔽基因型變異,維持表現型穩定。由於某些遺傳變異不適合生物的原始環境,卻能被保護,使在各種環境中持續演化。從前人的果蠅研究發現,若剔除熱休克蛋白90能夠使其不同遺傳品系間的基因型變異被顯露出來;而在酵母菌的研究中,剔除熱休克蛋白90會增加在環境擾動時的生長差異,因此熱休克蛋白90被認為有參與遺傳緩衝效應。更重要的是,熱休克蛋白家族普遍存在於所有真核生物中。為一窺遺傳緩衝效應機制的原貌,本研究誘發釀酒酵母菌菌種196的突變、增加其基因型的多樣化,並以doxycycline環境及高溫環境營造環境壓力,以降低酵母菌196及其突變株的基因Hsc82之表現量,找出含有因為突變而被熱休克蛋白90所保護的基因的突變株。希望透過找到這些突變株以了解,有哪些基因突變會被熱休克蛋白90所保護,並進而推論人類基因的突變是否也能依循此機制被隱蔽。

乾坤大挪移

會議室圓桌上有n個座位,順時針依序放有編號①、②、③、 、n,共n張名牌。將參與這場會議的人也編碼,依序為1、2、3、 、 ,假設編號1的人一定會先抵達並坐到了名牌②的位置,剩下的人則依亂序到來,先找到自己名牌的座位,如果位置是空的就坐下,如果位置被佔了就往順時針方向找到下一個空位坐下(例如3到達時,若③、④均被坐了,而⑤位置是空的,則3就坐到名牌⑤的位置)。等到一個人坐定後,另一個人再進入會議室,依此規則,最後此n人到底會有幾種不同的坐法? 我們以遞迴手法以外的方法解決了這個的問題,並深入探討: 1.能否從入座的順序立刻得知最後坐定的位置? 2. 能否從最後坐定的位置,找出進入會議室的順序?同時得知有幾種不同進入會議室的順序會符合同一種坐法? 3. 每個人坐錯位置的機率為何?恰k人坐錯位置的機率為何?坐錯位置人數的期望值為何?

Sustainable Graphene Oxide Support for Ruthenium Catalysts to Improve the Efficiency of the Hydrodesulfurization of Thiophenes

沙烏地阿拉伯 is the largest oil exporter in the world. 64,000,000 tons of sulfur oxides are produced every year through the combustion of organic sulfur compounds in the oil industry. This leads to several environmentally serious problems, including air pollution. This research provides a novel strategy to utilize natural-based Graphene Oxide (GO) as a support for ruthenium (Ru/GO) to functionalize as a green catalyst for hydrodesulfurization. Physical activation of camel bone samples was carried out by carbonizing them at 500oC to produce camel bone charcoal. Modified hammer’s method was employed for GO production, followed by doping of ruthenium in a simple synthesis step. The prepared catalyst has been characterized by XRD, SEM and EDX techniques. Thiophene and 3-methylthiophene were used as model compounds in the hydrodesulfurization process. The catalytic reactions were carried out at atmospheric pressure in a continuous up-flow fixed-bed quartz reactor. The composition of the sulfur containing gaseous products was analyzed by gas chromatography. The product distribution achieved for thiophene was 3-6% butadiene and 76-77% butane. And for 3-methylthiophene, it was 32.3% of pentaned 1-pentene and 2-pentene and the selectivity percentage was 45%. Ru/GO has been found to be an excellent catalyst of thiophene and 3- methylthiophene hydrodesulfurization and is a considerable improvement when compared to the commercially available catalysts. The prepared catalyst shall potentially lead to the reduction of sulfur pollution in the future. The positive effect on the environment could be substantial.