推著離子跑
在本次實驗中，我們發現溶液中的帶電離子，會因為離子團的熱運動，和電偶極的庫倫吸引力(electric dipole)的交互作用下，使得電解質溶液的I-V curve(電流-電壓 曲線)，具有類似磁滯曲線(Hysteresis curve)的效果，同時我們運用光學干涉的原理，證實此時在電場作用下，離子團會互相順著電場方向作條列鍵結，而加熱實驗也證實，熱運動會使溶液的I-V curve(電流-電壓 曲線)變的不一樣。另一方面，我們也發現，在給予電解質溶液一外加的衝擊電壓時，該溶液的電荷分布，?會因為彼此的互相擠壓以及自由擴散的作用下，而形成一震盪分布，其所顯現出來的，則是電壓的震盪變化。最後由於震盪波紋的變化，在起始時與中段之後有著明顯差異，我們對此變化提出看法和證實，相信內容是精采可期的！ In this experiment, with the interaction of the heating action of ionic atmosphere and electric dipole, we find that ionic in the liquor makes the I-V curve in the electrolyte liquor show up with the effect similar to Hysteresis curve. Meanwhile, we practice the principle of interference to prove that at this moment, under the influence of electric field, ionic atmosphere will connect to each other in line following the direction of the electric field. It is also proven that in the heating experiment, heating action will make I-V curve in the liquor different.On the other hand, we also find with extra electric impact, the charge distribution of the liquor will form a oscillation, that is, the changes of the voltage oscillation under the inter-collision and the free spread. We offer our viewpoints and proofs about the obvious changes of oscillation wave in their beginning stage and after their middle stage. We believe that the marvelous content is surely worth of your expectation.
「渦」藏「聖」機--以渦流脫離重新詮釋聖嬰發生的原因
If we place a block in continuous, steadily flowing water, some periodic eddy currents will appear behind it. In my report, I would like to introduce a new way to explain how the periodical movement of eddy currents would help to triggering El Nino. According to my experiment, these eddy currents have a certain life cycle, and the eddy current give a force, which drag water form the area they just went by. It will cause water level became lowest for a period of time. These phenomena are also shown in the real data of “Sea Surface Height Anomaly”, it is a quiescence period, and then changes into the highest one it is interesting that highest one always follows by the starting of El Nino. Another important result from my experiment is that, in the same fluid, the frequency of eddy currents is controlled by 2 variables: Size of the block and velocity of the flow, From this result, then get the frequency of eddy current-occur every 3.2 years. It is just correspond with frequency of historical data the El Nino from the 70’s to the present.
本報告嘗試以南極繞極環流在南美洲南端產生週期性渦流脫離的現象來解釋聖嬰的發生根據水槽實驗的結果，水流在通過障礙物後渦流脫離瞬間，會形成一水位低的空區，之後在周圍的水大量湧入，水位突然升高，並有一段時間的振盪。另外，實驗結果也顯示，渦流形成和脫離頻率大致上和注水流速成正比，且和障礙物的大小成反比。根據此結果，對照實驗結果，我認為1993 年3-4 月，1996 年1-6 月及2001 年7-10 月三個「海平面高度異常」的最低值密集帶，此極可能是渦流脫離的時段。且對照「海平面高度異常」實際資料後，發現「海平面高度異常」的「最低值密集帶」後均伴隨水面「寧靜期」，接著就出現周圍暖水流大量湧入的「最高值密集帶」，此時南美洲東南側海水溫度驟增，接著馬上接續著聖嬰的到來。「海平面高度異常」分析的結果，指示渦流脫離的「最低值密集帶」和顯示著聖嬰到來的「最高密值密集帶」間約間隔半年左右。我們推算水的史托爾數約為1，以這個值代入實際南極繞極環流通過南美洲南端，得到渦流脫離的頻率約每3.2 年一次，和長期聖嬰發生的平均頻率非常接近。
生生不息-正五邊形的繁衍及算術法則
This study was to explore the nature of two basic constitutes of the regular pentagon,With these two constitutes, the regular pentagon could be multiplied into any times in size. We used four multiplication methodsto show how the regular pentagon enlarge and to verify that the enlarged regular pentagons derived from computer did exist. By integrating these four multiplication rules, we were able to arrange regular pentagon of any length of side, and evidenced the equation was ( If m,n is the number of A,B of a regular pentagon respectively ) When we tried to verify if any regular pentagon could be constituted by other smaller regular pentagons, we found that it was un-dividable only if the length of pentagon side were (the number of A, B were the 2n and 2n-1 item of Lucas Sequence), otherwise, any regular pentagon is able to be constituted by other smaller regular pentagons. The divided forms could be multiple. We also found that any pentagon could be divided by two successive un-dividable pentagons, which is called “standard division rule”. We expected to derive all kinds of division by analysis of two successive un-dividable pentagons in standard division rule.
這個研究起源於一個拼圖玩具：利用兩種黃金三角形排出指定大小的正五邊形。我們的研究動機是：一、 假如無限量供應A 和B，能夠拼出哪些邊長的正五邊形？二、 哪些拼好的正五邊形不能拆成一些較小的正五邊形？我們將研究的主要結果分述如下：
n x n 方格表中的計數問題
對4 × 4 方格表中計數問題的二個解題方法(1..解方程式的方法， 2.分割圖形的方法)作分析和研究後，首先我推廣分割圖形的方法來証明 : “好的n × n 方格表” 存在若且惟若n 為偶數。同時証明這種“好的n × n 方格表”內所有n2 個數的總和f(n) 為n(n+2)/4。當討論一般的n×m 方格表時，發現分割圖形的方法盲點，無法繼續推廣來証明。再經過深入分析與推廣解方程式的方法，藉由n×m 變數方格表，我們終於找到構造所有“好的n × m方格表”的方法。同時計算“好的n × m 方格表” (n≦m)內所有mn 個數的總和f(n,m), n≦7和証明好的nxm 方格表會有2(n+1)行一個循環的現象。We first studied two solution methods (1.solving equations,2.dissecting diagrams.) for calculations on 4x4 checkboard. Using the method of dissecting diagrams, we proved that``good nxn checkboard'' exists if and only if n is even. Furthermore, the sum f(n) of those n2 numbers in a ``good'' nxn checkboard is equal to n(n+2)/4.In studying the more general nx m checkboards, we found that the method of dissecting diagrams does not work, However, by extending the method of solving equations, and by considering nx m variable checkboards, we obtained a way of obtaining all ``good nxm checkboards.'' By way of computing the sum f(n,m) (n≦7) of those mn numbers in a ``good nxm checkboards,'' periodicity in every 2(n+1) rows is observed.
宇宙演化的黑手
We study the effect of dark energy on the evolution of cosmic structure in a scenario where the dark energy is treated as free particles and thus can be localized. By theoretical derivation and numerical simulations, we found that:
1. The dark energy particles gain kinetic energy from a moving dark matter particle through gravitational interaction. Due to energy conservation, the dark matter particle will slow down with time
Ek(t) = Ek0 - 9 × 10-5[|1+3w|ρDE]1.92t where Ek(t) is the kinetic energy of the dark matter particle,Ek0 is its initial kinetic energy, w is the coefficient of equation of state for dark energy, ρDE is the mean energy density of dark energy, and t is the time.
2. The formation history and structure of galaxy clusters are different in the presence of localized dark energy. The more the localized dark energy, the earlier the formation of the cluster core. In addition, the kinetic energy Ek(R) as a function of R will be different if the ρDE is different. Thus we can compare the observed Ek(R) of clusters with our results to deduce the ρDE in our universe. The results here can be applied to the observations in the near future.
我們探討宇宙結構演化受到可局部叢集之黑暗能量粒子的影響。藉由理論推導及電腦模擬，我們發現：
一、黑暗能量粒子會透過重力交互作而從運動中的黑暗物質粒子獲得力學能。因力學能守恆，黑暗物質粒子的速率會減慢，滿足
Ek(t) = Ek0 - 9 × 10-5[|1+3w|ρDE]1.92t
其中Ek(t) 為黑暗物質粒子的動能，Ek0 為其初始動能，w 為狀態方程式係數，ρDE 為黑暗能量的平均密度，t 為時間。
二、星系團的形成過程及結構，會因可局部叢集之黑暗能量的存在而改變。黑暗能量越多時，星系團的核心會越早形成。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，因此可以將量測到的 Ek(R) 和這裡的結果比對，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。