關於渦旋〈二〉
在做這實驗之前，我花了很長一段時間思考一個問題：我如何能得到同\r 樣大小（均勻）的水珠陣列？我在家中各個角落放置許多水瓶，看看哪\r 個地方能培養出顆粒相同的水珠？ 往往肉眼見到整齊排列的水珠，一經\r 顯微鏡觀察，可就大小不齊整了。\r 第一篇中的實驗，幾乎是「水珠日記」，記載冷凝過程；其中我特地比對\r 「穩定的水蒸氣氣流」與「擾動的水蒸氣氣流」、「水蒸氣氣流與凝結盤\r 間溫度差別」、「凝結盤密度差別」、「凝結因子的重量百分濃度差別」、「水\r 蒸氣氣流之流速差別」，並加以複合比對。希望能找到產生均勻排列的條\r 件–探討水分子的自我組裝機制（Self Mechanism of Water Droplets）。\r 這其中提出『均勻假說』： 當條件合宜時，冷凝下降的細微水珠會產生\r free vortex ring，形成整齊的渦環組合，進而產生均勻排列的細微水珠陣\r 列。\r 實驗是藉由溶液密度小於水的設計，讓水蒸氣冷凝於液面上，並且因密\r 度較大而下沉。設計的要點是：儘量減少細微水珠自冷凝後的堆疊\r （coalescence），以呈現水珠原貌。\r 在第二篇實驗中，將對渦旋比例尺修正。渦旋本身難測大小，在空氣中\r 也不易觀察，但是若由水中觀看，可藉由空氣蕊長短估算。這次更進一\r 步考慮到排水速率、水深、排水口形狀、與極值。\r \r I have tried to ask a famous math professor if he can create a formula\r describing the ordered array of water droplets。〝Then, I should study Physics\r first !〞He said。\r Condensation is the thing we live with , being found everywhere, passing\r without notice。But we never know0 when it does start？\r This experiment presented here is actually the diary of the growth of water\r droplets through condensation。Through convection and vortex ring, it\r discusses the self assembly mechanism of water droplets and peep into the\r uniformity of the size of water droplets。\r Here, vortex ring plays an important role in the self assembly mechanism of\r water droplets which is not triggered in the daily life。\r By coalescence, water droplets grow bigger, but are not round again。We used\r the polymer film as template and designed the solution lighter than water, so\r the minute droplets will sink to the bottom and layer by layer。After seconds\r we may have multilayers of ordered array。\r This is the first step in discovering the uniformity of water droplets, besides, I\r made some correction to the Vortex-Ruler。Vortex-Ruler will be useful in\r researching the flying mechanism of butterfly and dragonfly as to judge\r which one induces more vortices。
利用雷射光實驗研究液的折射率梯度
溶液和溶劑置於同一容器中，當溶質向上擴散時，會形成濃度梯度及折射率梯度 dn/dy，且dn/dy 對高度y 的關係圖會呈現隨著高度改變的現象。 半徑r 的Ｄ形容器，下方置溶液，上方置溶劑，以雷射光照射容器的平面部份時， 雷射光沿著法線出射，受折射率梯度的作用而向下偏Ζ距離，a 為容器至屏的距離， 得到dn/dy=Z/ar 的關係式；改變雷射光的高度y 可得dn/dy 圖。 以硫代硫酸那作實驗，其dn/dy-y 圖為以原始界面為對稱軸，因其擴散係數不隨濃 度改變；甘游水溶液的dn/dy-y 圖呈現不對稱，圖形的極大值往甘油方偏，主要係因 為甘油的擴散係數隨濃度的增大而減少。 我們成功第把不同時間對同一溶液的實驗結果予以模型化，得到的dn/dy-y 曲線隨 時間改變，並發現該曲線所涵蓋的面積為定值。 雷射光經光柵再照射半圓筒，可直接測出各高度的折射率，量出y、 dn/dy、n、及濃度可算出擴散係數。The mixing between a pure liquid and a solutionin a vertical column produced a concentration gradient , which in turn produced the refractive index gradient . As the solute particles diffused upward into the pure liquid , a gradient was generated because of the varying solute concentration . The plot of the refractive index gradient versus vertical position y (dn/dy vs y) is found to vary with time . A D-shape container of radius r is partly filled with a dense solution , and partly filled with solvent which is on the top of the solution. When laser beam pendicularly enters the flat surface of the container, the outgoing beam strikes the container at a normal incidence , and is deflected down a vertical distance Z by the refractive index gradient . We can get dn/dy=Z/ar , where a is the distance between the container and the screen . By changing the vertical position (y)of laser beam , we can get the plot of dn/dy vs y . We have successfully modeled the time dependent experimental gradient curves on the same solution . The area beneath the trace of dn/dy vs y at different time is found to be constant . Additionally, with a grating at the center of the semicircle, we can measure the index of refraction n and get the plot of n vs y. The diffusion coefficient D of the solute can be calculated using the plot of dn/dy,y,and time t.
枯木潛盾機──石氏煙管蝸牛 (Euphaedusa sheridani shihi Chang) 取食策略之研究
When one time we beautified our campus. It made us meet the snails, Euphaedusa sheridani shihi Chang, unexpectedly. Maybe snails make people associate with the holes on vegetables tops in thinking. Do all of the snails make vegetables tops as their food? We compared with the weight of the wood which has been stayed by snails or not. After a week, the weight of the wood which has been stayed by E. sheridani shihi Chang decreased obviously. It showed they also make wood as their food. What do they decompose wood become? First, we used the basic Carbohydrate's detection means to test the eluate of the wood which has been stayed by E. sheridani shihi Chang. However, we found both the eluate of the wood which has been stayed by E. sheridani shihi Chang or not can examine the Pentose out. So next, we plan to use SDS-PAGE to analyze the left enzyme on the wood, and use it to prove whether they secrete enzyme in mouth to decomposed wood or not. In addition, the holes these snails made and the environment are connected. By means of changing light, temperature and humidity to experiment with how much wood can these snails decompose. We found in the dark, about 20℃ and moist environment, they could decompose the wood the most. Finally, the holes they made on the wood also have its ecological niche. They decomposed the wood not only hastened the dissolution of the wood, but also provided the microhabitat for alga, fungi and small bugs.一次綠化校園的活動，製造了我們與石氏煙管蝸牛的邂逅。蝸牛，或許使很多人想到蔬菜上的洞，但真的所有的蝸牛都以蔬菜為食嗎？比對有無蝸牛棲息的兩組木頭，結果一星期之後有蝸牛棲息的木頭重量明顯減少，顯示蝸牛也以木頭為食。那麼牠們把木頭分解成什麼呢？我們先以基本的醣類檢測方法，檢測蝸牛棲息過的木頭表面洗出液，不過發現不管有無蝸牛棲息皆可檢驗出五碳醣，接著預計用SDS 膠體電泳看是否可以分離分析出蝸牛在消化木頭時殘留在木頭上的酵素，以證明蝸牛是否在口腔分泌酵素以分解木頭。至於環境和蝸牛消化木頭的關係，我們藉著改變光線、溫度、溼度等變因進行實驗，發現牠們在陰暗、潮濕、約20℃的環境下可以分解最多的木頭。最後，牠們分解木頭形成的洞也具有其生態意義，不僅加速木頭的分解，也製造了微棲地提供藻類、真菌及小型生物的生存空間。
高中各學期成績與指定考科相關性
在升學主義越來越興盛的社會中，考試成績成為人人關心的重點，這\r 次研究就是藉由數理資優班同學的各學期在校成績和指定考科成\r 績，透過迴歸分析，找出各學期成績與指考成績之間的關係，並利用\r 圖表來解釋各種科目在各學期的課程，在高中三年所學的重要性，在\r 藉由此結果，希望能對目前老師的教育重點及學生學習方式能有所幫\r 助，亦可了解學生在高中求學過程中，哪些階段對指考成績較有正面\r 影響，進而強化該學習階段，以有助在指定考科時能充分發揮所學。\r \r In a society that emphasize on degrees, examination scores become the\r spotlight, and the ultimate goal for a high school student who had worked\r so hard for three years is to achieve high scores in the J.C.E.E. In the\r three years of high school, each subject has different topics each semester,\r but which semester has the most decisive effect on the J.C.E.E. score?\r This research is to study the effect of each semester on the J.C.E.E. by\r analyzing the grades of a science and math talented class in Senior High\r School using Regression analysis to find out the connections between\r term grades and the J.C.E.E. Then finding out which term grades had the\r most decisive effect in each subject. By using the result, we hope it can\r help teachers in their teaching and students in their learning. Also, it can\r provide the information about which stage in high school has positive\r effects on J.C.E.E. grades, therefore enabling students to emphasize on\r that stage in order to perform well on the J.C.E.E.
長方體中切割正立方體之研究
在1940 年代，Bouwkamp 提出一系列有關如何將矩形切割成若干個正方形的研究報告，但是如何找出正方形個數最少的方法仍是長久以來懸而未決的問題。在本研究報告中，首先引進「四角切割」的方法，並結合輾轉相除法的概念，來研究矩形的切割問題。我們的方法能大幅度降低正方形的個數，也適合做為此問題的上界函數。有關如何在長方體中切割出正立方體的組合，我們也將輾轉相除法的概念延伸到三維空間，進而建立所切割出最少個正立體數的一個上界模式。此外，藉由四角切割概念的延伸，我們也發現這個上界亦可再予修正。In 1940’s, Bouwkamp proposed the study of dissecting squares from rectangles. Among the study, the problem of the least number of dissected squares has been open for decades. In this project, we first propose a corner dissection method, associated with the famous Euclidean algorithm. By reducing nearly three fourths of the number dissected by the primitive Euclidian algorithm, our method indeed establish a suitable upper bound of the minimal number of dissected squares from the given rectangles Meanwhile, the Euclidean algorithm has also been considered to dissect the cubes from cuboids. We analyze the fundamental properties of the method and establish a prototype of upper bound function for the minimal number of dissected cubes. Moreover, the method of corner dissection has also been implemented for some cuboids, which also exhibits the acceptable improvement being a suitable upper bound.
醇類凝膠的安定與老化及其結晶情形
在這篇報告中，特別針對了凝膠的機制去做探討，以許多的實驗數據，再輔以凝膠的基本定義，去臆測各種有關於凝膠的老化機制，並藉由其過程中推斷出一些有趣的性質： 1. 當膠體內水分含量不同，與凝結後的醇類膠體有相當的影響。 2. 凝膠老化後形成的結晶形狀，因凝膠溶質、溶液內互溶性的不同，形成了不同凝聚程度的絮聚現象。 3. 同種陰陽離子在不同碳數的醇類凝膠中，因為與水溶液的互溶性也有所不同，間接影響了凝膠的形成速度，這對於安定來說，包含了很大的意義存在。 4. 對於其老化的速度，會因其安定程度而有所影響。 5. 老化後的溶液內的陰陽離子濃度，會直接影響其再次安定與老化的情形。 In this report, we especially do the discussion to the mechanism of the gel. With a lot of experimental data and the basic definition of gel, we conjecture various kinds of aging mechanism about the gel, and infer some interesting problems from its course: 1. Moisture content in the gel effect the gel’s quality after alcohol condensed greatly. 2. Because of dissolving difference between the alcohol and the other substances, crystallization forms after the gel aged have formed different degrees phenomenon of gathered. 3. The same kind of negative and positive ion among the alcohol gel that have different carbon atoms. Because of dissolving difference between the ions and the solution, the ions influence forming speed of gel indirectly. To being stable of the gel, this phenomenon includes very great meaning. 4. Stable degree of the gel can influence its speed of aging. 5. The consistency of negative and positive ion in the aging solution of the gel can influence its stable and aging situation again directly.
包埋酵母菌的幾丁球珠對含銅、鐵、鋅、鉛離子之廢水處理及應用
本實驗的目的，就是希望利用幾丁質除污的效果，再配合酵母菌所能累積金屬的能力，以酵母菌包埋於幾丁質的方法，吸附廢水中的重金屬離子。用Langmuir理論求得飽和吸附量，進而求出休眠酵母菌-幾丁質所能吸附金屬離子0.14─0.027(g/g)的數量，與活化酵母菌-幾丁質所能吸附金屬離子1.15─0.050(g/g)，並比較回收效率，以應用於處理工業上工廠所排放的廢水。 筆者在偶然的機會將處理過的蟹殼幾丁質固體置於石綿心網上，竟然在數分鐘內像塑膠般熔化，探討原因竟然是石綿心網上的某些金屬鹽所造成，因此筆者希望能透過這發現，用簡單的方法製造出低去乙醯化、高強度及耐中度酸的幾丁基質，並可應用在廢水處理上。;The purpose of this experiment is to explore the effect of using chitin and yeast plat to clarify the heavy metal cation, and that yeast plat works on the accumulation. In the process, the yeast plat is embedded in chitin to absorb the metal cation, therefore, by the theory of Langmuir, the impregnate absorption of dormant yeast-plat-chitin (0.14-0.027[g/g]) can be obtained and yeast-plat-chitin (1.15-0.050[g/g]) can be activated as well. In this way, the efficiency can be compared to apply to work on the effluent in industry. By putting shell-chitin-solid on the wire gouze by chance, we found it melted like plastic in just a few minutes. Some kinds of metal salt on wire gouze cause this change. Therefore, this easy ways can be used to makelow-deamide function group become of high strength and durable under acid environment. The results obtained from this experiment can be applied for the processing of waste liquid.
芯電感應
Based on Ampere，s Law, the magnetic field intensity of the solenoids is B=μ0μr?n?I, where μ0 is the magnetic permeability of free space, μr is the relative magnetic permeability, n is the number of coils per unit length and I is the solenoidal current. The end magnetic field of the solenoid must multiply by one half. According to the above result, it can be greatly strengthened by the addition of a ferromagnetic core. First, we observe three different inserted materials of coils (wood, iron and magnetite), whose magnetic induction in different solenoidial current. By experiment, when the iron and magnetite materials were inserted into the coil, it would produce larger magnetic induction. The calculated relative magnetic permeabilities of wood, iron and magnetite materials are 0.57, 18.37 and 18.32, which are close to the reported paper (1). When the driving field is removed, the fraction of the saturation magnetization of the magnetite is retained, which is called hysteresis and is related to the existence of magnetic domains in the material. In the second part, we change the frequency of circuit switch, which induced different current. Compared with the result of the first part, it would fit the result, which is the induced magnetic field is proportion to the solenoidal current. 根據安培定律，螺線管的磁場為B=μ0μr?n?I。其中μ0為真空中的導磁率，μr為相對的導磁率，n為單位長度的線圈匝數，I則為通入螺旋管的電流。至於螺旋管的端點磁場須再乘上1/2。所以根據上述的結果，當螺旋管插入鐵磁性物質，會增強螺旋管的磁場。首先，觀察三種不同的芯物質；非鐵磁性材料，軟磁材料，硬磁材料（木棒，低碳鋼棒，磁鐵棒）在不同的外加磁場下的感應磁場，得到芯物質的磁化曲線，而計算出來的相對導磁率分別為0.57, 18.37 和18.32與參考文獻(1)接近。而當外加磁場移走時，硬磁性物質的磁性仍然存在，稱為殘磁現象。在第二部分，我們改變線路開關的頻率。發現不同的開關頻率，會得到不同的螺旋管電流，而造成不同的感應磁場。再度驗證了感應磁場大小是正比於螺旋管電流的大小。
低溫二次燃料電池
本實驗係以台灣常見之數種植物(甘蔗、橡膠、破布子、苦苓)乾餾所成之多孔性碳棒鍍上銅和拷上Chitin 為電極兼電容，而以NaOH(aq)為電解液，製成化學電池。希望能研究出一低污染、低成本、能在常溫下經濟運作、並具有教學演示功能之電池。This research is based on the poromeric carbons which are made of several Taiwanese common plants (including: sugarcane, babul, Sabastan Plum Cordia [Cordia dichotoma Forst] , and Chinaberry tree [Melia azedadach L.]) by means of destructive distillation. The copperplating poromeric carbons later covered with Chitin functions as an electrode ac well as capacitance. Along with NaOH(aq) eletrolyte, a accumulator is then produced. The chief objective of this research is to produce a accumulator with low class of pollution and low cost, which is able to function economically under the normal atmospheric temperature. Also,this accumulator can serve as a teaching demonstration.