全國中小學科展

二等獎

強磁場下電漿孤立子的演化

本計畫採用數值模擬進行研究,並建立一維電漿模型來模擬電漿孤立子在不均勻背景中的演化。藉由模擬及觀察一維電漿系統中的各種振盪,驗證模型之正確性。在模型建構的過程中,曾針對數值精度問題、能量、動量不守恆提出各種解決辦法,最終完成的模型可以完全詮釋馬克士威方程組中所有電場與磁場的行為。此模型已檢驗過幾種在電漿中的波,包括:Plasma oscillation、Ion acoustic wave、Hybrid oscillation、Extraordinary wave(X wave)以及Magnetosonic wave。其模擬結果與理論值相當接近,代表此模型可以正確演示真實電漿之行為。接著模擬在強磁場以及不均勻磁場中,孤立子的各種行為表現以及演化方式,我們可以尋找某些物理量,其足以代表孤立子在系統中的行為,這個結果或許可以提供線索幫助我們了解星雲的能量來源。且這個模型未來將用於預測電漿物理學的未知現象及分析電漿態星體。

不同形態之銀奈米結構及銅銀雙金屬對電催化二氧化碳還原產物的研究

近年來全球暖化與能源危機成為眾人關心的議題,將太陽能轉換成電能並電解還原二氧化碳,生成運用於替代能源的產物,可同時解決兩個議題。本研究以水熱反應製備銅奈米線,以無電電鍍將銀鍍上銅奈米線,並以油浴反應、改變硝酸銀與聚乙烯吡咯烷酮的莫耳數比,合成銀奈米材料。塗布至玻璃碳盤電極後,以穿隧式電子顯微鏡、紫外光-可見光光譜儀、X射線繞射儀鑑定、以氣相質譜層析儀分析其電催化還原二氧化碳之產物與法拉第效率,發現產氫之法拉第效率以奈米銀立方電極 ,在電壓為-0.65 V至 -0.7 V時最高;產一氧化碳之法拉第效率以銀奈米粒,在電壓約為 -1.1 V時最高。銀奈米電極可以產熱值高的氫氣以及可進行多種反應、作為工業原料的一氧化碳,而銅鍍銀之奈米線電解之產物多元,包括碳氫化合物、一氧化碳、甲醇、乙醇等。

球狀銀奈米粒子結合金屬離子所誘導出之仿生物酵素活性與其應用

近年來新的仿生物酵素奈米材料,尤其是雙金屬奈米粒子或混合奈米材料如許多貴金屬奈米粒子,包括金鉍、金鉑、金汞、金鉛、銀金和銀鉑雙金屬合金奈米粒子表現出高的催化活性。金奈米粒子的仿生物酵素活性(氧化酶、過氧化酶和過氧化氫酶)可以經由與不同的金屬離子反應進行調整,例如金奈米粒子分別加入鉍離子、銀離子和汞離子後,在粒子表面分別會形成金鉍、金銀和金汞奈米層,表現出過氧化酶、氧化酶以及過氧化氫酶活性。 本研究藉由加入不同金屬離子誘導出13 nm球狀銀奈米粒子的仿生物酵素活性(氧化酶、過氧化酶)。銀奈米粒子與金離子於pH 9.0的環境中反應後會誘導出氧化酶活性。銀奈米粒子和鉍離子於pH 9.0的環境中反應後會誘導出過氧化酶活性。我們用葡萄糖氧化酶作為模型酶催化葡萄糖以產生過氧化氫 (H2O2),其與Amplex red(AR)在鉍/銀奈米粒子催化劑存在下反應形成螢光產物。由於AR產物-試鹵靈的螢光強度與葡萄糖濃度呈正比。未來期望能將金/銀奈米粒子用於抑菌實驗,鉍/銀奈米粒子結合葡萄糖氧化酶可用於血糖偵測。

迪化汙水處理廠降解雌激素之菌種純化

雌激素為一種固醇類的環境賀爾蒙,若水生動物長時間暴露於低濃度的雌激素中,即會導致其生理及行為異常。我們企圖從迪化汙水處理廠中分離純化出能有效降解雌激素之菌株,希冀了解這些菌株的生理特性與降解雌激素的能力。首先在活性污泥中加入高濃度雌二醇(1mM),以增進雌激素降解菌在菌群中的比例,接著利用十倍序列稀釋進行菌株純化。培養期間以薄層層析檢測雌激素降解活性。隨後以固態培養基培養法取得單一菌落,並進行聚合酶連鎖反應及核酸定序。之後我們亦將純化出之菌株進行其他固醇降解測定。目前純化出一株Novosphingobium屬的變形菌,其為一新的菌種,確實能降解雌二醇及其他固醇,包含雌酮、雄烯二酮、膽酸、孕酮和睪酮。然而,其並不能降解乙炔雌二醇。該菌株具有修復受汙染環境及製備雌激素相關藥品之應用潛力。

金屬奈米粒子/還原氧化石墨烯於直接甲醇燃料電池之應用

本研究的方向是以還原氧化石墨烯(RGO)為基礎,利用本材料具有優異的電子傳導以及高比表面積之特性,可成為燃料電池的優良電極觸媒材料。再進一步修飾上金屬奈米粒子以加強其電化學催化活性,並探討其用於甲醇氧化反應的效果。 本研究中藉由調整金屬奈米粒子成長的時間、反應溫度和與RGO的合成比例,探討改變不同變因下製備出的金屬奈米粒子/還原氧化石墨烯材料對催化效能的影響。最後藉由此最佳化的奈米複合材料做為直接甲醇燃料電池的陽極催化劑並探討其催化效果。

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。

GAS SENSOR APPLICATIONS WITH PHOTONIC CRYSTAL FIBER AND CARBON DIOXIDE SENSOR DESIGN

It’s very important to control and monitor gases that are produced by industrial applications in different values and kinds because they can cause environmental pollution and health problems. Photonic Crystal Fiber (PCF), which is a different kind of optical fiber, is a new alternative for gas sensors due to their small sample volumes, low transmission losses and high flexibility properties. PCF’s are silica-glass fibers, made by periodic sequence of hollows along the fiber. By filling these hollows with optical liquids or gases very sensitive sensors can be made. In this project, we aimed to design a sensitive sensor by filling the hollows with proper gases and liquids in the solid core PCF. For these applications ethanol, methanol, toluene vapors and carbon dioxide was used. And to observe carbon dioxide’s effects ionic liquid (EMIMBF4), which carbon dioxide can dissolve in, was filled then the experiments were repeated. It was observed that the transmission of light in PCF changed depending on the refractive index of the gas that was filled. With this change, it was understood that there were another gas besides the usual containments of air. Our system could measure the absorbtion peak of toluen so it can be used as a toluen dedector and when ionic liquid filled the fiber, two steps that occur in the spectra of corbon dioxide so it can also be used as a carbon dioxide dedector. The system was customized as a carbon doxide sensor in a cost-efficient and portable way. Our system can be specialized and easiliy used with right light source, which is efficient to see the absorbtion peaks, and proper liquids to dedect intended gas. Making a carbon dioxide sensor by filling PCF with ionic liquid was never attempted before. Also the lack of carbon dioxide sensor studies supports the originality of our project. That’s why we think our project will contribute very importancies to the existing literature.

Seeing Dots.

一樂隊表演,攝影師站在這樂隊的外圍拍攝。由於樂隊排列的位置,攝影師必須在外圍移動才能拍攝完整個樂隊。現在將樂隊移至直角座標中整數格子點上。攝影師依序在原點,x軸,y軸整數上的拍攝點拍攝位於平面上mxn (n→∞)的陣列。但有些點會被其他的點擋住,而無法拍攝到,討論如何用拍攝點拍攝到全部的陣列的方法探討其點數。要解決這問題需要其他的點去輔助。隨著mxn的陣列變大需要越多的拍攝點才可以看完。想要用最少的拍攝點拍攝,需要固定且有理論的方法。經過研究,找到mxn陣列(1≦m≦100, n→∞)的結果,若y軸上取一個拍攝點,其結果會使拍攝點個數都是優於先前文獻之結果。由於拍攝點點數是全新的數列,我們使用數學方式預測。由二維平面拓展到三維空間,其二維平面結果仍適用於三維空間。可探討天文望遠鏡拍攝恆星間的關係。

Determining Crystal Orientation via Reflection High Energy Electron Diffraction

1 Purpose of the Research Nanocrystal thin films exhibit many useful properties, including electrochromicity and superconductivity. When synthesised via Molecular Beam Epitaxy (MBE), selection of substrate, specifically knowledge of crystal orientation, is critical. Reflection High Energy Electron Diffraction (RHEED) is an in situ crystal characterisation method highly compatible with MBE. This study explores a new method of RHEED analysis to determine crystal orientation. 2 Procedure/Theoretical Framework RHEED characterization is the incidence of a beam of high-energy electrons at a low angle with respect to the sample surface. Electrons diffract, and interfere to form patterns on the detector. Traditionally, studies of RHEED analyse one static image as a representation of the surface structure, or observations of RHEED patterns over time. The approach to RHEED analysis in this study exploits changes in RHEED patterns given a rotating substrate. Having specific rotational symmetries along different axes, crystal structures can be differentiated by determining rotational symmetry through RHEED. Electrons scatter upon incidence with crystal planes within the crystal to form Kikuchi lines on the RHEED detector (Fig. 2). The orientation of crystal with respect to incident electron beam affects the Kikuchi line patterns. If the crystal is rotated, crystal planes change orientation, and electrons would diffract from crystal planes in different directions. As such, as the crystal is rotated, the Kikuchi lines move. When the degree of rotation of the crystal corresponds to the rotational symmetry of the crystal (Fig. 1), the Kikuchi lines return to their original position. As crystals with different crystal plane orientations exhibit different orders of symmetries, analyzing the Kikuchi line patterns of the crystal at different degrees of rotation can reveal the rotational symmetry and consequently crystal plane orientation of a crystal. 3 Data/Experimental Testing In order to assess the practical viability of the proposed method, experiments were conducted on SrTiO3 (001), (110), and (111). SrTiO3 exists as a typical perovskite structure (Fig. 3), often used in the synthesis of superconductors via MBE. 3.1 Methodology RHEED images of each sample were taken at 0◦, 60◦, 90◦ and 180◦. Curves were fit to each Kikuchi line observed in the image (Fig. 4). These Kikuchi line approximations are compared by superimposing the curves traced and qualitatively assessing the degree of similarity between the Kikuchi lines of 2 images, to verify the order of symmetry and crystal orientation of the crystal. In the images of the superimposed Kikuchi lines illustrated in Fig. 5, there is similarity between the Kikuchi lines when only when the sample has been rotated by an angle corresponding its degree of symmetry. 4 Conclusions This study offers a method to determine the crystal orientation of thin film through determining the degree of rotational symmetry of the sample, by observation of Kikuchi lines in the RHEED pattern as the sample is rotated. Experimental data was analyzed qualitatively to verify the viability of this theoretical method in practice. This method could be extended to analyze the symmetry of other crystal structures. As it does not require information on the machine settings or usage of complex functions to produce a reliable output, this method is fast and straightforward, opening doors to more streamlined RHEED analysis.

世界向你招手:文化智商、個人因素與國際地理知識之關係探討

本研究的目的為探討文化智商(CQ)、個人因素與國際地理知識之間的關係。本研究以便利抽樣的方式選取台灣北部、中部、南部的三所普通高中的學生為研究樣本發放紙本問卷,期間為1個月,共發放402份紙本問卷,回收的有效問卷數為364份,問卷回收率為90.5%。資料以描述性分析、差異分析、相關分析和迴歸分析進行變數之間的關係探討。研究結果顯示:經過差異分析,我們得知文化智商、國際地理知識並不會因性別不同而有差異;同時也得知,國際地理知識會因個人文化智商分數的高低而有不同。而經過相關分析可以得出,國際地理知識與自評英文能力、人格開放性、文化智商、日常習慣呈正相關。最後,經由迴歸分析後可以了解到文化智商對國際地理知識有正向影響,同時人格開放性對國際地理知識也具有正向關係。最後,本文提供研究討論、結論、與研究限制以供讀者參考。