Blog-Filling—Part 3

Note: A long Update was added on 23 November 2017, at the end of the post.


Today I got just a little bit of respite from what has been a very tight schedule, which has been running into my weekends, too.

But at least for today, I do have a bit of a respite. So, I could at least think of posting something.

But for precisely the same reason, I don’t have any blogging material ready in the mind. So, I will just note something interesting that passed by me recently:

  1. Catastrophe Theory: Check out Prof. Zhigang Suo’s recent blog post at iMechanica on catastrophe theory, here [^]; it’s marked by Suo’s trademark simplicity. He also helpfully provides a copy of Zeeman’s 1976 SciAm article, too. Regular readers of this blog will know that I am a big fan of the catastrophe theory; see, for instance, my last post mentioning the topic, here [^].
  2. Computational Science and Engineering, and Python: If you are into computational science and engineering (which is The Proper And The Only Proper long-form of “CSE”), and wish to have fun with Python, then check out Prof. Hans Petter Langtangen’s excellent books, all under Open Source. Especially recommended is his “Finite Difference Computing with PDEs—A Modern Software Approach” [^]. What impressed me immediately was the way the author begins this book with the wave equation, and not with the diffusion or potential equation as is the routine practice in the FDM (or CSE) books. He also provides the detailed mathematical reason for his unusual choice of ordering the material, but apart from his reason(s), let me add in a comment here: wave \Rightarrow diffusion \Rightarrow potential (Poisson-Laplace) precisely was the historical order in which the maths of PDEs (by which I mean both the formulations of the equations and the techniques for their solutions) got developed—even though the modern trend is to reverse this order in the name of “simplicity.” The book comes with Python scripts; you don’t have to copy-paste code from the PDF (and then keep correcting the errors of characters or indentations). And, the book covers nonlinearity too.
  3. Good Notes/Teachings/Explanations of UG Quantum Physics: I ran across Dan Schroeder’s “Entanglement isn’t just for spin.” Very true. And it needed to be said [^]. BTW, if you want a more gentle introduction to the UG-level QM than is presented in Allan Adam (et al)’s MIT OCW 8.04–8.06 [^], then make sure to check out Schroeder’s course at Weber [^] too. … Personally, though, I keep on fantasizing about going through all the videos of Adam’s course and taking out notes and posting them at my Web site. [… sigh]
  4. The Supposed Spirituality of the “Quantum Information” Stored in the “Protein-Based Micro-Tubules”: OTOH, if you are more into philosophy of quantum mechanics, then do check out Roger Schlafly’s latest post, not to mention my comment on it, here [^].

The point no. 4. above was added in lieu of the usual “A Song I Like” section. The reason is, though I could squeeze in the time to write this post, I still remain far too rushed to think of a song—and to think/check if I have already run it here or not. But I will try add one later on, either to this post, or, if there is a big delay, then as the next “blog filler” post, the next time round.

[Update on 23 Nov. 2017 09:25 AM IST: Added the Song I Like section; see below]

OK, that’s it! … Will catch you at some indefinite time in future here, bye for now and take care…


A Song I Like:

(Western, Instrumental) “Theme from ‘Come September'”
Credits: Bobby Darin (?) [+ Billy Vaughn (?)]

[I grew up in what were absolutely rural areas in Maharashtra, India. All my initial years till my 9th standard were limited, at its upper end in the continuum of urbanity, to Shirpur, which still is only a taluka place. And, back then, it was a decidedly far more of a backward + adivasi region. The population of the main town itself hadn’t reached more than 15,000 or so by the time I left it in my X standard; the town didn’t have a single traffic light; most of the houses including the one we lived in) were load-bearing structures, not RCC; all the roads in the town were of single lanes; etc.

Even that being the case, I happened to listen to this song—a Western song—right when I was in Shirpur, in my 2nd/3rd standard. I first heard the song at my Mama’s place (an engineer, he was back then posted in the “big city” of the nearby Jalgaon, a district place).

As to this song, as soon as I listened to it, I was “into it.” I remained so for all the days of that vacation at Mama’s place. Yes, it was a 45 RPM record, and the permission to put the record on the player and even to play it, entirely on my own, was hard won after a determined and tedious effort to show all the elders that I was able to put the pin on to the record very carefully. And, every one in the house was an elder to me: my siblings, cousins, uncle, his wife, not to mention my parents (who were the last ones to be satisfied). But once the recognition arrived, I used it to the hilt; I must have ended up playing this record for at least 5 times for every remaining day of the vacation back then.

As far as I am concerned, I am entirely positive that appreciation for a certain style or kind of music isn’t determined by your environment or the specific culture in which you grow up.

As far as songs like these are concerned, today I am able to discern that what I had immediately though indirectly grasped, even as a 6–7 year old child, was what I today would describe as a certain kind of an “epistemological cleanliness.” There was a clear adherence to certain definitive, delimited kind of specifics, whether in terms of tones or rhythm. Now, it sure did help that this tune was happy. But frankly, I am certain, I would’ve liked a “clean” song like this one—one with very definite “separations”/”delineations” in its phrases, in its parts—even if the song itself weren’t to be so directly evocative of such frankly happy a mood. Indian music, in contrast, tends to keep “continuity” for its own sake, even when it’s not called for, and the certain downside of that style is that it leads to a badly mixed up “curry” of indefinitely stretched out weilings, even noise, very proudly passing as “music”. (In evidence: pick up any traditional “royal palace”/”kothaa” music.) … Yes, of course, there is a symmetrical downside to the specific “separated” style carried by the Western music too; the specific style of noise it can easily slip into is a disjointed kind of a noise. (In evidence, I offer 90% of Western classical music, and 99.99% of Western popular “music”. As to which 90%, well, we have to meet in person, and listen to select pieces of music on the fly.)

Anyway, coming back to the present song, today I searched for the original soundtrack of “Come September”, and got, say, this one [^]. However, I am not too sure that the version I heard back then was this one. Chances are much brighter that the version I first listened to was Billy Vaughn’s, as in here [^].

… A wonderful tune, and, as an added bonus, it never does fail to take me back to my “salad days.” …

… Oh yes, as another fond memory: that vacation also was the very first time that I came to wear a T-shirt; my Mama had gifted it to me in that vacation. The actual choice to buy a T-shirt rather than a shirt (+shorts, of course) was that of my cousin sister (who unfortunately is no more). But I distinctly remember she being surprised to learn that I was in no mood to have a T-shirt when I didn’t know what the word meant… I also distinctly remember her assuring me using sweet tones that a T-shirt would look good on me! … You see, in rural India, at least back then, T-shirts weren’t heard of; for years later on, may be until I went to Nasik in my 10th standard, it would be the only T-shirt I had ever worn. … But, anyway, as far as T-shirts go… well, as you know, I was into software engineering, and so….

Bye [really] for now and take care…]

 

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Machine “Learning”—An Entertainment [Industry] Edition

Yes, “Machine ‘Learning’,” too, has been one of my “research” interests for some time by now. … Machine learning, esp. ANN (Artificial Neural Networks), esp. Deep Learning. …

Yesterday, I wrote a comment about it at iMechanica. Though it was made in a certain technical context, today I thought that the comment could, perhaps, make sense to many of my general readers, too, if I supply a bit of context to it. So, let me report it here (after a bit of editing). But before coming to my comment, let me first give you the context in which it was made:


Context for my iMechanica comment:

It all began with a fellow iMechanician, one Mingchuan Wang, writing a post of the title “Is machine learning a research priority now in mechanics?” at iMechanica [^]. Biswajit Banerjee responded by pointing out that

“Machine learning includes a large set of techniques that can be summarized as curve fitting in high dimensional spaces. [snip] The usefulness of the new techniques [in machine learning] should not be underestimated.” [Emphasis mine.]

Then Biswajit had pointed out an arXiv paper [^] in which machine learning was reported as having produced some good DFT-like simulations for quantum mechanical simulations, too.

A word about DFT for those who (still) don’t know about it:

DFT, i.e. Density Functional Theory, is “formally exact description of a many-body quantum system through the density alone. In practice, approximations are necessary” [^]. DFT thus is a computational technique; it is used for simulating the electronic structure in quantum mechanical systems involving several hundreds of electrons (i.e. hundreds of atoms). Here is the obligatory link to the Wiki [^], though a better introduction perhaps appears here [(.PDF) ^]. Here is a StackExchange on its limitations [^].

Trivia: Kohn and Sham received a Physics Nobel for inventing DFT. It was a very, very rare instance of a Physics Nobel being awarded for an invention—not a discovery. But the Nobel committee, once again, turned out to have put old Nobel’s money in the right place. Even if the work itself was only an invention, it did directly led to a lot of discoveries in condensed matter physics! That was because DFT was fast—it was fast enough that it could bring the physics of the larger quantum systems within the scope of (any) study at all!

And now, it seems, Machine Learning has advanced enough to be able to produce results that are similar to DFT, but without using any QM theory at all! The computer does have to “learn” its “art” (i.e. “skill”), but it does so from the results of previous DFT-based simulations, not from the theory at the base of DFT. But once the computer does that—“learning”—and the paper shows that it is possible for computer to do that—it is able to compute very similar-looking simulations much, much faster than even the rather fast technique of DFT itself.

OK. Context over. Now here in the next section is my yesterday’s comment at iMechanica. (Also note that the previous exchange on this thread at iMechanica had occurred almost a year ago.) Since it has been edited quite a bit, I will not format it using a quotation block.


[An edited version of my comment begins]

A very late comment, but still, just because something struck me only this late… May as well share it….

I think that, as Biswajit points out, it’s a question of matching a technique to an application area where it is likely to be of “good enough” a fit.

I mean to say, consider fluid dynamics, and contrast it to QM.

In (C)FD, the nonlinearity present in the advective term is a major headache. As far as I can gather, this nonlinearity has all but been “proved” as the basic cause behind the phenomenon of turbulence. If so, using machine learning in CFD would be, by the simple-minded “analysis”, a basically hopeless endeavour. The very idea of using a potential presupposes differential linearity. Therefore, machine learning may be thought as viable in computational Quantum Mechanics (viz. DFT), but not in the more mundane, classical mechanical, CFD.

But then, consider the role of the BCs and the ICs in any simulation. It is true that if you don’t handle nonlinearities right, then as the simulation time progresses, errors are soon enough going to multiply (sort of), and lead to a blowup—or at least a dramatic departure from a realistic simulation.

But then, also notice that there still is some small but nonzero interval of time which has to pass before a really bad amplification of the errors actually begins to occur. Now what if a new “BC-IC” gets imposed right within that time-interval—the one which does show “good enough” an accuracy? In this case, you can expect the simulation to remain “sufficiently” realistic-looking for a long, very long time!

Something like that seems to have been the line of thought implicit in the results reported by this paper: [(.PDF) ^].

Machine learning seems to work even in CFD, because in an interactive session, a new “modified BC-IC” is every now and then is manually being introduced by none other than the end-user himself! And, the location of the modification is precisely the region from where the flow in the rest of the domain would get most dominantly affected during the subsequent, small, time evolution.

It’s somewhat like an electron rushing through a cloud chamber. By the uncertainty principle, the electron “path” sure begins to get hazy immediately after it is “measured” (i.e. absorbed and re-emitted) by a vapor molecule at a definite point in space. The uncertainty in the position grows quite rapidly. However, what actually happens in a cloud chamber is that, before this cone of haziness becomes too big, comes along another vapor molecule, and “zaps” i.e. “measures” the electron back on to a classical position. … After a rapid succession of such going-hazy-getting-zapped process, the end result turns out to be a very, very classical-looking (line-like) path—as if the electron always were only a particle, never a wave.

Conclusion? Be realistic about how smart the “dumb” “curve-fitting” involved in machine learning can at all get. Yet, at the same time, also remain open to all the application areas where it can be made it work—even including those areas where, “intuitively”, you wouldn’t expect it to have any chance to work!

[An edited version of my comment is over. Original here at iMechanica [^]]


 

“Boy, we seem to have covered a lot of STEM territory here… Mechanics, DFT, QM, CFD, nonlinearity. … But where is either the entertainment or the industry you had promised us in the title?”

You might be saying that….

Well, the CFD paper I cited above was about the entertainment industry. It was, in particular, about the computer games industry. Go check out SoHyeon Jeong’s Web site for more cool videos and graphics [^], all using machine learning.


And, here is another instance connected with entertainment, even though now I am going to make it (mostly) explanation-free.

Check out the following piece of art—a watercolor landscape of a monsoon-time but placid sea-side, in fact. Let me just say that a certain famous artist produced it; in any case, the style is plain unmistakable. … Can you name the artist simply by looking at it? See the picture below:

A sea beach in the monsoons. Watercolor.

If you are unable to name the artist, then check out this story here [^], and a previous story here [^].


A Song I Like:

And finally, to those who have always loved Beatles’ songs…

Here is one song which, I am sure, most of you had never heard before. In any case, it came to be distributed only recently. When and where was it recorded? For both the song and its recording details, check out this site: [^]. Here is another story about it: [^]. And, if you liked what you read (and heard), here is some more stuff of the same kind [^].


Endgame:

I am of the Opinion that 99% of the “modern” “artists” and “music composers” ought to be replaced by computers/robots/machines. Whaddya think?

[Credits: “Endgame” used to be the way Mukul Sharma would end his weekly Mindsport column in the yesteryears’ Sunday Times of India. (The column perhaps also used to appear in The Illustrated Weekly of India before ToI began running it; at least I have a vague recollection of something of that sort, though can’t be quite sure. … I would be a school-boy back then, when the Weekly perhaps ran it.)]

 

Haptic, tactile, virtual, surgery, etc.

Three updates made on 24th March 2016 appear near the end of this post.


Once in a while I check out the map of the visitors’ locations (see the right bar).

Since hardly any one ever leaves any comment at my blog, I can only guess who these visitors possibly could be. Over a period of time, guessing the particular visitors in this way has become an idle sort of a past-time for me. (No, I don’t obsess over it, and I don’t in fact spend much time on it—at the most half-a-minute or so, once in a while. But, yes, check, I certainly do!)

Among the recent visitors, there was one hit on 6th March 2016 coming from Troy, NY, USA (at 11:48:02 AM IST, to be precise). … Must be someone from RPI, I thought. (My blog is such that mostly only academics could possibly be interested in it; never the people with lucrative industrial jobs such as those in the SF Bay Area. Most of the hits from the Bay Area are from Mountain View, and that’s the place where the bots of Google’s search engines live.)

But I couldn’t remember engaging in any discussion with any one from RPI on any blog.

Who could this visitor possibly be? I could not figure it out immediately, so I let the matter go.


Yesterday, I noticed for the first time an ad for “several” post-doc positions at RPI, posted on iMechanica by Prof. Suvranu De [^]. It had been posted right on the same day: 6th March 2016. However, since recently I was checking out only my thread on the compactness of support [^], I had missed out on the main front page. Thus, I noticed the ad only today.

Curious, I dropped an informal email to Prof. De immediately, almost more or less by cognitive habits.


I am not too keen on going to the USA, and in fact, I am not even inclined to leave India. Reasons are manifold.

You, as every one else on the planet, of course comes to know all that ever happens to or in the USA. Americans make sure that you do—whether you like it or not. (Remember 9/11? They have of course forgotten it by now, but don’t you remember the early naughties when, imagining you to be just as dumb and thick-skinned as they are,  the kind of decibels they had pierced into your metaphorical ears (and in fact also in your soul)? Justifiable, you say? How about other big “controversies” which actually were nothing but scandals? Can’t you pick up one or two?)

Naturally, who would want to go to that uncivilized a place?

And even if you want to argue otherwise, let me suggest you to see if you can or cannot easily gather (or recollect) what all that has happened to me when I was in the USA?

So, the idea of trying to impress Dr. De for this post-doc position was, any which way, completely out of the question. Even if he is HoD at RPI.

And then, frankly, at my age, I don’t even feel like impressing any one for a mere post-doc; not these days anyway (I mean, some 6 years after the PhD defense, and after having to experience so many years of joblessness (including those reported via this blog)). … As far as I am concerned, either they know what and who I am, and act accordingly (including acting swiftly enough), or they don’t. (In the last case, mostly, they end up blaming me, as usual, in some or the other way.)

OK, so, coming back to what I wrote Dr. De. It was more in the nature of a loud thinking about the question of whether I should at all apply to them in the first place or not. … Given my experience of the other American post-docs advertised at iMechanica, e.g. those by Prof. Sukumar (UC Davis), and certain others in the USA, and also my experience of the Americans of the Indian origin (and even among them, those who are JPBTIs and those who are younger to me by age), I can’t keep any realistic expectation that I would ever receive any reply to that email of mine from Prof. De. The odds are far too against; check out the “follow-up” tag. (I could, of course, be psychically attacked, the way I was, right this week, a few days ago.)

Anyway, once thus grown curious about the subject matter, I then did a bit of a Web search, and found the following videos:

The very first listing after a Google search (using the search string: “Suvranu De”; then clicking on the tab: “videos”) was the one on “virtual lap band – surgical simulation”: [^].

Watching that video somehow made me sort of uneasy immediately. Uneasy, in a minor but a definitely irritating way. In a distinctly palpable way, almost as if it was a physical discomfort. No, not because the video carries the scene of tissue-cutting and all. … I have never been one of those who feel nervous or squeamish at the sight of blood, cuts, etc. (Most men, in fact, don’t!) So, my uneasiness was not on that count. …

Soon enough (i.e., much before the time I was in the middle of that video), I figured out the reason why.

I then checked out a few more videos, e.g., those here [^] and here [^]. … Exactly the same sense of discomfort or uneasiness, arising out of the same basic reason.

What kind of an uneasiness could there possibly be? Can you guess?

I don’t want to tell you, right away. I want you to guess. (Assume that an evil smile had transitorily appeared on my face.)

To close this post: If you so want, go ahead, check out those videos, see if it makes you uncomfortable watching some part of an implementation of this new idea. Then, the sin of the sins (“paapam, paapam, mahaapaapam” in Sanskrit): drop me a line (via a comment or an email) stating what that reason possibly could be. (Hint: It has nothing to do with the feely-feely-actually-silly/wily sort of psychological reasons. )

After a while, I will come back, and via an update to this post let you know the reason.


Update 1:

Yahoo! wants you to make a note of the “12 common mistakes to avoid in job interview”: [^]. They published this article today.


Update 2 (on 24th March 2016):

Surprise! Prof.  De soon enough (on 18th March IST) dropped me an email which was brief, professional, but direct to the point. A consequence, and therefore not much of a surprise: I am more or less inclined to at least apply for the position. I have not done so as of today; see the Update 3 below.


Update 3 (on 24th March 2016):

Right the same day (on 18th March 2016 about 10:00 PM IST), my laptop developed serious hardware issues including (but not limited to) yet another HDD crash! The previous crash was less than a year ago, in last June  [^].

Once again, there was  loss of (some) data: the initial and less-than-25%-completed drafts of 4+ research papers, some parts (from sometime in February onwards) of my notes on the current course on CFD, SPH, etc., as well as some preliminary Python code on SPH). The Update 2 in fact got delayed because of this development. I just got the machine back from the Dell Service last evening, and last night got it going on a rapid test installation of Windows 7. I plan to do a more serious re-installation over the next few days.


Update 4 (on 24th March 2016):

The thing in the three videos (about haptics, virtual surgery) that made me uncomfortable or uneasy was the fact that in each case, the surgeon was standing in a way that would have been just a shade uncomfortable to me. The surgeon’s hands were too “free” i.e. unsupported (say near elbow), his torso was stooping down in a wrong way (you couldn’t maintain that posture with accuracy in hands manipulation for long, I thought), and at the same time, he had to keep his eyes fixed on a monitor that was a bit too high-up for the eyes-to-hands coordination to work right. In short, there was this seeming absence of a consideration of ergonomics or the human factors engineering here. Of course, it’s only a prototype, and it’s only a casual onlooker’s take of the “geometry,” but that’s what made me distinctly uncomfortable.

(People often have rationalistic ideas about the proper (i.e. the least stress inducing and most efficient) posture.  In a later post, I will point out a few of these.)

 


 

A Song I Like:
(filled-in on 24th March 2016)

(Marathi) “thembaanche painjaN waaje…” [“rutu premaachaa aalaa”]
Singers: Avadhoot Gupte, Vaishali Samant
Music: Shashank Powar
Lyrics: Ravi Wadkar (?)

[An incidental note: The crash occurred—the computer suddenly froze—while I was listening to—actually, watching the YouTube video of—this song. … Somehow, even today, I still continue liking the song! … But yes, as is usual for this section, only the audio track is being referred to. (I had run into this song while searching for some other song, which I will use in a later post.)]


[Some editorial touches, other than the planned update, are possible, as always.]

[E&OE]

 

The Infosys Prizes, 2015

I realized that it was the end of November the other day, and it somehow struck me that I should check out if there has been any news on the Infosys prizes for this year. I vaguely recalled that they make the yearly announcements sometime in the last quarter of a year.

Turns out that, although academic bloggers whose blogs I usually check out had not highlighted this news, the prizes had already been announced right in mid-November [^].

It also turns out also that, yes, I “know”—i.e., have in-person chatted (exactly once) with—one of the recipients. I mean Professor Dr. Umesh Waghmare, who received this year’s award for Engineering Sciences [^]. I had run into him in an informal conference once, and have written about it in a recent post, here [^].

Dr. Waghmare is a very good choice, if you ask me. His work is very neat—I mean both the ideas which he picks out to work on, and the execution on them.

I still remember his presentation at that informal conference (where I chatted with him). He had talked about a (seemingly) very simple idea, related to graphene [^]—its buckling.

Here is my highly dumbed down version of that work by Waghmare and co-authors. (It’s dumbed down a lot—Waghmare et al’s work was on buckling, not bending. But it’s OK; this is just a blog, and guess I have a pretty general sort of a “general readership” here.)

Bending, in general, sets up a combination of tensile and compressive stresses, which results in the setting up of a bending moment within a beam or a plate. All engineers (except possibly for the “soft” branches like CS and IT) study bending quite early in their undergraduate program, typically in the second year. So, I need not explain its analysis in detail. In fact, in this post, I will write only a common-sense level description of the issue. For technical details, look up the Wiki articles on bending [^] and buckling [^] or Prof. Bower’s book [^].

Assuming you are not an engineer, you can always take a longish rubber eraser, hold it so that its longest edge is horizontal, and then bend it with a twist of your fingers. If the bent shape is like an inverted ‘U’, then, the inner (bottom) surface has got compressed, and the outer (top) surface has got stretched. Since compression and tension are opposite in nature, and since the eraser is a continuous body of a finite height, it is easy to see that there has to be a continuous surface within the volume of the eraser, some half-way through its height, where there can be no stresses. That’s because, the stresses change sign in going from the compressive stress at the bottom surface to the tensile stresses on the top surface. For simplicity of mathematics, this problem is modeled as a 1D (line) element, and therefore, in elasticity theory, this actual 2D surface is referred to as the neutral axis (i.e. a line).

The deformation of the eraser is elastic, which means that it remains in the bent state only so long as you are applying a bending “force” to it (actually, it’s a moment of a force).

The classical theory of bending allows you to relate the curvature of the beam, and the bending moment applied to it. Thus, knowing bending moment (or the applied forces), you can tell how much the eraser should bend. Or, knowing how much the eraser has curved, you can tell how big a pair of fforces would have to be applied to its ends. The theory works pretty well; it forms of the basis of how most buildings are designed anyway.

So far, so good. What happens if you bend, not an eraser, but a graphene sheet?

The peculiarity of graphene is that it is a single atom-thick sheet of carbon atoms. Your usual eraser contains billions and billions of layers of atoms through its thickness. In contrast, the thickness of a graphene sheet is entirely accounted for by the finite size of the single layer of atoms. And, it is found that unlike thin paper, the graphen sheet, even if it is the the most extreme case of a thin sheet, actually does offer a good resistance to bending. How do you explain that?

The naive expectation is that something related to the interatomic bonding within this single layer must, somehow, produce both the compressive and tensile stresses—and the systematic variation from the locally tensile to the locally compressive state as we go through this thickness.

Now, at the scale of single atoms, quantum mechanical effects obviously are dominant. Thus, you have to consider those electronic orbitals setting up the bond. A shift in the density of the single layer of orbitals should correspond to the stresses and strains in the classical mechanics of beams and plates.

What Waghmare related at that conference was a very interesting bit.

He calculated the stresses as predicted by (in my words) the changed local density of the orbitals, and found that the forces predicted this way are way smaller than the experimentally reported values for graphene sheets. In other words, the actual graphene is much stiffer than what the naive quantum mechanics-based model shows—even if the model considers those electronic orbitals. What is the source of this additional stiffness?

He then showed a more detailed calculation (i.e. a simulation), and found that the additional stiffness comes from a quantum-mechanical interaction between the portions of the atomic orbitals that go off transverse to the plane of the graphene sheet.

Thus, suppose a graphene sheet is initially held horizontally, and then bent to form an inverted U-like curvature. According to Waghmare and co-authros, you now have to consider not just the orbital cloud between the atoms (i.e. the cloud lying in the same plane as the graphene sheet) but also the orbital “petals” that shoot vertically off the plane of the graphene. Such petals are attached to nucleus of each C atom; they are a part of the electronic (or orbital) structure of the carbon atoms in the graphene sheet.

In other words, the simplest engineering sketch for the graphene sheet, as drawn in the front view, wouldn’t look like a thin horizontal line; it would also have these small vertical “pins” at the site of each carbon atom, overall giving it an appearance rather like a fish-bone.

What happens when you bend the graphene sheet is that on the compression side, the orbital clouds for these vertical petals run into each other. Now, you know that an orbital cloud can be loosely taken as the electronic charge density, and that the like charges (e.g. the negatively charged electrons) repel each other. This inter-electronic repulsive force tends to oppose the bending action. Thus, it is the petals’ contribution which accounts for the additional stiffness of the graphene sheet.

I don’t know whether this result was already known to the scientific community back then in 2010 or not, but in any case, it was a very early analysis of bending of graphene. Further, as far as I could tell, the quality of Waghmare’s calculations and simulations was very definitely superlative. … You work in a field (say computational modeling) for some time, and you just develop a “nose” of sorts, that allows you to “smell” a superlative calculation from an average one. Particularly so, if your own skills on the calculations side are rather on the average, as happens to be the case with me. (My strengths are in conceptual and computational sides, but not on the mathematical side.) …

So, all in all, it’s a very well deserved prize. Congratulations, Dr. Waghmare!

 


A Song I Like:

(The so-called “fusion” music) “Jaisalmer”
Artists: Rahul Sharma (Santoor) and Richard Clayderman (Piano)
Album: Confluence

[As usual, may be one more editing pass…]

[E&OE]