The books once interested me

coolboy

The examples shown in previous several posts on mis-translation of “eddy” into Chinese leading to misconceptions were obvious and easy to understand. On this cfluid forum there was a member 对月 who once posed an interesting question that inspired a fruitful discussion by many well known cfluid members for a long time:

湍流与黏性有什么关系?  [对月]
http://www.cfluid.com/thread-45389-1-6.html

This particular question and its discussion were actually somewhat related to the issue of whether people have misunderstood the meaning of “eddy” or not.

By the way, I once had the following appraisal to 对月:

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为什么非定常湍流流场也可以采用时间平均法或非均匀流场可用空间平均法 [5楼]
http://www.cfluid.com/thread-118732-1-3.html
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尽管后面的有些帖子对错误的解释具有非常清晰和科普的特性，但实际上最专业、最给力论述还是由[6楼]的对月给出：

[6楼] 对月：RANS使用的是系综平均啊！

从对月的这一及其它的一些发言来看，他的流体力学功底还是不错的。
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“其它的一些发言” mentioned above include his views and statements shown in the above post.


Q: What is the connection or is there a connection between turbulence and viscosity?

A: There may or may not be a connection between turbulence and viscosity. In any case, it is a misunderstanding to think that there is a connection between turbulence and viscosity due to the following reasoning: “Turbulence is associated with 涡 and 涡的级串. Furthermore, the generation and dissipation of 涡 often involve viscosity. As a result, turbulence and viscosity are closely connected.” The problem in the above reasoning is obvious: the word 涡 in the first statement refers to “eddies” whereas the same Chinese word 涡 in the second statement refers to “vortex”. Eddies and vortex are often different in their physical meanings.

coolboy

I mentioned above that Cauchy laid a rigorous foundation for the calculus and A. N. Kolmogorov laid a rigorous foundation for the probability theory. Some people may feel surprised that the probability theory has or needs a rigorous foundation because the probability theory itself is a field about uncertainty. Another field that also carries great uncertainty is the quantum mechanics. I once took a course of quantum mechanics. The major textbook and secondary reference book for the course were:

Shankar, R., 1980: Principles of Quantum Mechanics. Plenum Press, New York, 612 pp.

Messiah, A., 1990: Quantum Mechanics. Vols. 1 and 2. Dover Pub., Inc., New York, 1136 pp.

One feature of Shankar’s textbook is that the author proposed four postulates from which the nonrelativistic quantum mechanics can be developed. Such an approach or the style of presentation is similar to the above mentioned works of Cauchy and Kolmogorov of laying a rigorous foundation for a field. The professor spent two lectures on discussing those postulates and emphasized the importance of those postulates to the field, while sometimes referring to Messiah’s textbook for more detailed explanations or related background materials.

coolboy

So, Augustin Cauchy was really a very brilliant mathematician who laid a rigorous foundation for the calculus. Yet, he also made mistakes in his mathematical papers. One famous and interesting mistake he made was on his proof to Fermat’s Last Theorem in the field of number theory. Fermat’s Last Theorem states:

There are no whole number solutions for the following equation

x^n + y^n = z^n

for n greater than 2. I once also mentioned the Fermat’s Last Theorem:

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关于流体力学的讨论   [97楼]
http://bbs.lasg.ac.cn/bbs/thread-56846-10-6.html

coolboy [2009-3-12 21:52] （关于猜想）

哥德巴赫猜想是数论里面的一个很有名的猜想。费马定理在证明之前也是数论里面的一个猜想。数论一开始就是当年一些富家子弟在饭后茶余为消磨时间玩弄数字游戏而发展起来的。当年各式各样的数字猜想有很多很多。哥德巴赫当年就有名气，因为他的数字猜想多数是对的。所谓猜想是“对的”其实包含两层意思：（１）数学上严格证明了使之成为定理，（２）用一个个数字从小到大地不断地去试（验证）猜想，发现都是对的，则称为一个正确的猜想。早期的数论研究主要涉及整数， 从而使得方法（２）成为可能。

当然玩弄数字游戏中提出来的猜想绝大多数是错的，是错误的猜想。说某猜想是“错的”可比说它是“对的”简单得多了。用一个个数字从小到大地不断地去试猜想，若发现有一个数字试得不对，则猜想就错了。不过当年也是乐意提新猜想的人比证明或试猜想的人多。除非是象哥德巴赫这种名人又有什么新猜想，则大家也都一窝蜂的来试试，一步步地用很多很多数字来试。

一些不太有名的人提了些猜想，用十几，二、三十个数字试了发现都是对的，大家也就不再去追究了（猜想太多了哈），反正没什么名气的猜想多那么几个也无所谓。二、三十年后有人读到那些猜想，再用大一点点的数字来试试。哈！猜想是错的！
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On March 1, 1847, the French Academy of Sciences offered a series of prizes, including a gold medal and 3,000 Francs, to the mathematician who could prove Fermat’s Last Theorem. On that day, Gabriel Lame and Augustin Cauchy both claimed that they had (independently) proved the theorem. They both had a few weeks to formally submit and publish their complete proofs. It turned out that both proofs were wrong. Another mathematician Ernst Kummer later found that Lame and Cauchy essentially made the same mistake in their proofs. Their proofs relied on the so-called fundamental theorem of arithmetic in number theory, stating that any number can be uniquely factorized into a combination of a set of prime numbers. The fundamental theorem of arithmetic does not hold for imaginary numbers whereas in Lame and Cauchy’s proofs, those factors could be complex numbers. Thus, their proofs were not valid.

Fermat’s Last Theorem was finally proved by Andrew Wiles in 1995. The above story on Lame, Cauchy and Kummer was taken from the following book:

Singh, S., 1997: Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem. Anchor Books, New York, 315 pp.

coolboy

So, Cauchy made a mistake in mathematics even though he was a brilliant mathematician in his scientific researches. This should not be surprised because many or most scientists make mistakes in their scientific careers. I once told another story in the following link about Albert Einstein who too made a mistake on the formation of the m_a_g_n_e_t_i_c fields of a planet or a star:

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大气海洋领域有没有“通才”啊？  [18楼]
http://bbs.lasg.ac.cn/bbs/thread-1903-2-69.html

Albert Einstein made many important contributions in physics. However, this does not mean that he was right in everything he pursued. “地心引力跟电磁场” was one important example that Albert Einstein was wrong. Here is a true story. In 1920s, Albert Einstein was well known to the world that he was famous and was a great physicist. Many young scientists liked to visit Albert Einstein to get his advice on their own researches and ideas. One time, there was a young man in his 20s visited Albert Einstein. He proposed and discussed his own idea with Einstein on how the Earth’s m_a_g_n_e_t_i_c field was formed. He believed that the Earth’s m_a_g_n_e_t_i_c field was generated by convection (fluid motion) because very deep inside the Earth, the rock/iron became the ionized fluid. Albert Einstein disagreed with this young man’s view. Einstein thought that the m_a_g_n_e_t_i_c field of the Earth, a planet or a star such as the Sun existed due to the universal gravitational force influenced by the rotation of that body (Earth, planet or star).

It turned out that, this time, the young man was right! Later, he became the “father” of the field called “geodynamo” that explains how the m_a_g_n_e_t_i_c field of the Earth or other astronomic bodies is generated.

That young man’s name was Walter M. Elsasser.

Reference:
Elsasser, W. M., 1978: Memoirs of a Physicist in the Atomic Age. Watson Pub Intl, 268 pp.
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It is now generally believed that it was De Broglie who first showed electrons too having wave properties and proposed the famous wavelength-momentum relation of [lambda]=h/p. In fact, Walter M. Elsasser also independently proposed the same relation and his《Nature》paper describing the wave-particle relation was published before De Broglie’s work became public. However, since De Broglie’s work was his PhD thesis that was comprehensive and in detail whereas Elsasser’s work was brief and short, only a few people were aware of and cited Elsasser’s paper afterwards. As time passes, De Broglie becomes the only one to be remembered by the people in this field.

coolboy

I mentioned a few books in the comments I made recently. Those books are copied below together with the context of the comments:

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【科学网】千元人民币 悬赏求解题  [38楼]
http://www.cfluid.com/thread-145992-3-2.html

coolboy (2015-7-24):

简言之，对流体运动的欧拉描述和拉格朗日描述的区别主要体现在运动方程上。无论是欧拉描述还是拉格朗日描述，时间始终是自变量，流体的压强与密度始终是因变量。此外，对于欧拉描述，空间坐标（系）[x,y,z]是自变量，速度场[u,v,w]是因变量。对于拉格朗日描述，流体质点（或微元）的（固定）标记[a,b,c]是自变量，流体质点的空间位置[X,Y,Z]是因变量。

比如说，对于连续性方程，它的欧拉描述由Batchelor(An Introduction to Fluid Dynamics)书中74页的方程（2.2.2）给出。而它的拉格朗日描述则由同一书中79页中间的习题方程给出。比较一下两方程应该很清楚地看出：欧拉描述有速度但没有质点坐标，拉格朗日描述有质点坐标但没有速度。求解欧拉描述的方程得到速度场之后，也同时可求出质点坐标（例如齐成伟的工作）。同理，求解拉格朗日描述的方程得到流体质点的空间位置随自变量时间的变化之后，也应该可求出质点在某坐标系中的速度场。

关于拉格朗日描述的动量方程组，可以在比较老的流体力学经典著作中找到，如Lamb的Hydrodynamics或Milne-Thomson的Theoretical Hydrodynamics。
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Batchelor, G. K., 1967: An Introduction to Fluid Dynamics. Cambridge Univ. Press, Cambridge, 615 pp.
Lamb, H., 1932: Hydrodynamics, Sixth edition. Dover, New York, 738 pp.
Milne-Thomson, L.N, 1962: Theoretical Hydrodynamics, Fourth Edition. The Macmillan and Co, Ltd., 660 pp.

coolboy

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[趣闻轶事]闲聊几句郭汉英（转载）  [11楼]
http://www.cfluid.com/thread-147468-1-1.html

coolboy (2015-7-30):

光速不变原理是狭义相对论根据实验结果提出的两大假设之一。
“光速不变原理：相对于每个惯性参考系，光在真空中都以恒定的速度c传播，并与光源的运动无关。”

上面的光速不变原理是一字不改地从梁昆淼、吴秀芳《狭义相对论初步》的书中摘录下来的。书中同时介绍了好几个导致这一原理的实验背景和结果。

在Landau和Lifshitz的名著《The Classical Theory of Fields》中，相关叙述如下：
The velocity of light is the same in the K and K’ systems. If the interval ds between two events is defined as ds^2=c^2*dt^2-dx^2-dy^2-dz^2, then ds^2=ds’^2 or s=s’. This invariance is the mathematical expression of the constancy of the velocity of light.

在爱因斯坦的《The Meaning of Relativity》一书中，他是这样说的：r=c*dt and r’=c*dt’ must be mutually consistent with each other with respect to the transformation which transforms from K to K’.
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梁昆淼、吴秀芳，1988:《狭义相对论初步》, 湖南教育出版社，241页。
Einstein, A., 1956: The Meaning of Relativity, Fifth Edition, Including the Relativistic Theory of the Non-Symmetric Field. Princeton Univ. Press, 166 pp.
Landau, L. D., and E. M. Lifshitz, 1975: Course of Theoretical Physics. Vol. 2: The Classical Theory of Fields. Fourth Edition. Pergamon Press, New York, 402 pp.

coolboy

An interesting book from the discussion on recent news:

美宇航局确认火星表面存在流动的液态水
http://www.cfluid.com/forum.php?mod=viewthread&tid=147896

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下一专著是关于地外生命的研究的世界名著：

I. S. Shklovskii and Carl Sagan, 1966: Intelligent Life in the Universe. Holden-Day, Inc., San Francisco, 509 pp.

这一专著出名的原因除了内容全面、系统之外，也与两位作者的名气及尤其是该书的成书过程有关系。I. S. Shklovskii与Carl Sagan分别是前苏联和美国的知名天文学家。我在下一个帖子中还专门提到过Carl Sagan

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天文学家对全球气候变暖的贡献
http://bbs.astron.ac.cn/thread-94236-1-1.html

我在科学院大气所的动力论坛上发了一个帖子，讨论和科普全球气候变暖的问题。最近聊到了天文学与之相关的内容，在此也转载一下吧：

关于全球气候变暖   [coolboy]
http://bbs.lasg.ac.cn/bbs/thread-42150-13-1.html
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列出两篇有关金星大气的二氧化碳温室效应导致金星地面高温的相关论文：
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（2）Sagan,C., 1962:Structure of the lower atmosphere of Venus. Icarus, Volume 1, p. 151-169.

“If the centimeter microwave emission from Venus arises from its surface, the radar reflectivities and microwave brightness temperatures give mean dark side surface temperatures of about 640K. Extrapolations of the phase data to small phase angles indicate mean bright side surface temperatures of about750K.......”

C. Sagan就是Carl Sagan，是非常有名的天文学家。此外，他还非常热衷于天文科普，故也为大众所熟知。
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Iosef Shmuelovich Shklovskii在写作最初俄文版专著的时候采纳了Carl Sagan相关论文的一些内容。Carl Sagan在把俄文版专著翻译成英文的过程中添加了大量的评论和注解，以至于添加的评注都几乎超过了原著的内容。在此基础上，I. S. Shklovskii又对英文版作了不少补充及辩解。当时苏美两国是处于严重的敌对状态，两位作者也从未见面。尤其是两人的政治、科学观点存在很大的区别，但最后的英文版专著还是以共同作者的形式出版了。也正是由此原因，该书的特色就是书中凡是Carl Sagan的评论、观点或写作都用记号标明。

该书中还提到了当时苏联天文学会的一些会员认为地外生命的存在是辩证唯物论(dialectical materialism)的必然结果。若火星或甚至木星上不存在生命则也相当于对共产主义哲学基础的否定(a clear disproof of the philosophical basis of Communism)，而后者是不可想象的事，呵呵。
#################################################

coolboy

It was pointed out above that the book by Shklovskii and Sagan published in 1966 was quite unique in its quality and, especially, in its style that the two authors coming from different counties represented two leading experts in the field. They worked collaboratively to write a book to present materials in a systematic way as if the book were written by a single author and yet their personal views were also distinguishingly presented in the book. However, such a style of writing is common nowadays in the internet age where a group of people may compose a threat of writings through the internet media even without knowing each other’s true identities. The following link shows an interesting example:

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Let's cook a story  (by jlo, funnydd, and 9494)
http://bbs.lasg.ac.cn/bbs/thread-35343-1-1.html
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coolboy

Often, a common way of two or a few leading experts working collaboratively to publish a book in science fields is to serve as editors to publish a collection of papers in a particular field. One such book on my bookshelf is:

Holton, J. R., and T. Matsuno, (Editors), 1984: Dynamics of the Middle Atmosphere. Terra Sci. Pub., Tokyo, 543 pp.

The authors were from USA and Japan, respectively, and were leading experts in the field as described by the book title.

coolboy

Another interesting book of the same style on my bookshelf is:

叶永煊（W.-H. Ip），吕保维，（主编），1988，空间物理学进展，四川科学技术出版社，成都，800页。

There were totally eight interesting papers included in the above book:

叶永煊（W.-H. Ip）：彗星与太阳风的相互作用过程
黄云潮（Y. C. Whang），章公亮：外日球太阳风相互作用区的演化
吴京生（C. S. Wu），霍泰山：在太阳风中的离子捕获加速过程
涂传诒（Chuan-yi Tu）：行星际等离子体的起伏及其对太阳风的加速和加热作用
李罗权（L. C. Lee），刘振兴，地球磁层中的多重X线磁场重联
吕达贤（A. T. Y. Lui，吴寄萍译）：地球磁尾
吴京生（C. S. Wu），陈奎宁：回旋激射不稳定性---地球极光区千米波辐射的机制
资民筠，沈长寿：对流电场、场向电流和磁层-电离层偶合

Among all the authors listed in the above papers, I believe the most interesting and famous one should be 陈奎宁 who worked at 四川科学技术出版社 at the time and later edited or published many, many other interesting books (thus should be famous) such as《格兰特船长的儿女》。 Of course, 陈奎宁 was the least knowledgeable and completely a moron in the field of space physics.

coolboy

The above book later became volume one of a book series:

空间物理学进展（第1卷）- 1988
空间物理学进展（第2卷）- 1992
空间物理学进展（第3卷）- 2001
空间物理学进展（第4卷）- 2013

coolboy

The above book series (空间物理学进展) was published in Chinese. There was also an English title on its cover page: Advances in Space Physics. Generallly speaking, “Space Physics” is mostly concerned with “Plasma Physics”. I had one post in this bbs mentioning the plasma physics:

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闲聊等离子体物理(Plasma Physics)  (coolboy)
http://www.cfluid.com/forum.php?mod=viewthread&tid=141007
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“Plasma” is translated into Chinese as “等离子(体)” in Mainland China and as “电浆” in Taiwan. I believe the translation of “等离子(体)” emphasizes its quasi-neutrality whereas the translation of “电浆” emphasizes the nature of its long-range force of plasma fluid. Quasi-neutrality and long-range force of a plasma fluid are closely connected, as was discussed in my above post.

Below are some of the books on plasma physics on my bookshelves:

Chen, F. F., 1984: Introduction to Plasma Physics and Controlled Fusion. Vol. 1: Plasma Physics. Second Edition. Plenum Press, New York, 421 pp.

Baumjohann, W. and R. A. Treumann: 1996: Basic Space Plasma Physics. Imperial College Press, London, 329 pp.
Treumann, R. A., and W. Baumjohann, 1997: Advanced Space Plasma Physics. Imperial College Press, London, 381 pp.

Bellan, P. M., 2006: Fundamentals of Plasma Physics. Cambridge Univ. Press, Cambridge, 609 pp.
Boyd, T. J., and J. J. Sanderson, 2003: The Physics of Plasmas. Cambridge Univ. Press, 532 pp.
Ginzburg, V. L., 1989: Applications of Electrodynamics in Theoretical Physics and Astrophysics. Gordon and Breach Science Pub., New York, 475 pp.
Goldston, R. J., and P. H. Rutherford, 1995: Introduction to Plasma Physics. Institute of Physics Publishing, Philadelphia, 491 pp.
Gurnett, D. A., and A. Bhattacharjee, 2005: Introduction to Plasma Physics – With Space and Laboratory Applications. Cambidge University Press, 452 pp.
Kadomtsev, B. B., 1965: Plasma Turbulence. Academic Press, New York, 149 pp.
Melrose, D. B., 1986: Instabilities in Space and Laboratory Plasmas. Cambridge Univ. Press, Cambridge, 280 pp.
Schunk, R. W., and A. F. Nagy, 2009: Ionospheres. Physics, Plasma Physics, and Chemistry. Second Edition. Cambridge Univ. Press, 628 pp.
Smirnov, B. M., 2001: Physics of Ionized Gases. John Wiley & Sons, Inc., New York, 381 pp.
Stix, T. H., 1992: Wave in Plasmas. Amer. Inst. Phys., New York, 566 pp.
Sturrock, P. A., 1994: Plasma Physics: An Introduction to the Theory of Astrophysical, Geophysical and Laboratory Plasmas. Cambridge Univ. Press, 335 pp.

The book by F. F. Chen remains to be the most popular textbook in the field.

coolboy

The book by F. F. Chen remains to be the most popular textbook in the field. Authors often use simple examples to illustrate certain important physical processes in textbooks that are not rigorously correct. One such example was described in the following post:

闲聊等离子体物理(Plasma Physics)   [12#]
http://www.cfluid.com/thread-141007-1-2.html
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下面定量地再来描述一下。我们知道力是一个矢量。对于有势力来说，它是位势（即能量）场的梯度。因为位势是一个数量，故对于有势力来讲用它的位势场来表达更简洁。既然求了空间梯度（导数）的作用力与距离的平方成反比，则其所对应的位势场应该是反比于距离（的一次方）。例如，重力场与静电场的位势分别是：
[phi]_g = -G*m/r
[phi]_c = q/(4*pi*epsilon_0*r)
在“准中性”条件下考虑了抵消作用或屏蔽作用之后的位势分布则是：
[phi]_p = q*exp(-r/D)/(4*pi*epsilon_0*r)
即比库仑电场多出了一个指数衰减的因子。尽管[phi]_p只是空间r的一维函数，但它已包含了三维空间的球形效应。若在推导中（有些教科书）只考虑一维直角坐标沿x方向的变化，则得到的位势函数会少一个距离因子：
[phi]_p=[phi]_p0*exp(-x/D).
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The above “（有些教科书）” actually referred to the textbook by F. F. Chen (1984) in which one-dimensional Cartesian coordinate was used to derive and solve the Poisson’s equation for the potential.

coolboy

The book by F. F. Chen remains to be the most popular textbook in the field. The fundamental concepts described by a popular textbook, regardless whether it is right or wrong, will be repeated by others and thus will be widely spread. In other words, it is very difficult to correct a misconcept in an old popular textbook. One example of a misleading concept in plasma physics has been described in my post:

闲聊等离子体物理(Plasma Physics)   [2#]
http://www.cfluid.com/thread-141007-1-2.html
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根据上面的讨论，我们应该可以得知，上面所提的两项的无量纲比值应该可以描述电磁场对流体的作用。这一无量纲参数被称之为等离子体beta(plasma beta)。它是上述方程中p与B*B/(2*[mu])两项之比：beta=2*[mu]*p/(B*B)。某教科书上是如此定义它的：“the ratio of thermal-to-m_a_g_n_e_t_i_c energy density in the plasma”。当然，也有些书的作者（或更多的作者）由于受了p是压力（pressure，实际上是压强或是压力位能）的影响，把B*B/(2* [mu])也当作磁场压力来理解。从而把plasma beta定义成两压力项之比：“one can define a plasma beta parameter as the ratio of thermal and m_a_g_n_e_t_i_c pressure”。

根据上面该帖子中的讨论，B*B/(2*[mu])当然应该按照磁场能量而不是按照磁场压力来理解。导致混淆的原因则是那些作者没有意识到我在该帖子讨论中一开始就解释的一个“力-能”的对应关系：
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The above “也有些书的作者” also referred to F. F. Chen and his textbook. Since the first edition of his textbook was published in 1974 and the popular textbook of the second edition was published in 1984, it was not surprised to find that the misleading concept of considering B*B/(2* [mu]) to be m_a_g_n_e_t_i_c pressure rather than m_a_g_n_e_t_i_c energy was followed by most other authors (i.e., “（或更多的作者）”), who sometimes lack the independent thinking and only blindly follow or compile what the previous authors said in old textbooks.

On this particular issue, one interesting case was given by W. Baumjohann and R. A. Treumann who also wrote a set of two-volume textbooks on space plasma physics. In Volume 1 of the textbook of “Basic Plasma Physics” published in 1996, the authors misleadingly stated “one can define a plasma beta parameter as the ratio of thermal and m_a_g_n_e_t_i_c pressure”. In Volume 2 of the textbook of “Advanced Plasma Physics” published in 1997, the authors apparently realized the mistake and made a correction by restating the plasma beta to be “the ratio of thermal-to-m_a_g_n_e_t_i_c energy density in the plasma”.

coolboy

It was interesting to learn and understand how the word “plasma” was translated into Chinese in different science communities, i.e., “等离子(体)” in Mainland China versus “电浆” in Taiwan. Another example was the word “laser”. It was translated into Chinese in “激光” in Mainland China and in “镭射” in Taiwan and HongKong. The word “laser” is the acronym of “Light Amplification by Stimulated Emission of Radiation”. The word “激光” was a very nice translation based on its physical meaning of “laser”. On the other hand, “镭射” was primarily a phonic translation of “laser”. However, since the character “镭” refers to a radiatively active chemical element the word “镭射” also partially catches the physical meaning of “laser” (though it was an incorrect physical meaning to professionals).

I once wrote an essay in which I mentioned that I also learned “laser physics” while studying “plasma physics”:

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Encounter with a bright angel
http://bulo.hujiang.com/diary/919788/

coolboy (2005/6/28):
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Luckily, it turned out that the "physics of fiber optics" was very closely related to "laser physics", which in turn happened to be loosely related to "plasma physics" that was the field I was working on at the time.”
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The textbook for me to learn laser physics was:

Eastham, D., 1986: Atomic Physics of Lasers. Taylor & Francis, London, 230 pp.