物理

液體中之球體運動與液體的黏滯性有關，本實驗找出球體半徑與終端速度之間的關係。利用攝錄機作為紀錄工具，拍攝三種材質（壓克力、玻璃、水晶）的球體在沙拉油中的自由落體過程。使用電腦影像處理軟體將影像分解成幅影像，時間的解析度為1/30秒。測量球體的高度與時間，分析高度與時間的變化情形，發現終端速度與球體半徑之間的關係。 流體中之運動方程Fdrag = -k1V，無法符合實驗結果。我們的實驗結果顯示油中的自由落體的運動方程應該是Fdrag = -（k1V+ k2V2）。由不同材質的壓克力球（~1.18g/cm3）、玻璃珠（~2.47g/cm3）與水晶球（~2.66g/cm3）所獲得的終端速度（Vt）與球體半徑（a）的關係為a3(ρ-ρ') = 0.00003（a Vt）2 + 0.00021（a Vt） + 0.00575，其中ρ與ρ'分別為球體密度與沙拉油密度（0.90 g/cm3）。 再者，在相同半徑的條件下，密度越大的球體終端速度越大，在靜止下落後，越久達到終端速度。 The motion of a sphere which is falling through a fluid is subject to the fluid viscosity. In this study, we find out the relation between the radius of a sphere and the terminal velocity. We used a digital camera to record the sphere's descent in the oil. The three kinds of sphere we choose are acrylic（~1.18g/cm3）, glass （~2.47g/cm3）and crystal （~2.66g/cm3）. Frame-by-frame analysis of the video footage yielded rough estimates of the sphere's location within 1/30 seconds accuracy for statistically consistent results. By measuring the location and time and analyzing them, we find out the relation between the radius of a sphere and the terminal velocity. The expression of the drag force,Fdrag = -k1V, is not cosistent with our results. The study indicates the expression of the drag force should be Fdrag = -（k1V+ k2V2）. The expression for the terminal velocities of the three kinds of sphere is of the form：a3(ρ-ρ') = 0.00003（a Vt）2 + 0.00021（a Vt）+ 0.00575, where a is the radius, ρ is the sphere density and ρ' is the oil density（0.90 g/cm3）. In addition, if the radius is the same, the terminal velocity of a denser sphere is higher and the time to approches the terminal velocity is longer.

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.

當流體由圓管流下，在碰撞到物體後水流會產生類似駐波的形狀。為瞭解此現象的產生機制，及影響此現象的變因，我們改變流體的表面張力、流速及與碰撞物體間的距離，以探討各變因對波形所產生的影響，進而研究此現象的成因。由實驗結果發現波形會因流速加快、擋板距離增加、表面張力減少而有波長變短的趨勢，且可以用表面張力波的理論解釋。由理論推導的結果，可測量液體表面張力。由於圓球狀的外型使表面積增大，可增加液體之散熱的面積，因此可應用在水冷系統方面。A phenomenon similar to the standing wave, which occurs when a slow-velocity fluid jet collides with an obstacle, was observed. Because the free surface profile was observed to be stable, the phenomenon was not considered as standing wave. To understand the mechanism of this phenomenon and the factors that can affect the free surface profile, the surface tension of the fluid, jet velocity and the distance between the exit of the tube and the obstacle are varied to study their influences on the free surface profile. According to our experiment, the wave length is shortened when the jet velocity or the distance between the tube and the obstacle increases or when the surface tension decreases. The tendency of the investigated phenomenon can be explained by the capillary wave theory. Based on Bernoulli’s principle, continuity principle and surface tension\r equation, an ODE (ordinary differential equation) could be formulated. By using numerical method to solve this ODE, we predict the free surface profile which could match the experimental photo well. The tendency of the phenomenon can also be explained by the ODE. In order to measure the surface tension of the fluid, we wish to minimize the experiment apparatus. To enhance our assumption we use laser to locate the individual particle that we add in the fluid and calculate the velocity field of the flow jet.

本實驗一開始主要探討超聲波在水中的基本性質，如：指向性、衰減性…等。實驗發現，超聲波的衰減會同時與其指向性以及衰減性有關。 接著希望利用超聲波在水中的物理性質，近一步測量超聲波在水中的聲速，實驗中則利用駐波以及聲光效應測量。在駐波法測量聲速的實驗中，用洗淨機當作聲源，內部放置量筒，量筒內盛水後放入木屑，並使聲波在其中產生駐波即聲浮現象，求出波長後反推聲速，測量出的聲速誤差值僅有1.13%，而在使用聲光效應測量聲速的實驗中，使1.65 MHz 的超聲波在自製的壓克力容器內部所裝的水中產生駐波後，以波長650 nm 的紅光雷射通過，在遠處屏幕即產生似於光柵繞射現象，藉著屏幕上的繞射條紋反推該液體聲速，測量出聲速誤差均在5%以下。 在觀察聲光效應實驗中，發現過段時間後有氣泡產生，由文獻上，得知此現象為超聲空蝕現象(Acoustic cavitation)，就設計實驗測量聲場中聲壓分部，並利用蠟紙觀察氣泡的成長。實驗發現聲場中的聲壓強度以及液體的表面張力和蒸汽壓會影響到產生空蝕的臨界值及產生氣泡的數量。 ;At the beginning this experiment explores the ultrasonic base in the water, including its velocity, the physics property of liquid, direction, and attenuation etc. . . At first, we use methods of standing wave to measure the velocity of sound under the water, using an ultrasonic cleaner as the sound source and putting some wooden powder in the water. As the standing wave accrues/produces, the powder will “stand still.” To measure the length between two grains of powder, in this way we can calculate sound velocity. Another method we use is diffraction of optics. Put 1.65 MHz source and water in a transparent container; then using laser through it. At the board much diffraction light stripes are created. By this way, we can estimate the velocity. Following these ways can calculate velocity precisely. In these experiments, some bubbles create in the container are discovered. We learn it is so-called “Acoustic Cavitation” based on the reference paper. Besides, we design experiment to know the bubbles’ growth and the number of the bubbles is connected to the physics property of liquid. We use different kinds of liquid with different vapor pressure and surface tension. Finally, we know when it has the smaller surface tension and bigger vapor pressure, the liquid makes bubble velocity grow faster and larger amount of bubbles are produced.

本研究主要探討電解液之帶電離子在磁場中的動力行為。為了觀察更細微的結果，共歷經三代裝置改良，第一代用五個電錶及探針測量徑向橫截面上五點的電壓，所測數值電壓有下降趨勢但不足以呈現細微部份的變化。第二代利用電壓感應線、搭配平移台及電腦，呈現連續性且經數位處理之結果，出現電壓升降的電荷堆積現象。第三代為了更精確，將裝置結構及器材上改良。觀察到在磁場作用下有旋轉現象，改變電極極性時，會有順逆時鐘方向的改變，且只有電解質液才會有旋轉。更可以使用帶電質點受到勞倫茲力F=q(VxB)理論解釋。且旋轉中的電解液比沒有旋轉時，析出的銅量少，反應溫度升高快，電解液內電壓分布因電荷堆積造成的高低起伏。經過改變磁場強度、電解液濃度，不銅價離子電解液，結果濃度大、磁場大、離子數較多者，呈現電壓分布圖快速變化，彎曲大。This thesis report is the study of combining the moving charged particles under the perpendicular magnetic field. By using the theory of moving and electrolysis, the electrolytic liquid will swirl through the particular arrangement of the horizontal cylinders enclosed in a circular enclosure container and strong magnet. Then, the researcher observes the force situation of the charge in the magnetic field and discusses the differences of the electrolysis effect, which is experimented under the different conditions, such as, in the magnetic field or no-magnetic field. Furthermore, the researchers discuss the conduction of voltage spreading and interfering when the moving electrons under different position of two electrodes and under the different interaction of electric field and the magnetic field. And the changing reason as follow: （1）the magnetic field strength. （2）the concentration of the electrolytic liquid. （3）electrolytic solution. When the experiment group compared with the comparison group, the result may provide fundamental understanding as follow：（1） The researchers can find out the charged particles rotating in the magnetic field. And it proved the moving condition when the moving electrons in the magnetic field. （2） This experiment can be used in judging the solution, which I electrolytes, or not. （3） This experiment also proved for Arrhenius’s ionic theory. （4） The researchers found out the quantity of Cuprun decrease, the rise in temperature and the reducing in voltage.

我們的研究包括兩部份，第一部份是實地調查訪問。瞭解地震成因、傷害及現有防震方法，並調查坊間各種建築物類型，及常見私自改變建築物結構現象，做為研究的基礎。第二部份為建築物抗震實驗。研究發現：牆面挖空、頂樓加蓋、樓層挑高，建築物會在該處產生弱點，由此斷裂。柱子數量相同下，散開時支撐力較弱。不對稱建築物遇震時會不自然扭轉且易倒。隔震素材恰當，能有效提高耐震力。滑軌、彈珠隔震效果很好，但位移太大，為實際建築所不容許。建物下加裝阻尼材料，能吸收部份地震能量，降低地震對建築物的危害，並有效控制位移問題，是良好的隔震素材。樓頂加裝消能設施亦能減震，但設計極其不易。 The research includes two parts. In the first part the work is concentrated on on-site visiting and investigation such as understanding the cause of earthquake, the damage and the preventive method currently available, investigating the different types of building and the phenomenon of altering the structure of an existing building without permission by government authorities which is popularly seen in Taiwan. These are considered as the basis of the research. The second part is the experimental study of earthquake resistance of a building. The test results showed that weak-point can be caused at the place where the existing wall is moved or an extra building is attached to the roof or the structure of building has extended space between floors, and fracture always occurs at the weak-point. If the number of columns of a building is the same, then the scattering arranged location of columns is weaker than concentrating type of arrangement of columns. The building having unsymmetrical structure will twist in uneven fashion that causes the building apt to collapse in case of earthquake. Employing proper vibration-absorption material can effectively increase earthquake resistance. Sliding rails and balls can provide satisfiable vibration-isolation effect, but can also cause too much displacement of building structure. Install damping material beneath the building can absorb part of the energy of earthquake, and decrease the damage, and can solve the problem of displacement of building, therefore, damping material can be considered as an ideal vibration-isolation material. Install energy-attenuation equipment can also reduce vibration but the design of the equipment is extremely difficult.

This research divides into two subjects. The first subject aims at single-hole-swirls, we use single-hole-swirls to discuss water volume to the eddy current influence. The experiment obtains the relations between the aperture and the bottom area of the vessel. It also produces difference between free vortexes and forced vortexes of the eddy current. Our another discussion subject is twin-hole-swirls, which is extremely complex but actually an interesting part. Twin-hole-swirls is easy to be disturbed by the external factors. The result is different from our supposition. But from the experiment we discovered twin-hole-swirls is a mini version of twin-typhoons. Twin-hole-swirls has the same phenomenon with Fujiwhara effect. 本研究探討分為兩個主題。首先是針對單孔，我們利用單孔漩渦探討水量對漩渦的影響，並實驗求得孔徑與容器底面積的關係，以及自由渦流與強制渦流所產生之漩渦的差異。我們另一個探討的主題是雙孔，也是實驗中非常複雜但卻有趣的一部份。雙孔漩渦極易受到外在因素干擾，產生的結果與我們在實驗前的假設出入頗大，但從實驗中我們發現雙孔漩渦其實是雙颱的縮小版，雙孔漩渦與雙颱效應有著許多相符的現象。

We study the magic power of dark energy and dark matter by using theoretical derivation and numerical simulations. We found that: 1. The dark energy will gain kinetic energy from the moving dark matter through gravitational interaction. Due to the law of energy conservation, the motion of the dark matter will slow down and satisfy Ek(t)−Ek0 ∝ρDE1.92 t, where Ek(t) is the kinetic energy of the dark matter, Ek0 is its initial kinetic energy, ρDE is the energy density of the dark energy, and t is the time. 2. The formation history and the structure of galaxies will be different due to the existence of dark energy. The more the dark energy, the earlier the formation of the galaxy core. In addition, the kinetic energy Ek(R) as a function of R will be different if the ρDE is different. Thus we can observationally measure the Ek(R) of galaxies, compare it will our results here, and then deduce the ρDE in our universe. The results here can be applied to the observations in the near future. 我們藉由理論的推導，配合電腦模擬的手段，來探討宇宙中黑暗物質和黑暗能量的神祕力量。我們發現：一、黑暗能量會透過重力交互作用而從運動中的黑暗物質獲得力學能，而且因力學能守恆，致使黑暗物質的速率減慢，滿足 Ek(t)−Ek0 ∝ρDE1.92 t, 其中 Ek(t) 為黑暗物質的動能， Ek0 為其初始動能， ρDE 為黑暗能量的密度，t 為時間。二、星系的形成過程及結構，會因黑暗能量的存在而改變。黑暗能量越多時，星系的核心會越早形成。而且動能 Ek(R) 隨著至星系中心距離 R 的變化，會因 ρDE 的不同而不同，因此可以試圖量測宇宙中星系的 Ek(R) ，然後和這裡的結果比對，即可推導出宇宙中的 ρDE 。這些研究成果，將可直接應用在未來的觀測結果上。

Up to this time we have spent almost three years in studying condensation and water droplets. Little could we have done as compared with the almighty nature. However we are rewarded by the nature as we gradually found the secrets about electro-magneto field and water droplets: The size of water droplets turn smaller upon electro-magneto field and grow more uniformly especially upon electric field. This experiment presented here is actually the diary of the growth of water droplets in condensation, upon magnetic field and electric field. Through convection, it discusses the self assembly patterns of water droplets and peep into the uniformity both of the size and the distribution mode of water droplets. In former basic experiment, we focus on temperature and the speed of water moisture; generally speaking, higher temperature speeds up the coalescence procedure but does not affects the nucleation size of water droplets in simple plain surroundings; while speed of moisture does affects the nucleation size. As we went farther, deep into convection and found magneto-electric force did play an important role 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 experiment anchors the first step in discovering the uniformity of water droplets in different environment, and providing insights into the self assembly mechanism of water droplets upon electro-magneto field with nano sizes. 這是一系列關於水蒸氣冷凝為極細微小水珠的實驗。其中可以分為兩大部分； 第一部分是基礎實驗。將水蒸氣導入至潔淨的介面上(蓋玻片)，觀察冷凝水珠的結構。雖然看似簡單平常，但卻有令人驚奇的發現；不同溫度的水蒸氣，其冷凝最初始的細微顆粒之尺寸是相同的 ！爾後隨著溫度的升高，堆疊速率也跟著上升；以致於最後一起呈現出來的水珠大小不一，尺寸不一。 第二部分是將水蒸氣導到磁場及靜電場上，觀察其冷凝結構。這部分的實驗推翻了一般「水分子是電中性在電磁場中不受影響？」的刻板觀念 ！實驗所呈現出來的冷凝水珠，不但於附加磁場中尺寸縮小又不易長大，同時還有固定的自我組成模式( Slef-assembly pattern);而且也發現在磁場中的冷凝小水珠的尺寸比電場中的小，可是電場中的小水珠則表現出較大的均勻特質。

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。