“Blog” less; write journal papers!

“‘Blog’ less; write journal papers.”

That’s my NYR for 2018.

Allow me to explain.


My research is not experimental, neither is it connected with, say, design of a new machine or development of a new manufacturing process. The most concrete aspect my work involves only computational modeling. But that too is not of the kind which engineering researchers typically undertake. I don’t do FEM of this multi-physics problem or that. What I work on are some very fundamental issues of physics and engineering.

My research thus is decidedly theoretical, often bordering on being “speculative.” It tends to concentrate on fundamental aspects. For decades by now, I have been trying to tackle some of the trickiest, deepest or very abstract problems (e.g. foundations of QM). At other times, I have been busy just isolating something new as a problem in its right (e.g., instantaneous action-at-a-distance in diffusion, or non-uniqueness of solution to the diffusion equation, or the fundamentality of stress vis-a-vis strain, or mode transitions in ideal vibrations and their relation to vibrations in the real mechanical system, or the physical meaning of the delta of calculus of variations….).

OK, there are some simple experiments here and there I might do. But they are not a very significant aspect of my work. The experiments are more in the nature of illustrations (e.g. melting snowman). They are not even fully in the nature of quantitative validations, let alone the prime vehicles to discovery. So, they are just “potatoes” of my research. The meat is: deep theoretical issues themselves. That’s what it’s like when you say “fundamental.”

The only way in which you can formulate or tackle such problems—fundamental or foundational—is by being a bit “relaxed” about both the specifics of your topic and the way you go about tackling it.

If you believed too much in the existing theory, you wouldn’t be able to spot unidentified problems with it or find new solutions to the known ones. If you try to do theoretical research and if you still try to stick to a schedule like what they do in experimental research (say in designing and fabricating a gadget, complete with bill of materials, or in developing a process, complete with prototype 1, prototype 2, etc.), you wouldn’t able to even get off to a decent start. After all, a schedule can be made from only those ingredients that are already known to you, not of never seen possibilities or unknown ideas. And, while in experimental research, reality has a wonderful way to throw up new possibilities, you have no such luxury in theoretical research. Every “never seen” possibility has to be forged by your own mind. If you don’t think in a relaxed manner, you are never going to believe that the issue is easy enough for you to tackle it.

But one unintended consequence of it all is that, in theoretical research like mine, it’s easy (far too easy in fact) to get a bit too relaxed. It is easy to pursue too many diverse theoretical threads, and in examining them, to run around in circles and so keep on getting back to the same points again and again.

But now I have come to realize that perhaps time has come to stop pursuing new threads in my research and to consolidate what has already been learnt.

The best way I can think of for doing the latter is: writing papers.

In particular, I have to kick aside this one habit: writing things down only when and as “inspiration” strikes.

Writing thoughts down (maintaining pocket diaries) has done a world of good to me. But this long-pursued activity seems to have by now come, in my case, to the point of diminishing marginal utility.

In place of this habit (of keeping on idly brain-storming and noting down possibilities it throws up) I would now like to put in place another habit: writing things (papers, actually) down in a structured, routine, regular, day-to-day, and time-bound manner. Allow me to explain this part too.

Given the way I have pursued my research (and in fact, given even the very nature of problems I ended up tackling), it would have been impossible for me to say something like this:

“OK! January, diffusion paper! February, stress-strain paper! March and April, QM position paper!”

“… What, in February, I don’t write something on QM? neither on diffusion? How ridiculous?”

That is how I would have reacted. But not any more.

Instead, I am now going to be a bit “bureaucratic” about my research. (UGC and AICTE folks ought to be happy in discovering a new soul-mate in me!)

What I am going to do is what I indicated just minutes ago. I am going to make some kind of a “time-table”: this period, work (i.e. actually write papers about) only this particular problem. Leave aside all other issues. Just finish that particular paper. Only then move to those other, more interesting (even alluring) issues in a next delimited period specifically allocated for that. I will have to pursue this policy. And I had better.

After all, while “passively” letting myself jump from issues to issues has yielded a lot of new insights, there are any number of issues where I have “hit the plateau” by now—and I mean those words in a positive sense. By “hitting the plateau,” I mean not a loss of creativity or originality, but a sense, even a firm realization (based on logic) that a certain stage of completeness is already achieved.

And that’s why, I am going to concentrate on “professionally” writing papers, in the next year. Following some kind of a time-bound schedule. As if I were writing a report, or delivering a software product on its schedule. So, it’s high time I became a bit less “creative” and more “professional,” to put it vaguely.

Since I will not be pursuing this bit of this idea or that bit of that idea a lot, I will be blogging less. And since a lot of my research seems to have actually “hit the plateau” in the above-mentioned, positive sense, I would instead be writing papers.

Hence the “slogan”: “`Blog’ less, write journal papers!”

That’s my NYR for 2018…. though I wouldn’t wait for 2018 to arrive before getting going on it. After all, a new year is just an excuse to make resolutions. The digits in the date aren’t important. A definite, demarcated change (“quantum jump” if you will! [LOL!]) is. But a change of the last digit in the YYYY, since it comes only after as long a period as one complete year, is a good time to making the required definite change.

So, there. I will keep you posted, with very brief notes here and there, as to how this paper-writing “business” is actually progressing in my case. My immediate plan is to get going writing the diffusion papers, and to finish writing them, right in January 2018.

Let’s see how things actually progress.


A Song I Like:

This is that Marathi song which I said I had liked a lot during my childhood vacation (see my last 2–3 posts). I still like it. It is the one which has a decidedly Western touch, but without spoiling or compromising on the Indian sense of melody. …

(Marathi) “raajaa saarangaa, maajyaa saarangaa”
Music: Hridaynath Mangeshkar
Singer: Lata Mangeshkar
Lyrics: Shanta Shelke


Bye for now, make a time-table you can stick to, and also take care to execute on it. … Best wishes for a happy and prosperous new year!

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I’ve been slacking, so bye for now, and see you later!

Recently, as I was putting finishing touches in my mind as to how to present the topic of the product states vs. the entangled states in QM, I came to realize that while my answer to that aspect has now come to a stage of being satisfactory [to me], there are any number of other issues on which I am not as immediately clear as I should be—or even used to be! That was frightening!! … Allow me to explain.

QM is hard. QM is challenging. And QM also is vast. Very vast.

In trying to write about my position paper on the foundations of QM, I have been focusing mostly on the axiomatic part of it. In offering illustrative examples, I found, that I have been taking only the simplest possible examples. However, precisely in this process, I have also gone away, and then further away, from the more concrete physics of it. … Let me give you one example.

Why must the imaginary root of the unity i.e. the i appear in the Schrodinger equation? … Recently, I painfully came to realize that I had no real good explanation ready in mind.

It just so happened that I was idly browsing through Eisberg and Resnick’s text “Quantum Physics (of Atoms, Molecules…).” In my random browsing, I happened to glance over section 5.3, p. 134, and was blown over by the argument to this question, presented in there. I must have browsed through this section, years ago, but by now, I had completely forgotten anything about it. … How could I be so dumb as to even forget the fact that here is a great argument about this issue? … Usually, I am able to recall at least the book and the section where an answer to a certain question is given. At least that’s what happens for any of the engineering courses I am teaching. I am easily able to rattle off, for any question posed from any angle, a couple (if not more) books that deal with that particular aspect best. For instance, in teaching FEM: the best treatment on how to generate interpolation polynomials? Heubner (and also Rajasekaran), and only then Zienkiwicz. In teaching CFD: the most concise flux-primary description? Murthy’s notes (at Purdue), and only then followed by Versteeg and Mallasekara. Etc.

… But QM is vast—a bit too vast for me to recall even that much about answers, let alone have also the answers ready in my mind.

Also, around the same time, I ran into these two online resources  on UG QM:
1. The course notes at Reed (I suppose by Griffiths himself): [^] and [^]
2. The notes and solved problems here at “Physics pages” [^]. A very neat (and laudable) an effort!

It was the second resource, in particular, which now set me thinking. … Yes, I was aware of it, and might have referred to it earlier on my blog, too. But it was only now that this site set me into thinking…

As a result of that thinking, I’ve decided to do something similar.

I am going to start writing answers at least to questions (and not problems) given in the first 12 or 14 chapters of Eisberg and Resnick’s abovementioned text. I am going to do that before coming to systematically writing my new position paper.

And I am going to undertake this exercise in place of blogging. … It’s important that I do it.

Accordingly, I am ceasing blogging for now.

I am first going to take a rapid first cut at answering at least the (conceptual) questions if not also the (quantitative) problems from Eisberg and Resnick’s book. I would be noting down my answers in an off-line LaTeX document. Tentatively speaking, I have decided to try to get through at least the first 6 chapters of this book, before resuming blogging. In the second phase, it would be chapters 7 through 11 or so, and the rest, in the third phase.

Once I finish the first phase, I may begin sharing my answers here on this blog.

Believe me, this exercise is necessary for me to do.

There certainly are some drawbacks to this procedure. Heisenberg’s formulation (which, historically, occurred before Schrodinger’s) would not receive a good representation. However, that does not mean that I should not be “finishing” this (E&R’s) book either. May be I will have to do a similar exercise (of answering the more conceptual or theoretical questions or drawing notes from) a similar book but on Heisenberg’s approach, too; e.g., “Quantum Mechanics in Simple Matrix Form” by Thomas Jordan [^]. … For the time being, though, I am putting it off to some later time. (Just a hint: As it so happens, my new position is closer—if at all it is that—to the Schrodinger’s “picture” as compared to Heisenberg’s.)

In the meanwhile, if you feel like reading something interesting on QM, do visit the above-mentioned resources. Very highly recommended.

In the meanwhile, take care, and bye for now.


And, oh, just one more thing…

…Just to remind you. Yes, regardless of it all, as mentioned earlier on this blog, even though I won’t be blogging for a while (say a month or more, till I finish the first phase) I would remain completely open to disclosing and discussing my new ideas about QM to any interested PhD physicist, or even an interested and serious PhD student. … If you are one, just drop me a line and let’s see how and when—and assuredly not if—we can meet.


Which Song Do You Like?

Check out your city’s version of Pharrell Williams’ “Happy” song. Also check out a few other cities’. Which one do you like more? Think about it (though I won’t ask you the reasons for your choices!)

OK. Take care, and bye (really) for now…

 

Explicit vs. implicit FDM: reference needed

The following is my latest post at iMechanica [^]:


“The context is the finite difference modeling (FDM) of the transient diffusion equation (the linear one: \dfrac{\partial T}{\partial t} = \alpha \dfrac{\partial^2 T}{\partial x^2}).

Two approaches are available for modeling the evolution of $T$ in time: (i) explicit and (ii) implicit (e.g., the Crank-Nicolson method).

It was obvious to me that the explicit approach has a local (or compact) support whereas the implicit approach has a global support.

However, with some simple Google searches (and browsing through some 10+ books I could lay my hands on), I could not find any prior paper/text to cite by way of a reference.

I feel sure that it must have appeared in some or the paper (or perhaps even in a text-book); it’s just that I can’t locate it.

So, here is a request: please suggest me a reference where this observation (about the local vs. global support of the solution) is noted explicitly. Thanks in advance.

Best,

–Ajit

[E&OE]”


Self-explanatory, right?


[E&OE]

 

An introductory course on CFD—3

The Beamer slides for Lecture # 3 are uploaded; see here [^].

This lecture is not directly concerned with CFD, or for that matter, even with fluid dynamics proper. It instead concerns itself with some material that is pre-requisite to both. Namely, the topic of tensors. However, Indian universities don’t cover this topic very well during the earlier, pre-requisite courses—esp. at the UG level. So, I decided to throw in some formulae and a few points concerning vectors and tensors, that’s all.

The material for this lecture, thus, is totally “extra” (at least in a course on CFD). The treatment here is, therefore, very cursory. The idea was to give students at least some background into these topics, by way of a rapid review.

As usual, feel free to point out errors and offer criticism.

Further, this topic being challenging to present to a newcomer in a brief manner, this lecture is the one where I am confident in the least. (At least, it’s the first lecture of this kind.) So, any suggestions for a better presentation would be highly appreciated (though, given my experience of this blog, really speaking, I don’t expect any comments to come in, anyway.)

All the same, I am happy that so much of typing in of these equations is, finally, out of the way!

“Enjoy”!

* * * * *   * * * * *   * * * * *

A Song I Like:

I still have not yet reviewed and taken a decision as to the song I like, also for this time round.

So, this section will continue to remain suspended.

[E&OE]