S-duality

In theoretical physics, S-duality (also a strong-weak duality) is an equivalence of two quantum field theories, string theories, or M-theory. An S-duality transformation maps the states and vacua with coupling constant g in one theory to states and vacua with coupling constant 1 / g in the dual theory. This has permitted the use of perturbation theory, normally useful only for “weakly coupled” theories with g less than 1, to also describe the “strongly coupled” (g greater than 1) regimes of string theory, by mapping them onto dual, weakly coupled regimes.

— Wikipedia on S-duality

2010.07.01 Thursday ACHK

Rinus Michels

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Marinus (“Rinus”) Jacobus Hendricus Michels (9 February 1928 – 3 March 2005) was a Dutch football player and coach who was named “coach of the century” by FIFA in 1999. He played his entire career for the club Ajax Amsterdam, whom he later coached, and was a member of the Netherlands national team both as a player and as manager.

Michels became most notable for his coaching achievements, having won the European Cup with Ajax and the Spanish league with Barcelona, and having had four tenures as coach of the Netherlands national team, whom he led to reach the final match of the 1974 World Cup and to win the 1988 European Championship. He is credited with the invention of a major football tactic known as “Total Football” in the 1970s.

— Wikipedia on Rinus Michels

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2010.07.01 Thursday ACHK

選圖三部曲

選圖問題 3

Choosing a graph 3

1991-CE-PHY II-7 b

這段改篇自 2010 年 3 月 18 日的對話。

因為這 4 條式,假設了「constant acceleration」,所以,在不是「constant acceleration」的情況下,就不可以用。換言之,如果題目提到「constant acceleration」的話,即是暗示了你要用那四條 kinematic equations 的其中一條。

Constant force –> constant acceleration –> kinematic equations

那現在應該用這 4 條公式中的哪一條呢?

題目給你選的圖全部也是 vt graph,所以你應該用有 tv 的那一條式,即是

除了「constant force(恆力)」外,你剛才還間底了「initially at rest(初始時,物體為靜止)」。 「constant force」這個資料已經用了。現在是用「initially at rest」的時候。「initially at rest」,即是 u = 0 。 所以方程式可以化簡為

凡是這類「選圖問題」,如果你不是立刻「感受」到哪個是答案的話,你就一定要用以下的三部曲

1. 寫下一條方程式,連繫起 x-軸 和 y-軸 的 variables(變量)。

2. 看看該條公式是 一次方()還是 二次方()。如果是一次方(linear)的話,該圖就是一條直線。如果是 二次方(quadratic)的話,該圖就是一條曲線(拋物線)。

3.1 如果是直線的話(),看看 m 是正還是負,就可以知道那條直線的斜率(slope)是正還是負,因為 m 本身就是代表斜率。

3.11 m 正的話,那條直線就是向右上發展的。

3.12 m = 0 的話,那條直線就是一條平線。

3.13 m 負的話,那條直線就是向右下發展的。

3.2 如果是拋物線的話(),看看 a 是正還是負。

3.21 a 正的話,那條拋物線就是向上張開的(open upwards)。

3.22 a 負的話,那條拋物線就是向下張開的(open downwards)。

— Me@2010.07.01

2010.07.01 Thursday (c) All rights reserved by ACHK