2004年

This research primarily aims to observe how does the electric work, why does it work and the relationship between the surrounding circumstance and the repulsive torque. The electric whirl is made of an enameled wire bent into right angle with sharpened ends. When an AC high voltage is applied, the electric field intensity around the whirl ends is strong due to the small curvature radius of the ends. The molecules in air at both ends are ionized. This cause the phenomenon of point discharge. The positive and negative ions produced by alternating current forms AC ion wind, and produce a torque to make the whirl rotate. The object of this experiment is to observe the relationship between the surrounding circumstance and the torque repulsion. We design an apparatus to measure the angular velocity of the rotating whirl. We also calculated the kinetic energy of the whirl and the work done by the torque. The repulsive torque can be obtained by Work energy theorem. Result: (1)The angular velocity of the electric whirl is direct ratio to repulsive torque. When we want to find out the relationship between the manipulate reason and the repulsive torque, we can just compare the angular velocity with the manipulate reason. (2)The angular velocity of the electric whirl is only related to the peak voltage, and it does not make difference whether we apply AC high voltage and DC high voltage. (3)When the humidity is over 68%, the electric whirl cannot function normally. (4)Under the low-pressure circumstance, the electric whirl will rotate with glow discharge and the angular velocity will decrease to zero gradually.本實驗是探討電離轉輪的性質、原理與周圍環境的關係。「電離轉輪」為漆包線兩端折成直角並磨尖而成，接上交流高壓電源時，其尖端曲率半徑小，電場強度相對大，會游離尖端附近的空氣分子，產生尖端放電的現象，而交流電交替產生的正、負離子會形成交流離子風，並產生轉動力矩，使轉輪轉動。我們設計一個裝置，使其能偵測轉輪轉動的狀況，運用測得數據計算出轉動時的動能和作功狀況，套用功能定理便可求得轉輪通電時產生的斥力矩。實驗結果顯示(1)轉輪的角速度和尖端斥力矩成正相關，所以當我們想得知尖端斥力矩和實驗操縱變因的關係時，只要比較角速度和操縱變因就可以了，這簡化了原本繁複的計算和冗長的數據處理過程。(2)轉輪的角速度只和峰值電壓有關，和直流或交流沒有直接關係。(3)轉輪在超過溼度68%之後，就不會正常運作。(4)在低壓條件下，轉輪轉動時會伴隨淡紫色的輝光放電(glow discharge)現象，而抽氣塔中與轉輪尖端最接近的一點，也就是電場最強的一點，會和尖端同時產生光芒，相互輝映。

一、若Mn×n(s)表示在n×n 的正方形棋盤中，排列s 顆棋子在方格內，且每一方格最多只能排1子，其中s 顆棋子的配置需滿足兩個條件：1. 並無任意4 子可以形成矩形框的4 個頂點。（此矩形框的邊需與棋盤的邊平行）2. 在沒有棋子的方格中，無法再加入棋子。二、若Vn×n×n(a1,……,an) 表示在n×n×n 的正方體棋盤中，每層的棋子個數分別為a1,……,an，且s= a1+……+an，其中s 顆棋子的配置需滿足兩個條件：1. 並無任意8 子可以形成長方體的8 個頂點。（此長方體的邊需與立體棋盤的邊平行）2. 在沒有棋子的方格中，無法再加入棋子。本研究即在Mn×n(s)與Vn×n×n(a1,……,an) , s= a1+……+an 中探討s 的最小值、最大值及變化情形，並分析其配置方法。之後推廣至長方形Mn×m(s)及長方體Vn×m×k(a1,……,ak) , s= a1+……+ak。最後根據其研究結果設計一個「避開矩形框棋」，並加以分析出致勝的策略。一．If Mn×n(s) indicates in the n×n square chessboard, we put s chesses to line in the square and each square only can put one chess. Then the station of s chesses must satisfy the following two conditions：1. No any 4 chesses can form the tops of the rectangular frame ( The sides of rectangular frame must be parallel to the sides of chessboard )2. If there’s no chess in the square, we can’t add any chess. 二．If Mn×n×n(a1,……,an) indicates in the n×n×n square chessboard, the chess number in each layer are a1,……,an and s= a1+……+an. The station of s chesses must satisfy the following two conditions： 1. No any 8 chesses can form eight tops of the rectangular cube ( The sides of rectangular cube must be parallel to the sides of cubic chessboard ) 2. If there’s no chess in the square, we can’t add any chess. This research try to explore the minimum, maximum and variation of s which in Mn×n(s) and Mn×n×n(a1,……,an), s= a1+……+an, and analyze its station. Then we will extend the research to rectangle Mn×m(s) and rectangular cube Vn×m×k(a1,……,ak), s= a1+……+ak. Finally, according to the result of research we wish can design one “avert rectangular frame chess“ and analyze the strategies to triumph.

The aim of the work is inventing the way in which the power of the ICE is the same and consuming of the fuel decreases. The following methods of investigation were used: analysis of the experience of the improvement of ICE, modeling, the brainstorming, methods of Decition Theory of Invention’s Tasks (DTIT). In this work Ivan Semyonov based on a hypothesis that if the non-supporting combustion exhausts will be drawn with the vacuum from cylinder fuel for the same power it needed less. The practical meaning of this work is in the attempt of studying the question of improving the ICE for getting and making the more perfect ICE.

The zebrafish (Danio rerio) is a popular model organism used for elucidating complex\r developmental pathways and processes. Although the Zebrafish Genome Project is\r nearing completion, the function of most genes remains to be discovered. In zebrafish,\r where an efficient gene targeting method is still absent, costly Morpholinos (MOs) have\r been widely used to ‘knockdown’ specific genes.

本研究是[對於正n 邊形A1A2…An邊上一點P(含頂點)，想像自定點P 朝鄰邊發出一條光線，若依逆(順)時針方向依序與每邊皆碰撞一次，經一圈而可回到P 點，則此路徑稱為「光圈」。過程試著追蹤在正n 邊形內能形成光圈的光線行進路徑及其相關問題。 本研究令，且以逆時針得光圈來討論： 1.根據[光的反射原理]，探討光圈之存在性，發現除定點P 在正2m 邊形或正三角形的頂點外，其餘皆有光圈。 2.將可形成光圈的路徑圖展開成[直線路徑圖]來探討。 3.由[直線路徑圖]，觀察到形成光圈的光線行進路徑，可能存在下列情況： (1)不通過正n 邊形的頂點，且產生路徑循環與不循環問題。 (2)通過正n 邊形的頂點。 4.發現正2m 邊形光圈皆為[完美光圈]。 5.發現正2m+1 邊形光圈之路徑與有理數、無理數之特質有關。即當s 值為有理數時，路徑會循環；當s 值為無理數時，路徑不循環。 The research is about [on Point P (including the angles) on the side of regular polygons A1、A2…An , imagine the light goes from Point P to the closest side, then bumps each side sequentially counterclockwise. After going a circle, it’s back to Point P. The track is called “the circle of light.” I try to trace the light track of the circle of light and other correlative questions.] In this research, we suppose,and we discuss the circle of light according counterclockwise direction:1.According to the light reflective principles, we discuss whether the circle of light exists or not. And then we discover that the circle of light really exists except when Point P is on the angles of regular triangle or regular 2m polygons. 2.Spread out the circle of light’s track to [rectilinear track.] 3.By [the picture of rectilinear track], observing there are two kinds of the circle of light’s track: (1)If the light doesn’t go through the angles of regular polygons, it can be a circulative track or a non-circulative track. (2)When the light goes through the angles, it stops. 4.We discover that all the circles of light in regular 2m polygons are [the perfect circles of light.] 5.We discover the circle of light’s track is correlative with rational numbers and irrantional numbers. When s is a rational number, the track is circulative, if s is a irrantional number, the track is not circulative.

In recent years, sandstorms have seriously attacked Taiwan day by day. Combining with the observations of Central Weather Bureau and the satellite images of NASA, the study has been collected the data of suspension grain in decades. And the study hopes the sandstorms’ information could be observed in early period. Still it hopes to find out the possible transmission paths in the atmosphere. Then we know how to cope with sandstorms in early time. Sandstorms attack Taiwan frequently in alternation of the spring, the autumn, and the winter. Compared with thecharts of sandstorms and the satellite images, we could broadly aware hat the moving paths of sandstorms are related to the currents and the characteristics of the atmosphere. When El Nino happens, the times of sandstorms attacking Taiwan decrease, and that increase when La Lina happens. From the observation data of acid rain, when sandstorms attack Taiwan, acid rain would diminish. Combining actual Measures and satellite data in the future, maybe we can establish a prediction mechanism of sandstorms.近年來，大陸沙塵暴侵襲台灣的情況日趨嚴重影響。本研究中收集了近十年來懸浮顆粒資料，配合中央氣象局所觀測的資料與美國太空總署的衛星影像資料，希望能夠在早期觀測發現大陸地區沙塵暴訊息，和沙塵暴所帶至大氣中的懸浮顆粒可能傳輸的路徑期能早期應映。發生沙塵暴侵臺事件的季節，主要在秋冬及冬春兩季交替期間發生的次數為最多。由沙塵暴監測氣候圖表及美國太空總署的衛星影像進行綜合比對之後，可大致瞭解大陸沙塵可能的移動路徑與大氣環流及特徵有關。聖嬰現象（El Nino）發生時，侵襲臺灣的沙塵暴次數會減少。在「反聖嬰現象」（La Lina）發生時，侵襲臺灣的次數相對增加。由酸雨中得知大陸沙 塵暴侵襲台灣時，酸雨情況會減緩。未來結合實測及衛星資料或許我們可以預報大陸沙塵暴的侵襲。

在高中光學裡，介紹了許多有關光波之特性，而聲波與光波皆具有波動性，因此聲波應具有如干涉、反射、聚焦等特性，但在物理課本上並未詳加敘述，所以我們開始了本項的研究，希望可以籍由改變聲源及邊界的各項條件，而探討其發生之現象。在本研究中，我們利用聲波之基本原理在電腦上進行聲場的模擬並加以改變其變因（頻率、相位、聲源數、聲源間距、強度、邊界反射），進而明瞭聲場之各項特性及應用與控制方式。經電腦模擬聲場圖中，我們觀察到，兩聲源干涉所形成之圖形為多組雙曲線所組成，近似於光學之雙狹縫干涉，增加聲音頻率與聲源間距離皆可使腹(節)線數目增加。如同現實世界中所知的，隨著頻率的增加，將會具有指向性的產生並且在聲源數目越多時越明顯，但發現頻率增加至一定值之後，指向性反而會降低而形成冠狀面。在延遲了多點聲源間相位之後，聲場分佈有偏轉之現象，利用相位延遲的方法，在多聲源中，將兩旁之聲音偏向中央將可造成聲音的聚焦。在兩聲源干涉中，調整其中一聲源之強度，將可完全消除兩音源連線間一點之聲音，可適當的應用在工業上消除噪音。聲場分佈在具有邊界的環境下，我們試著找出聲源位置及邊界條件對聲場分佈的影響與關係以模擬室內聲場，但在簡化的數學模式下，即無法有我們所希望之最均勻聲場分佈產生。最後我們將實驗中的結果與文獻上的實驗數據加以比較，以探討其誤差。 The optical course in senior high school , which introduced many characteristics of optical wave. However, both of sound and light have the characters of wave; therefore, sound wave should have the characteristics, such as interference, reflection and focalizing. Nevertheless, there are not many details of sound wave in the section of acoustic on our textbook. So we began this research, and discuss the different phenomena by changing many kinds of variables. In our research, we simulated the sound field on the computer, based on sound wave’s principle, furthermore we change many variables, which like frequency, phase, source number, distance, intensity and reflection. It helps us understand the characteristics of\r sound, how to control sound and how to apply these findings. According to the result of computer simulation, we discovered that the graph of two acoustic source’s interference comprised by many pairs of hyperbola, just like optical double slit interference. As the frequency or the sound source distance increased, acoustic direction became more and more obvious. But when the frequency was high enough to over the extreme, instead increasing, the acoustic direction would lower down like a crown. After we make phase differences on one of the two sound sources, sound field generated\r deviation. So if we use this method in multiple sound source, and delay the middle source, the sound field might be converged. In such two-sound-source interference pattern, when we control the intensity of one, a certainly point on the line of the two sources disappeared When the sound field enclose by borderline, the standing wave appear, and we discovered many funny phenomena. We put large amount of source in a narrow slit, the phenomenon of diffraction appeared. Finally, we discussed the discrepancies between interference pattern previously done by others experiments and the simulated one conducted by us.

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.

這是一系列關於水蒸氣冷凝為極細微水珠的實驗。其中可以歸納為三大部分，第一部分是基礎實驗，將水蒸氣導引至親水性介面上，觀察冷凝水珠的結構。雖然看似簡單平常，但是卻發現：不同溫度的水蒸氣，其冷凝最初始的細微珠粒，尺寸相同；爾後溫度高者，堆疊速率較大，以至於最後同時呈現的水珠大小不一，尺寸不同！ 第二部分，是針對冷凝水珠自我組裝機制的探討。實驗是將水蒸氣導引至密度小於1的高分子溶液上，並藉由揮發性溶劑快速揮發，將水珠粒「分層保留」以便更深入了解「解構」後的水珠群聚機制。在這組實驗中得到兩張有趣的圖片： 在討論時，我是從對流機制切入，嘗試解構上面兩張圖。 第三部分的實驗，是將水蒸氣導引到磁場及靜電場上，觀察冷凝的機構。這部分呈現出來的結果，推翻了一般「水分子為電中性應該在電場與磁場中不受影響？」刻板觀念，實驗呈現水分子：不但在電磁場上不易長大同時也有固定的散佈模式(assembly pattern)。同時也觀察到：水分子在正電場形成的凝結水珠較為均勻，在負電場則表現出較大親水性特質。這部分的實驗對日後研究細胞膜上水分子通道應有助益。 I have tried to ask a famous math professor if he can create a formula describing the ordered array of water droplets. “Then, I should study Physics first!” He said. Condensation is the thing we live with, being found everywhere, passing without notice. But we never know when it dose start? By coalescence, water droplets grow bigger, but are not round again. We used the polymer film as template and designed the solution lighter than water, so the minute droplets will sink to the bottom and layer by layer. After seconds we may have multilayers of ordered array. This experiment presented here is actually the diary of the growth of water droplets through condensation, upon volatile fluid, magnetic field and electric field. Through convection, it discusses the self assembly mechanism of water droplets and peep into the uniformity of the size of water droplets. In this experiment, convection and magneto-electric force did play important roles in the self assembly mechanism of water droplets. The topic is mostly concerned as we are surrounded by magneto-electric waves in today’s world. This is the first step in discovering the homogeneous state of water droplets, providing insights into the self assembly mechanism of water droplets with nano sizes.

To-be static objects, such as bridges, volcanoes, seldom move ordinarily but have mini displacement only under special conditions, like flood or earthquakes. Therefore, how to measure their mini displacement has never become fully popular with scientists’ research. Then, beginning with “ Optical Lever Theorem”, through a series of speculation and discussion, I decide to use laser ray as light source to perform an experiment ------- trying to find objects with mini displacement in our daily lives, such as revolving electric fans, engine-opening motorcycles, shaken trees, testing their magnifying effect first. Next, I try to use the control-experiment method to find out the magnifying relation and formula of the rotation angle of the plane mirror and the displacement quantity of light focus. As to the measure of mini displacement on objects, I utilize the pillar mirror as a reflection plane to research the magnifying relation of reflection light focus and original displacement quantity. The image made from the light focus of pillar mirror’s reflection, however, isn’t so perfect that I have to use a special plastic-made light-concentrating mirror, which is also called “ Fresnel Lens ”, to focalize the light for easy observation. Besides, I find out the “ function graph ” of the mini displacement quantity on to-be static objects and the displacement quantity of reflection light focus. At last, I try to build up a “ Bridge Alarm System ” of Optical Lever Theorem. 準靜物如橋樑、火山，由於平常不輕易移動，只有在特殊情況下（如洪水、地震）時，才會發生位移的現象。因此，其微小變位如何測量，一向是科學界較少探討的題目。於是，先由光學槓桿原理著手，經過一番思考、探討，決定採用雷射光作為光源，並作了第一個實驗－－找生活中具極微小變位的東西，如轉動中的電扇、引擎發動的摩托車、被搖動的樹木等，先測試其放大效果。接著就試圖用控制變因的方法，找出平面鏡旋轉角度和光點平移量的放大關係和公式。至於物體微小的平移量之測量，則是利用柱面鏡作為反射面，來探討反射光點的位移與本來的平移量之放大關係。然而，柱面鏡的反射光點成像並不理想，於是用一種特製的塑膠集光鏡，又稱Fresnel Lens，將光點集中以利觀測，並且找出準靜物之微小平移量及反射光點的位移量的函數圖形。最後，嘗試建立一套光學槓桿式的「橋樑預警系統」。