Selected topics useful for research work

1. Selected topics useful for research work Basic concepts and methods useful for theoretical research (but normally not given in formal classes) are discussed using simple examples.

2. Contents The following list is for reference only, the lectures may not follow it. 0. How to "learn" and "research" – attitude and psychology. 1. Dimensional analysis, self-similar solutions, and scaling laws. 2. Inertial flow, its generalization and implications. 3. Fourier transformation and Fourier series, eigenfunctions and eigenvalues, orthogonalility. 4. Wave-wave interaction, wave kinetics, turbulence. 5. Phenomenological (hand-waving) formulation of highly nonlinear or complex problems. 6. Other problems that may be of interest: the CMA diagram, mode conversion, wave reflection and absorption, etc. 7. How to select, write up, and publish your (great or not-so-great) results.

3. Learning versesResearch In learning, you try to understand the material in the lectures and text books, and follow the methods to solve the homework and examination problems. In research, you look for and work on a problem which you are interested in, and try to get new results, usually by trial and error. Research = search and search again!

4. In the university, you learn how to learnYour major is actually not that important. Note that the word “major” implies there should be many minors. Note that the word university comes from the word universal.

5. Just learning is not sufficient When you have really understood something which you are learning, you would get a special feeling: Ah so! Eureka! 原来如此！ But often such understanding comes only after several or many years!

6. Finding a research problem • Find your interest. Usually guided by your professors, seminars, papers, newspapers and magazines, … • Search and read the most relevant books, papers in the area. Nowadays this is easier: use Google, etc. But be careful, many are wrong!

7. How to read a theory paper Two different types of aims: • To find out what is new in the paper. Usually there is only one new idea or result. Find it and describe it in a few lines. • To learn from the paper certain methods. This is nowadays rather difficult since most papers are quite short. (Authors, referees, readers, and journals love short papers!)

8. Don’t follow the derivation of formulas in the papers. But find out what steps were taken. Try to derive the formulas yourself without following the paper. You should be able to do that at least for the beginning steps. Follow the derivation in a paper only if you become stuck, or when you suspect that it is wrong. Sometimes it is difficult to do the above, such as when the paper is poorly written and no reference is given. Don’t waste time on it unless it is well known! Don’t believe that all published papers are correct. Actually only very few of them are fully correct.

9. Attitude in basic research • Every problem is worth looking into Your problem selection should depend mainly on your interest. If you are in a company or research institute, this may be limited by your project. But many top companies and institutes do not have such restrictions.

10. 2. No topic is “not worth investigating” Any idea is worth looking into. There is always something new to be discovered or details to be more deeply understood. Do not underestimate the importance of any particular area or topic. However, you should first get familiar with the different areas. (In China, the normal undergraduate programs may be too specialized.)

11. 2. Try different ideas and approaches Do not follow any specific idea or method. Try different approaches. Make use of your intuition by guessing!

12. 3. Don’t be afraid of making mistakes Don’t worry about wasting time on unimportant or may-be-wrong problems (if they are not definitely wrong). No new problem is definitely correct. Often you gain more understanding by finding something wrong, since the more subtle points are exposed

13. Referee “report form” of PRL (Old) … please judge the manuscript regarding its: 1) Impact on the specific field: very low ( ) ( ) ( ) ( ) ( ) very high 2) Impact on physics research: very narrow ( ) ( ) ( ) ( ) ( ) very broad 3) Degree of innovation: very low ( ) ( ) ( ) ( ) ( ) very high 4) Validity: not valid ( ) ( ) ( ) ( ) ( ) valid 5) Readability for a nonspecialist: not accessible ( ) ( ) ( ) ( ) ( ) very accessible

14. Referee “report form” of PRL (NEW) Letters published in PRL must meet a high standard of importance and interest. a) Please judge the importance of the paper to its specific field.Not important O O O O O Very important b) Please judge the broad interest of the paper, apart from its importance to its specific field, to a wide spectrum of physicists.Not interesting O O O O O Very interesting c) Please judge the validity of the paper.Probably not validO O O O OProbably valid

15. 4. Look out for new results If your result differs from others or what you expected, it may be wrong, but it may be new! Check it very carefully by using a different approach or discuss with others. Many Nobel Prize discoveries are obtained accidentally!

16. Do not be disappointed if something you did turns out to be wrong, even after many months or years of work. You have actually still gained much experience that is useful in future work. Psychologically: if you believe that you have wasted time, this hard-earned experience will quickly disappear!

17. About “trial and error”, or guessing Actually the most natural process of learning is by trial and error! It is also more fun. All babies learn this way! In particular, foreign languages are most efficiently learned this way.

18. At the beginning, most of your trials will be unsuccessful. But with each unsuccessful trial, you gain much experience. After many trials, you will know how to make good trials! That is why many PhD works were actually done in the last 6 months. If you just complete a well-posed problem (like homework exercise) from your advisor, you really have not learned very much.

19. Any questions?