物理

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。

複雜系統廣泛地存在每個人生活的周遭，儘管這些系統在表象上有明顯的差異，卻不約而同的都呈現出臨界現象。一個簡單的物理概念卻能廣泛地使用在許多不同的場合當中，這是令人始料未及的。這份報告在尋找，是什麼原因導致這許多似乎與物理沒什麼關聯的系統，都呈現出臨界現象？以及這類系統是如何演化的？臨界現象在系統的演化歷史中，又是扮演怎樣的一個角色？一開始，先介紹臨界現象在實際系統中表現的形式，在這以文字系統作為範例。接下來，進入思考的階段，猜測系統個體間存有的關聯性，提出如何影響的假設，並建立模型。從模型結果，可以了解複雜系統隨時間演化的趨勢改變，並發現臨界現象在系統中扮演的角色以及代表的意義。這份報告有三項結論：1. 臨界現象在複雜系統中呈現的形式 2. 模型結果與實際系統十分相似 3. 臨界現象代表著系統的穩定態。The theory of Scaling Law and Universality was originally used in researching Critical phenomena, and now we find it existing in our normal life. A simple physical concept can be used extensively in different courses. This study try to find out the relation between individuals which causes Critical phenomena appear in such different courses in our normal life, and figure out the effect time brings about. To begin with, we introduce the sights of Scaling Law and Universality by exploring the formation of complicated system. Facing a complicated word system as a real example, we observe an extraordinary phenomena, and find out the Universality and Scaling Law in different kinds of linguistics. In the main part, to think further, what’s the relation between the individuals that leads to Critical phenomena? We will give hypotheses and build a model to simulate complicated system from the view of Universality, trying to find out the cause of the interaction of complicated system. From this model, we could understand: When a complicated system evolves with time, the Critical phenomena will naturally occur in this system that could be considered as dynamic equilibrium. From this study we found out(1) The Universality and Scaling Law in complicated systems, here we use linguistics as an example.(2) Under the hypotheses, the simulation is almost as same as the real result of linguistics system.(3) Time plays an important part in the Critical phenomena which can be found in many different complicated systems, and Critical phenomena symbolize a stable state of such systems.

從直徑數公分的小漩渦，到直徑可達10公尺的巨型海漩；由F1~F5級的龍捲風到輕重度颱風，大自然中有各種渦流。不久之前還有雙眼颱風（杜鵑颱風）經過台灣，颱風出現雙眼時其行進路徑常有不尋常的擺動，行進方向忽而偏北，忽而偏南，擺動的頻率比一般颱風來得頻繁，又其結構紮實，對流旺盛，常造成莫大的災害。研究這個主題主要的目的是嘗試探討此雙渦流運動的起因、其運動方式和可能的控制方法。

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。

A diffraction grating was fabricated from an elastic polymer. It was patterned after a plane reflection grating with a pitch of 1200 lines/mm. It was characterized using a HeNe laser to verify properties. Angular scanning as a function of applied strain was observed for two individual wavelengths. Intensity of fiber output was optimized as an application of angular scanning in fine alignment. Beam profiles showed consistency of first order diffraction intensities at different levels of strain. This showed that the elastomeric grating’s efficiency is independent from strain. The elastomeric grating’s variable pitch can be of immense utility in optical communication systems. A stretchable grating can be used to replace typical high-cost architectures of metal or glass gratings of different pitches that correspond to various spectral regions. By changing the pitch, the grating can be used for different wavelength ranges. The elastomeric grating’s variable pitch can be used to scan different wavelengths over a wide range of angles. Angular scanning is used for wavelength channel selection, and since an elastomeric grating diffracts different wavelengths differently, it can be used for wavelength switching and wavelength division multiplexing in optical communication systems. Laser beams of different wavelengths carrying different signals can be transmitted simultaneously through an optical fiber and diffracted to route the wavelengths onto separate wavelength-specific channels.

-to prove my original hypothesis that colour affects the power that is produced by solar panels. \r \r - that the wavelength of an elctromagnetic wave affects the photon or quanta energy that the wave has.

本研究計畫主要探討液晶摻雜奈米碳管後，液晶面板對可見光區之穿透光譜。由於奈米 碳管在應用上有一大缺點是容易聚結糾纏在一起，不容易排列整齊，為了使奈米碳管能夠依 照所希望的方向排列，並且能動態地改變碳管的排列方向，我們將奈米碳管散布在液晶內， 藉以控制奈米碳管的排列。為此，我們自製液晶面板以便能夠自由改變液晶材料的成分，即 調整奈米碳管的種類及粗細長短程度和奈米碳管與液晶材料的混合比例，並量測其穿透光 譜，探討奈米碳管對液晶分子偏轉程度的影響，及摻雜奈米碳管後的液晶面板，其穿透光譜 對各波長光的關係。 第一階段的基礎實驗中，我們先經由控制不同的外加電場，了解液晶分子對各波長的光 之穿透程度隨電場變化的關係；第二階段的實驗中，再進一步控制更多的變因，依需求將控 制不同變因自製液晶面板，並且逐步探討其穿透光譜對於種種變因的關係為何。

磁浮隔空旋轉器是由一個旋轉軸和底座構成，利用兩者間相互排斥的磁力， 產生隔空漂浮的效果。本研究首先對旋轉軸的結構加以分析，並設計啟動裝置， 探討啟動電壓、旋轉軸重量及底座磁力等因素對漂浮轉動的影響。 我們分析維持旋轉平衡的各種作用力，並探討旋轉軸重心位置與摩擦力的關 係，以驗證我們的分析結果。此外，我們也利用自行設計的啟動裝置，提供穩定 的初始轉速，探討旋轉軸重心位置不同時，持續轉動時間的變化，進一步驗證所 做的分析。 為了瞭解磁場在旋轉軸漂浮過程中發生的變化，我們設計了支架把空間座標 化，再以高斯計測量出各點的磁場，獲得各平面的磁場強度分佈圖。配合磁力線 分佈圖與所測得的磁場強度分佈圖，我們以一個嶄新的分析模式，將抽象的磁場 概念具體化，使我們對旋轉軸放置前後及磁力與重力平衡時的磁場變化，更深入 的了解，同時也發現磁場強度會隨距離的增加而減弱。 最後我們在旋轉器上裝置感應線圈，經由旋轉實驗測得感應電壓的存在，證 明旋轉器轉動時，磁場會產生變化。 經由對磁浮隔空旋轉器的探討，我們得以了解它的漂浮原理、磁力與摩擦力 間的平衡關係，以及旋轉前後磁場變化。The Magnetic Floating Spinner(MFS) is composed of one spinner with a magnetic base. The floating effect of the spinner is caused by the interaction between the two opposite magnetic fields. We first analyzed the detail structure of the MFS, and then designed a starter to rotate it. Later, we studied the effect of starting electric potential, the weight of the spinner and the magnetic force of the base on the floating movement. We presented an explanation for the forces that maintained the floating of the spinner and, to support that, we studied the friction force with the position change of the spinner gravity centre. We also used the starter designed by us to provide a stable initial rotating force and analyzed the relationship between the change of gravity centre position and the duration of rotation. In order to understand the magnetic field change during floating movement, we designed a spatial frame to coordinate the spinner that floated above the base. We measured the surrounding magnetic force with the Goth’s apparatus and conducted a magnetic force distribution diagram. According to this diagram and the line of magnetic force, we therefore provide a brand new analysis model , which bring the abstract concepts of the magnetic field into a concrete theory. This research not only brings us to understand the magnetic field change of the spinner before and after its placement over the base and the balance between the magnetic and the gravity force, but also reveals that the magnetic force will wane with the increase of distance. Finally, we placed an induction coil by the spinner to detect a voltage change during spinner movement. This is an evidence that the magnetic field will change during the spinner movement. Through the study of MFS, we can now understand why it floats, the balance between magnetic and friction force, and the change of the magnetic force before and after the spinner movement. MFS = Magnetic Floating Spinner

The set consist two units; the first shall be at the school headmaster office, a box with some openings at the front in which the number of the class is written. In each opening there is lamp which lighting to show the teacher attending in the class, each class has a certain colored lamp.

在實驗用共振法測量聲音在固體、液體、氣體中的駐波聲場，測量各介質中的聲速。研究超聲波在液體中的空腔效應，鋁箔在不同液體受空腔效應所破損面積與時間略成正比，並發現在水與各濃度的洗潔精水溶液中以水的破損效果最明顯。另外利用1.65MHz 高頻超聲波打入水中，因駐波使水有疏密不同產生狹縫，以雷射通過狹縫有光的繞射花紋產生，由干涉條紋可推估駐波波長。利用閃頻共振法研究光彈材料超聲波場，且發展出以肉眼觀測的裝置，由光彈材料的花紋級數與應力研究中，發現花紋級數與應力成正相關，由聲場中的花紋顏色判斷所受應力大小，並發現超聲波不僅有聲場產生並伴隨熱效應，會影響觀測花紋級數。This project began by studying the fundamental properties of acoustic waves, the relationship between its velocity, frequency and wavelength. Experiments regarding the distribution of sound waves in different mediums, and the induction of resonance in solid, liquid and gaseous materials were conducted. Results from utilizing suspending method to confirm theoretical prediction of sound velocity was accurate, and the sound wave patterns in photo-elastic materials were observed. It was also observed that an aluminum foil would be cut in an ultrasonic cleaning device. The effects of different liquids such as water and detergents on cleaning effectiveness were then experimentally determined, taking into account factors such as viscosity. From reference materials, we learned that ultrasonic waves would create Caritation in liquids. Traditionally, sound waves are expected to exhibit only longitudinal waves, yet in this study it was discovered that the residual\r stresses from resonance in photo-elastic materials also indicate the existence of transverse waves.