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.
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.
Learning verses Research
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!
In the university, you
learn how to learn
Your 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.
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!
Finding a research problem
1. Find your interest. Usually guided by
your professors, seminars, papers,
newspapers and magazines, …
2. Search and read the most relevant
books, papers in the area.
Nowadays this is easier: use Google,
etc. But be careful, many are wrong!
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!)
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.
Attitude in basic research
1. 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.
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.)
2. Try different ideas and approaches
Do not follow any specific idea or
method.
Try different approaches.
Make use of your intuition by guessing!
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
Referee “report form” of PRL (Old)
… please judge the manuscript regarding its:
1) Impact on the specific field:
2) Impact on physics research:
3) Degree of innovation:
4) Validity:
5) Readability for a nonspecialist:
very low ( ) ( ) ( ) ( ) ( ) very high
very narrow ( ) ( ) ( ) ( ) ( ) very broad
very low ( ) ( ) ( ) ( ) ( ) very high
not valid ( ) ( ) ( ) ( ) ( ) valid
not accessible ( ) ( ) ( ) ( ) ( ) very accessible
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 valid O O O O O Probably valid
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!
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!
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.
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.
Any questions?