全國中小學科展

2023年

DEVELOPMENT OF PAPER-BASED ORIGAMI BIOSENSOR PLATFORMS FOR COLORIMETRIC DETECTION OF BIOCONTAMINANTS

Infectious diseases caused by bacteria from biological pollutants pose a great burden in terms of diagnosis and treatment, and millions of people worldwide die from bacterial infections. Detection of bacteria plays a critical role in clinical diagnosis and control of contamination, but is not accessible due to the high cost, complex devices and equipment required. In the project, an alternative to existing methods, a paper-based biosensor for the detection of model organism E. coli bacteria, which is visible, low cost, easy to use, can be integrated with a smartphone, is based on rapid color change in the exposed environments, drinking and pool water, wastewater, beverage products. platforms were developed. For the specific detection of E.coli bacteria, two different biosensors have been developed that can perform colorimetric detection in a user-friendly origami design, minimizing microchip and processing steps based on antibody-bound PVDF membrane and filter paper-based immunological method. In the presence and absence of target bacteria E.coli, the lowest detection limit of the biosensors obtained by using paper-based platforms that create a distinctive color on them, depending on the concentration, was 0.9x103 bacteria/ml for origami biosensor, 2.7x103 bacteria/ml for microchip biosensor and the widest dynamic linear operating range was calculated as 103-107 bacteria/ml. With the biosensor platforms we have developed, the use of only one smartphone for both qualitative and quantitative, visible results and analysis within minutes constitutes the originality of our project. With these promising results, the biosensors we have developed can also be used for the detection of different biological pollutants, do not contain complex devices and can be easily produced in large scales. We believe that the biosensors we have developed for the detection of biological pollutants in water and beverages, especially in regions where test laboratory infrastructure is not available, will contribute to the literature, public health, health economy and sustainable development goals such as clean water and sanitation, health and quality life, and life in water.

龜兔賽跑中的兔子:蚤蠅的高頻率間歇性運動之探討

動物的移動過程並非連續,而是呈現經常性行走與停頓的「間歇性運動」,停頓頻率依物種而異。前人研究發現,間歇性運動可助動物恢復體力、增加對環境的感知、及減少被天敵的測知。蚤蠅是已知展現間歇性運動的動物中停頓頻率最高的類群之一,基於前人研究,我們推測蚤蠅可透過間歇停頓來達到更好的運動表現。為探討蚤蠅的高頻率間歇性運動,本研究運用高速攝影機,以每秒960幀的速率來拍攝腐肉蚤蠅、蟻客蚤蠅、及有翅蚤蠅的間歇性運動行為。數據分析結果顯示,所有蚤蠅的停頓時長與下一步的移動距離、移動時長、平均移動速率呈低度相關。藉由測量每次移動路徑方向的轉動角度,並進行種間比較,發現間歇性運動可透過增加轉角或頻率,來增加路徑的多變性。最後,當天敵存在時,蟻客蚤蠅的間歇性運動移動時長增加,頻率下降,或可減少被捕食的機會。

Forming Polygons with Broken Pick-up Chocolate Bars and Spaghetti Noodles

”The broken pick-up sticks problem” is proposed by T. Kyle Petersen and Bridget Eileen Tenner in 2020. We solve the problem by considering the discrete version using random variables, and the limit behaviour of the discrete version gives us a combinatorial solution to the original problem. We also evaluate the probabilities of the triangles formed by the broken/pick-up sticks satisfying some specific geometric conditions with various techniques, including calculus and elementary number theory.

Crossing Number of Join Product of Some Graphs

A drawing of a graph G is a representation of G on a plane, with its vertices represented by distinct points, and its edges by arcs connecting the corresponding points. The crossing number of G is the minimum number of intersections between arcs across all possible drawings of G.

整數模n的加法組合設計之探討

將兩個相同的n角齒輪重疊後,再砍去若干個特定重合的角,欲使上層齒輪在繞公轉軸旋轉一圈的過程中,兩齒輪皆有重合的缺角,在這個目的之下探討砍去的角數量,使其最小化,將其最小值稱為n角齒輪的最小可行數,以符號記為f(n)。我的研究是考慮自然數 ,對於砍去角的位置,制訂設計方法,在數量上求得f(n)較好的上界與下界。我將這個問題代數化,運用集合與數列的概念進行研究,進而轉換為組合設計的最佳化問題。特別的,若齒輪中任意兩個缺角在圓周上的最短距離皆相異,則表示砍去重合角的位置為最緊緻的狀態,將這些特殊的缺角位置稱為完美集合,我也試著探討缺角為最緊緻的特殊情形,分析完美集合的存在性。

搖頭擺尾 離子尾波形週期變化分析與原因探討

彗星離子尾受太陽風吹拂後,使其帶電粒子受力而改變噴發後的離子尾軌跡。C/2021 A1 Leonard的影像就可明顯看出它具有波狀的離子尾。我們透過影像軟體擷取彗尾影像的座標並將其代入分析軟體。依序分析2021年12月21日、12月31日與2022年01月02日的彗尾結構,利用不同的波函數擬合彗尾形狀並扣除擬合線,嘗試找出不同的彗尾結構是否具有相同週期或非週期的特徵。同一天內的不同離子尾去除穩定與漸進變化的週期後,發現具有相似形狀的變化區,應該為共同影響的非週期性因素,這個影響因素可能為太陽風的各種物理量(如:風速、磁場強度、質子密度等)。接著利用星圖軟體和數學幾何軟體推算出彗尾與其波結構的實際長度,並與太陽風資料互相比對。將三天的太陽風磁場南北分量(Bz)與各自的最後分析圖進行對照,發現兩者有高度相關性,推論太陽風磁場南北分量(Bz)的非週期變動是影響彗星離子尾不規則變化起伏的主因。

探究Nocardiopsis菌落環狀紋路與相鄰同宗菌落間隙的成因

我們研究自黑液污染土壤篩選出的Nocardiopsis(擬諾卡氏菌)菌落環狀紋路的成因,發現環狀紋路形成具有遺傳性且可能是基因變異產生。在低營養濃度(Tryptone濃度小於1g/L)條件下,菌落紋路明顯,推測是由於基層菌絲無法取得足夠養分供給氣生菌絲,氣生菌絲無法生長,直到基層菌絲往外拓展至有足夠的營養物質的區域,氣生菌絲才再次開始生長,因而產生一環一環的不連續生長帶。 此外我們發現多個Nocardiopsis菌落之間,會因抑制物質作用產生間隙,此間隙大小受營養物質濃度、菌落間初始距離、周圍菌落數目的影響,且其機制與形成環狀紋路的機制並不相同,可能與菌落間偵測感應等複雜機制有關。我們萃取此抑菌物質送液相層析串聯質譜儀(LC-MS/MS) 鑑定其成分,發現抑制物質可能是Streptogrisin C或其他非蛋白質物質。深入研究Streptogrisin C的濃度與抑制Nocardiopsis生長的關係,以及其他抑制物質的可能性是我們未來的研究方向。

Frieze Patterns、Farey Sequence關聯性探討與具1-鋸齒或0-鋸齒Frieze Patterns之研究

在這篇作品中,我們研究frieze patterns 的性質並探討其與法里數列(Farey sequence)的關係。本作品成功造出包含 n 階法里數列的 frieze patterns,並探討其對應三角剖分之雙重0 轉換圖與法里數列的關聯性,我們也找出具 1-鋸齒 frieze pattern 的充要條件及其幾何意義。在最後,我們作了一些 additive frieze patterns 相關性質的研究,並找出 additive frieze pattern 具 0-鋸齒的充要條件,也進一步探討 additive frieze patterns 所有可能的對稱變換。

Optimization of honey production by monitoring the behavior of bees based on studying their sounds

This is a first approach in the development of beekeeping and the preserving of bees, a crucial and important species in the balance of ecology on our planet. This project consists in designing and building a small affordable device that will help beekeepers keep an eye on their hives and prevent theft whenever and wherever they are by providing them with instant and continuous data and information about their beehive status through a mobile application. This IOT approach will rely on many physical variables especially the sound frequency of the bee buzz, which appears to be a way for the bees to communicate with each other in special circumstances. That is why; we aimed to analyze the sound frequencies of the bee buzz to detect beehive behavioral changes. Many other factors are also important for the keeping of a healthy beehive such us temperature, humidity, weight and fly activity. And as for security measures we are going to add a GPS tracker to the system to keep track of the hives and alert the beekeeper if there is any kind of danger. The development of this real time beehive monitoring system will not only help the beekeeper keep track of his hive and collect useful data but also increase the honey production and avoid many colony losses and thus preserve the bees and ensure their well-being.

提升纜車遭遇陣風之安全性-利用自製調諧質量阻尼器與可調式吊臂

遭遇強風是纜車停駛的條件之一,然而我們認為當低於停駛標準的陣風與纜車產生共振時,更會使纜車產生擺動造成危險。因此我們參考真實纜車的比例,製作出模型探討不同頻率及速度陣風對纜車造成的影響。我們發現即使風速未達停駛標準,但當其頻率與纜車接近時,即會發生共振並產生將近 30度的擺角、強度相較持續風吹拂增加 60分貝。 為了減低振動,我們首先製作可調式吊臂。但因為其在實際製作上具有困難,且可能造成乘客的不適。為此我們製作了調諧質量阻尼器,當共振發生時,將砝碼透過伺服馬達放下,使纜車的振動傳導至垂下的擺減緩振動。結果顯示阻尼器能將振動減低 10分貝,最佳的組別甚至有 16分貝的減振效果,能將擺角減低至小於 2度。期望將來能將系統自動化,在纜車遭遇陣風時自動調變阻尼器,抑制振動。