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.)]

 

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See, how hard I am trying to become a (Full) Professor of Mechanical Engineering in SPPU?

Currently, I am not only cashless but also jobless. That’s why, I try harder.

I am trying very hard to be a (Full) Professor of Mechanical Engineering, especially at the Savitribai Phule Pune University (or SPPU for short).

That’s right.

And that’s why, I have decided to adopt an official position whereby I abandon all my other research and study interests, especially those related to the mechanics of the quanta. Instead, I have officially decided to remain interested only in the official problems from the Mechanical Engineering discipline proper—not only for my studies, but also for my research interests.

… If only I were to have my first degree in Mechanical Engineering, instead of in Metallurgy! (It was some 37.5–33.5 years ago, with my decision to choose Metallurgy being from some 36.5 years ago.) … If only I were to choose Mechanical right back then, this problem wouldn’t have arisen today. …

Tch! …

…But, well, thinking of my first degree, its circumstances—where I got it from (COEP, the engineering college with the highest cut-off merit in the entire Maharashtra state), in what class (First Class with Distinction, the highest class possible), and, most crucially, for spending all my time at what place (The Boat Club)… You know, looking back some 3.5 decades later of all those circumstances—the circumstances of how I chose Metallurgy, back then, as I was sitting at the Boat Club… Hmmm… Boat Club. … Boat Club! Boat Club!!

It gives me some ideas.

So, to better support my current endeavors of becoming an Officially Approved Full Professor of Mechanical Engineering in SPPU, may be, I should solve some Mechanical Engineering problems related to boats. Preferably, those involving not just fluid mechanics, but also mechanisms and machine design—and vibrations! [Oh yes. I must not forget them! Vibrations are, Officially, a Mechanical Engineering topic. In fact even Acoustics. …]

Thinking along such lines, I then thought of one problem, and sort of solved it too. Though I am not going to share my answer with you, I certainly want to share the problem itself with you. (Don’t ask me for answers until I get the job as an Officially Approved Full Professor in Mechanical Engineering at SPPU.)

OK, so here we go.


The Problem Description:

Consider a boat floating on a stand-still lake. The boat has a very simple shape; it is in the shape of a rectangular parallelpiped (i.e., like a shoe-box, though not quite exactly like a punt).

In the plan (i.e. the top view), the boat looks like this:
mechanicalengineeringboat

 

 

 

 

 

As shown in the figure, at the centers of the front- and back-sides of the boat, there are two circular cylindrical cavities of identical dimensions, both being fitted with reciprocating pistons. These pistons are being driven by two completely independent mechanisms. The power-trains and the prime-movers are not shown in the diagram; in this analysis, both may be taken to be mass-less and perfectly rigid. However, the boat is assumed to have some mass.

We will try to solve for the simplest possible case: perfectly rigid boat walls (with some mass), perfectly rigid but mass-less pistons, complete absence of friction between the pistons and the cylinder walls, etc.

Assume also that both the boat and the lake water are initially stand-still, and that there are no other influences affecting the motions (such as winds or water currents).

Now, let’s put the pistons in oscillatory motions. In general, the frequencies of their oscillations are not equal. Let the frequency for the left- and right-side pistons be f_L and f_R Hz, respectively.

Problem 1:

Build a suitable Mechanical Engineering model, and predict how the boat would move, in each of the following three scenarios:

  • f_L = f_R
  • f_L > f_R
  • f_L < f_R

In each case, determine (i) whether the boat as a whole (i.e. its center of mass or CM) would at all undergo any motion at all or not, (ii) if yes, whether the motion of the CM would have an element of oscillations to it or not, and finally, (iii) whether the boat (i.e. its CM) would undergo a net displacement over a large number of pistons oscillations or not (i.e., the question asks whether the so-called “time-averaged” net displacement occurs in any one direction or not), and if yes, in which direction.

You may make other minor assumptions. For instance, in each of the above 3 cases, you may assume that at time t = 0, both the pistons are at their innermost positions, with each piston beginning its motion by pushing outwards. Also check out the effect of assuming, some other, suitable, values for the initial phases.

Though not at all necessary, if it will help you, you may perhaps consider the case where the higher frequency is an integer multiple of the lower frequency, e.g., in the second of the three cases, assume f_L = n f_R, where n \in \mathcal{N}. However, note that eventually, you are expected to solve the problem in the general case, the one in which the ratio of the frequencies may be any real number. The cases of practical interest may be where the ratio ranges from 0.0 to a real number up to, say, 2.67 or 3.14 (or, may be, 5.25).

Notice that nowhere thus far have we said that the oscillatory motion of the pistons would be SHM (i.e. simple harmonic). You may begin with an SHM, but as a further problem below illustrates, the piston motion may neither be simple-harmonic, nor even symmetrical in the to- and fro-directions.

On the fluid mechanics side: In your analysis, assume that the length of the boat is much, much greater than the stroke-lengths of the pistons. Essentially, we want to ensure that the water waves produced at one end do not significantly affect the local dynamics at the other end.

You may assume a highly simplified model for the fluid—the problem is not supposed to have a crucial bearing on what kind of a fluid you assume. I mean to say, we are not looking for so detailed a model that you would have to perform a CFD analysis. (That task, we will leave to the Naval Architecture engineers.) However, do make sure to note how your model behaves for an inviscid flow vs. for a viscous flow.

So, in short, the problem is to determine the nature of the motion of the boat, if there is any—i.e., to determine if its CM undergoes a net displacement in the time-averaged sense or not, and if yes, in which direction it occurs.

Problem 2:

Assume a relatively smaller stroke-length for one of the pistons, and repeat the problem.

Problem 3:

Assume that one of the frequencies is zero, which is as good as saying that the boat is fitted with only one cylinder-and-piston. Repeat the analysis.

Problem 4:

Continue to assume that one of the frequencies is zero. Now, also assume that the outward stroke of the moving piston happens faster than its inward stroke. Determine the nature of the motion, if any, for the CM of the boat.

Problem 5 (Optional):

Assuming that the prime mover outputs a uniform circular (or rotary) motion, design a suitable mechanism which will help implement the idea of having non-SHM motions—e.g., different stroke-times in the outward and inward directions. Conduct an informal (or a more formal, calculus-based) displacement-, velocity- and acceleration-analysis, if you wish.

Give it a thought whether this entire idea of transforming a circular motion to a nonuniform reciprocating motion can be done away with, thereby saving on energy—in real life, there is friction—using certain ideas from electrical engineering and electronics.

Ooops!

No, no, no! No!! Throw out that horrendous idea! I mean the very last one!!

We want to remain concerned only with the Mechanical Engineering Problems proper. That is the Official position I have adopted, remember?


That’s right. What I described above was, really, really, really only a Mechanical Engineering Problem.

It really, really, really has nothing to do with anything else such as electrical engineering or quantum physics.

[And if even Prof. Thanu Padmanabhan (IUCAA) does not know quantum physics (he told me so once, right in person), why should I be concerned with it, anyway?]

Anyway, so, Officially speaking, I made up this problem only because I want to become an Officially Approved Full Professor of Mechanical Engineering at SPPU.


If you are interested in some other Mechanical Engineering problems, especially on the fluids-thermal side, check out my recent posts on the Eco-Cooler, and see if you can take further the analysis given in them.

I myself had made a much more advanced engineering analysis right at that time, but I am not going to give it—or its results—until some time after I land and join the kind of job I am looking for—a Full Professor’s. (And I hope that you do have the sense to see that this is not a “prestige issue” on my part.)

The post having a preliminary (quantitative) fluids-thermal analysis is here [^], though the qualitative analysis of the problem begins with an earlier post, here [^].


[Guess the problem, as given, is enough for the time being. I may even come back and add one or two variations on the problem! But no guarantees.]

Update right on 2016.12.02: OK, here are a couple of minor variations. What happens if, when a piston comes to a rest at the extreme stroke, it continues staying idle for a while, before resuming its towards-the-center motion? What if the piston motion is such that the point of zero displacement does not occur exactly at the middle of its overall stroke-length?

I may post some further variations on the problem, or suggest alternative analogous problems, in future.

Currently, I am not just cashless but also jobless. That’s why, I try harder.


More, may be later. As to the Song I Like section, I don’t have anything playing at the back of my mind right away, so let me see if something strikes me by the time I come back tomorrow to give a final editing touch to this post. In that case, I will add this section; else, I will not!


[After the update right on 2016.12.02: I am done with this post now, and if there are any errors, I will let them stay. If you find the post confusing somewhere, please do drop me a line, though. Best, and take care.]

[E&OE]

 

More on the project ideas. Also, a new CFD software benchmark-cum-shop-floor test.

Update added on 2015.05.17; check out the near the end of this post.

* * * * *   * * * * *   * * * * *

More on the project ideas:

In my last post [^], I had given a description of 3 different ideas for student projects. I would be interested in guiding all these projects in the near future, once I get a suitable job.

If you had gone through my earlier post about my current research interests [^], you would have sure noticed how the project idea no. 2 and 3 relate to my current research in computational modeling of the ceramic injection moulding (CIM) process.

These ideas are basically meant to provide reliable experimental bench-marks for validating separate aspects of the software that I will be writing. (I am still considering and reconsidering the issue of whether to write the software starting from the scratch, or only adapt/extend OpenFOAM.)

The project idea no. 3 (viz., paste-filling in cavity) completely keeps out the aspects of heat transfer and phase transformations, and instead selectively focuses on the aspect of mould-filling using a non-Newtonian material. Thus, if the momentum equations are handled right, predictions about the progress in the filling and the instantaneous shapes of the front at different times would be accurate. If not, the software would have to address only the momentum equations, but with better models/parameter values for the wall friction, viscosity, and surface tension.

In contrast, the project idea no. 2 (viz., melting of wax by a source) tries to selectively focus on the heat transfer and phase transformation aspects, but without significantly involving any momentum transport. (It is anticipated that the symmetry of the configuration means that convection within the molten wax would not be of much significance. However, this part, too, will have to be carefully looked into, at a later stage.)

The CIM process itself involves a liquid-to-solid phase transformation. In contrast, what the idea no. 2 models is the opposite phase transformation, viz., from solid-to-liquid. However, it does have a travelling interface. If the software handles the energy equation, the phase-transformations, and the motion of the liquid-solid interface right, then the speed of the interface should get predicted accurately. If not, the software development work would have to selectively focus only on this part.

Thus, the two project ideas split up the CIM process into two different parts. The reason is the complexity of such problems—the accurate predictions of the instantaneous positions of the moving boundary.

I was only partly successful while comutationally modeling the melting snowman (which I did during my PhD research). The software I wrote had qualitatively predicted the evolution of the shape right, but the speed of the evolution was quantitatively off the mark. I therefore knew that I had to further simplify even just this much part: of transient heat transfer, phase transformation and moving interface, but without any momentum exchanges involved in it. The project idea no. 2 tries to do precisely that: simplify just the heat-related part even further.

In the case of the melting snowman, the outer boundary happens to be the singular location where all the action happens: heat enters, phase-transformation occurs, and then, importantly, the resulting liquid gets drained away, traveling under gravity over the outer surface, and in the process exposing a new surface for the heat to enter, and also moving back the phase-transformation interface. The process thus has a kind of a loop built into it, and so, despite the apparent simplicity, from a modeling viewpoint, it actually is quite complex. Something went wrong with the timings at which the successive processes took place in the simulation. But I could not reliably locate precisely where; I didn’t have any experimental data to be able to do so. My experimentation was too simple; I could not get funds for instrumented data logging, and therefore, I had to remain content with just photographically capturing the outer profiles at successive instants; continuous monitoring of temperatures at various points within the volume of the snowman was not possible.

The current project idea tries to rectify the situation. It reduces the complexity a bit further, by completely doing away with the draining part—the molten wax remains in the jar.

However, in the process, I now realized, the experimental part has become perhaps a bit too simple for a project at the ME level. Some more work could be thrown in. So, here are two possibilities:

1. Also model solidification of wax (instead of only its melting). The liquid-to-solid is anyway the direction of the phase transformation in the actual CIM process.

The simplest model to try would be just to take an instrumented jar, pour some molten wax in it, and let it solidify. If the predictions for the solidification front—its shape and size at various times—are accurate enough, then well and good.

Realize that the project idea no. 2 (viz., wax-melting using a rod for heat input) remains absolutely essential, because experimental errors involved in determining the geometry of the phase transformation front are minimal in it: the boundary of the front has a very simple geometry (ideally, circular on the top surface), and its biggest section remains at the top surface, and therefore easily visible, throughout the process. For both these reasons, its motion would be very accurately measurable. In contrast, in solidification studies, the shape of the solidification front would remain more complicated. Further,  since the front would lie interior to the block, it would not be as easy to measure ina continuous nondestructive manner.

2. Another idea is related to bench-marking and testing. I will later on post this part (may be with a little additions and editing) on iMechanica and CFD-related fora, so as to solicit some informal comments about it. Let me note down a preliminary description here, in the next section.

* * * * *   * * * * *   * * * * *

A new software benchmark-cum-shopfloor test:

In CFD, the utility of suitable bench-marks is well-established. Think of some typical cases: flow through a converging-diverging channel, flow at a corner or at a T-joint, lid-driven flow with formation of vortices at the corners, flow past an obstacle or over a step and the resultant vortex shedding, the Ahmed body, the Rayleigh-Taylor instability, the dam-break simulation, the falling droplet, etc. These have proved very helpful in validating CFD techniques and software codes/packages—at least for comparing different packages against each other. The idea I propose is in a similar vein.

The proposed experiment is very simple to perform, and yet, it is expected to be very useful. At least I am convinced about its utility enough that I have decided to write a short journal paper on it, just for proposing this test—I mean just for putting forth only the idea of the test, without performing any experimentation/simulation involving it.

Here is the idea.

Take a small solid object, say, a ball-bearing ball made of alloy steel, or a small machined cube of copper, or a small cone of brass. (The surface roughness would need to be specified.)

Hold the object at a suitably high temperature for a sufficiently long of time that it develops a steady temperature throughout its section. Or, assuming that it initially has  been at the room temperature for a sufficiently long time, now place it inside a furnace (or over a hot-plate) of a well-controlled constant temperature for a specified period of time. Basically, the idea is that we come to specify the entire temperature profile of the object.

Take a block of wax of a specified grade i.e. material properties. (Shape and size is to be given some thought, and the issue is to be finalied after some preliminary experiments.) Drill a small hole of a specified shape and size at the center of its top surface. The size of the hole should slightly exceed that of the heated small object.

Place the block snugly fitting inside a well-insulated enclosure (of specified dimensions and material/properties). Or, may be, just place it on a ceramic tile on the laboratory table. (This in fact should work better.)

Rapidly take the small object out of the furnace (or from the hot plate) and gently place it in the hole drilled in the block of wax.

Initially, the hot object will give off its heat to the air above and to the portions of the wax block surrounding it, and so, the wax will melt locally. The object being heavy will displace the molten wax underneath, and thus it will slide deeper into the block. The molten wax will rise from the side-ways. The object will soon get completely covered with a layer of the so-molten wax now convected also onto its top surface. Simultaneously, the column of the molten wax above the object will begin to solidify from the top, by giving off its heat to the air as well as to the surrounding unmolten portions of the block. Also, the heat of the object will continue to get transferred to the wax, and so, its own temperature will go on dropping down, even as it slides down. All these processes will continue until a time when the temperature of the object goes below the melting point of the wax, and so, unable any more to melt the wax, it will come to a stand-still. All of the molten wax wouldn’t have solidified by this time, and so, so we have to wait a little longer for this to happen.

Then (i.e., after waiting for sufficient time), carefully cut through the block, and measure the shape of the region of the wax affected by the heat—in particular, the depth of penetration.

The software should be able to accurately predict the extent of the heat-affected zone, esp. its depth, say as measured by the penetration depth of the object.

This experiment is very simple to perform—it involves no instrumentation. Yet it yields a very specific measure, viz., the extent of the heat affected zone, and most particularly, the depth of the penetration.

However, the process involved in the test is expected to pose a sufficiently difficult case for any CFD software to handle. There is transient heat transfer in two different phases, two successive phase transformations (solid-to-liquid, and then, also liquid-to-solid), convection of liquid wax, buyoancy effects for both the molten wax and the hot object, and motion of the solid-liquid interface. Yet, the overall geometry remains simple enough.

In CFD, people have been studying things such as rising of bubbles and rising/falling of droplets of a second-phase fluid. The process here is somewhat similar.

It is anticipated that during the experimentation, the test should also show good repeatability, provided the wax is homogeneous, and different blocks carry the same material properties.

For processes such as the CIM, the proposed test should be of definite help in two completely different ways: not just as a benchmark for validating software, but also in industrial practice, as a convenient shop-floor test for characterizing the feedstock (i.e. for the routine process quality-control purposes).

For the latter purpose, the feedstock would have to be pressed into the form of a block. This may be achieved via simple cold-pressing, say by filling the feedstock in a container of a square base and then simply placing a specified weight on its top for a specified period of time. These aspects need to be looked into and finalized after some preliminary experimentation.

* * * * *   * * * * *   * * * * *

Update added on 2015.05.17:

This update concerns the software benchmark. A couple of points occurred to me after publishing the post.

1. Note the difference of this test from the hot penetration test of bitumen, or the hot hardness test of metals.

In the proposed test here, the hot object gets completely immersed within the wax block. We are interested not only in melting, but also in the relative motion between the hot and cold objects even as cooling takes place simultaneously. Further, we are also interested in solidification. Finally, unlike those two tests, we are not interested in measurements of forces.

(Indeed, when I thought of this idea, the hot hardness/penetration tests were not even in my peripheral awareness; I was just trying to have as simple a test suitable for processing like CIM, as might be possible.)

2. On the second thoughts, completely doing away with instrumentation may not be such a good idea.

Going by my experience of simulating the melting snowman (as well as my browsing of the transient simulations, and their experimental validations), I think that if this test is to be used as an experimental benchmark for software validation (rather than just as a quick quality-control test on the shopfloor), then it should also specify measuring the precise positions of the hot object at different times, and not just the final depth of penetration it reaches.

In other words, the software should be able to predict the times required to reach the intermediate positions, too, accutately. The intermediate times would come out right only if the software handles the entire process right.

Coming to timings, we should not ask only for the final time when the object comes to a rest. After all, it is possible that the computational technique is such that it errs on the intermediate timings, but it does so in such a way that these errors get cancelled out, and so, the total time taken for the object to come to a rest still is predicted right. Such computational techniques will still not be reliable for modeling the actual CIM processing. So, the time-position profile is of primary importance.

Since the wax (and feedstock in general) is not transparent, for experimental measurements of positions, we cannot use light, and so, a simple technique like video shooting wouldn’t work.

However, since the hot object anyway would be metallic (read: electrically conducting), it would always be possible to sense its internal positions using electromagnetic induction. From my experience of the eddy current NDT, I think, it wouldn’t necessarily have to be an LVDT, and the sensing coil wouldn’t have to necessarily enclose the entire block of wax. If my feel is right (though this will have to be determined after a bit of a trial), a simple “one-way” coil placed on one side of the wax block, should also turn out to be sensitive and accurate enough. Of course, the issue of a differential vs. a direct solenoid is something that needs to be looked into separately.

Now, inductive sensing does make the test much more complicated—you have to firsst calibrate the output of the sensing coil. However, realize, the time-position measurements would be performed only in a laboratory, not under the routine production environments. So, it should be OK. …

… Research is always multi-disciplinary. Indeed, knowledge itself cannot be compartmentalized—regardless of what many influential academicians from the Savitribai Phule University of Pune evidently think. (Though, it was not to show them down that I wrote this post/update. I was mainly concerned only with the research, here.)

* * * * *   * * * * *   * * * * *

A Song I Like:

(Marathi) “manmohana juLatil naa, taaraa punhaa”
Music: Kedar Pandit
Singer: Ketaki Mategaonkar
Lyrics: ??

[There are two versions of this song, both by the same music director, the same singer, the same melody, and in fact, both also come in the same album! One is in the usual Marathi “bhavgeet” style, whereas the other one is in the “jazz” style. (Not quite jazz all the way through, but it does use some Western instruments someway along that genre.) Surprisingly, the melody fits both the styles so well! I honestly cannot decide which one I like better, though perhaps it’s an indication of my age that I am at times inclined ever so slightly towards the “bhavgeet” version. Or may be, it’s because of Kedar Pandit’s restrained but competent “tablaa” which comes only in that version. (I didn’t know anything about him, but the Wiki tells me that he accompanies Pandit Jasraj on all concerts.) Ketaki is young, and does have limitations to her voice, but the songs here have come out very well. May be with a little help coming in from all those track-editing and pitch-correcting software they all use these days. I don’t know really, but that could easily be the case. But it also is a fact that this kind of a melody would suit her well. And, in any case, the final outcome has come out pretty neat. That counts. … I was driving in the Pune city when I first heard the jazz version on radio, and wished I were driving through a lonely rural patch, instead. So, noted down the words, and looked up the ‘net later on. … Give both the versions a try, even if you don’t know Marathi.]

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The Mechanical-vs-Metallurgy “Branch-Jumping” Issue—Part II: Not Attending Inter-/Multi-/Trans-Disciplinary Conferences

0. To know the context and the primary intended readership of this post, please see my earlier post in this series, here: [^]. Of course, as mentioned earlier, everyone else is welcome to read this series, too.

1. The 57th (annual) Congress of the Indian Society of Theoretical and Applied Mechanics (An International Meet) was held at Pune this week, from 17th through 20th December, 2012 [^]. The venue was the Defence Institute of Advanced Technology (now a deemed university) [^]. (Caveat: Their Web site is often down, and with the PDF documents almost always missing. For example, try to download their faculty recruitment form.) I attended it, but this time round, without presenting any paper.

2. The conference was inaugurated by Dr. V. K. Saraswat [^], himself a PhD in combustion engineering. [Yes, the stupid primary intended readership [see part I to know exactly who all], this too is a topic common to both metallurgy and mechanical engineering.] The inaugural and valedictory functions were presided over by Dr. Prahlada [^], the vice-chancellor of the host institute (DIAT).

3. Some 180 papers were presented in the parallel sessions, many of them of multi-/trans-/inter-disciplinary nature, and with their authors coming from almost all departments of science and engineering. Even including electronics engineering, and mining engineering, apart from, of course, the usual ones: applied mechanics, mechanical engg., aerospace engg., civil engg., metallurgical/materials engg., mathematics, physics and astrophysics.

4. Even going just by my personal informal observations, people came to this conference from a lot of places: Guwahati, Kharagpur, Coimbatore, Kanpur, Chennai, Bangalore, Visakhapattanam, Hyderabad, Gulbarga, Surat, Mumbai, etc.

The foreign participation was somewhat limited this time round, with just a couple of Americans (both of Indian origin, both well-honored HoDs of mechanical or mechanics departments), and, off-hand, I suppose, one or two leading researchers or professors each from Canada, Germany, Israel, Japan, Taiwan, etc.

But, come, they did.

In contrast, the IIT Bombay QIP PhD D. W. Pande (of mechanical engineering branch from Aurangabad, now lording over at COEP); the meteorology (?) PhD degree holder G. B. Pant (sitting on the board of governors of COEP [a new addition to the stupid intended readership that should have been effected right the last time, and I will explain the reason for his inclusion the next time]); the Dean of the Faculty of Engineering of the University of Pune, PhD degree holder Gajanan Kharate (from Amaravati, now lording over at Pune, and per government, perhaps an OBC); his PhD guide the IIT Bombay QIP PhD Ashok A. Ghatol (formerly, Director, COEP, per government, certainly an OBC) did not come. Neither any of the others of their ilk.

Not even if they all are employed, and even if the places of their employment are all in or around Pune, and the conference was held right in Pune. [And that being academics, they would get discounts for the conference registration fees, and being government/university employed etc., they would get the conference fee refunded back anyway. Unlike me, who borrowed Rs. 3,500/- to attend it. Despite all that discount and its refunds, these characters still did not attend.]

And, of course, they didn’t send a single student of theirs to attend this conference either. Forget for paper presentation, not even for plain attendance.

The acceptance rate this time round was a bit higher, at about 60%. In the earlier ISTAMs which I attended, it has been 50% and lower; in fact, perhaps as low as 33% (if not 25%, but I don’t remember it too well, so let’s say, 33%). Pretty decent. Better than many reputed international journals. Even then, they still didn’t send a single student. [And, I am sure, this evil + stupid primary intended readership, while evaluating my employment application, would immediately pounce on the fact that I have no journal paper to my credit, only conference papers—if they could get past this metallurgy-to-mechanical “branch-jump” issue.]

These stupid idiots (and possibly evil characters—remember, free will as the basis of morality) with government-assured jobs and pensions and prestige, perhaps realized that if they attended the ISTAM conference, they might run into inter-/multi-/trans-disciplinary researches in mechanics and mechanical engineering. They perhaps also further realized that such a fact might then run counter to the one specific belief they fondly cuddle, cherish, openly advocate, defend and profess, and unhesitatingly act on: namely, that metallurgical graduates with PhD in mechanical cannot teach in or be hired by mechanical departments.

5. As to the research presented in the conference, much of it was not related to my current interests. But still, getting to know about the topics that other people are working on, the ideas they are pursuing, is always intellectually invigorating. I would like to write about the research part separately. Research, in fact any productive work, is such a noble thing. In contrast, for this post, I would not like to dilute the intensity of the focus on my joblessness due to the downright stupidity/evil of these above-mentioned professors/directors/government’s son in laws, etc.

However, I guess I could still mention just a couple of things in the passing.

5.1 One was the mention of the infinite speed of propagation of heat flux in conduction, during the invited lecture by Prof. I. Chung Liu of the National Chi Nan University, Taiwan. (I involuntarily sat up straight from my habitual slump while sitting in that cozy main auditorium at DIAT.) The approach Prof. Liu began with, was already known to me from my arXiv browsing. [No, the stupid intended readership of Mechanical Engineering Professors, Deans and Directors etc., arXiv usually does not have mechanical engineering related articles. So, you need not bother with this research any further, going by your government-funded and -enforced “logic.”] This approach consists of having a hyperbolic equation (the telegrapher’s equation) in place of the usual parabolic one. These days, a fairly neat Wiki page also exists to explain this approach; see here [^]. After his talk, I walked up to him and tried to explain how a particles-based approach makes it possible to remove the instantaneous action at a distance (IAD). However, Prof. Liu was not very well conversant with the Brownian movement/Weiner processes, and so, I could not pursue the conversation further. I just passingly mentioned my own research on diffusion equation to him. [The stupid primary intended readership of government-funded Mechanical Engineering Professors, University Deans and Directors etc., wouldn’t be able to make out why the IAD at all is an issue in the first place. They wouldn’t be able to make out even after being explicitly told twice.] Anyway, even if very brief, this discussion with Prof. Liu did help bring up some of my own thoughts. There is a certain paper on diffusion equation by a Berkeley professor which I had discovered after publishing my paper, and I would like to discuss it. Guess I will write a post at iMechanica (and, naturally, also here) about it, before sending a revised paper on this topic to a journal.

5.2 The second thing was this idea that had struck me while teaching a course on FEM to the COEP undergraduates in Spring 2009. [Yes, stupid/evil intended readership, I did teach the students of the mechanical branch as well, but only as a visiting faculty, and only for one semester. I was not repeated, despite very good student feedback [which Prof. Anil Sahasrabudhe, Director, COEP, didn’t quite share with me, unlike with his practice with other professors, but I do surmise with some pretty good basis—the direct feedback of students to me–that even my official student evaluation/feedback must have been pretty good.]] The idea is concerning finding a physical interpretation for the method of weighted residuals (MWR)—or, at the least, connecting some more mathematical context to MWR, anyway. My idea being too premature, I had not shared it with these undergraduate students back then. However, since the MTech-level students are a bit more mature, I did briefly hint at it while teaching the course on FEM at Symbiosis this year.

SPOILER ALERT: I may write a paper on this idea.

The idea is this: It first struck me that there was some kind of an analog between fitting a straight line to a scatter plot (say, the least-squares fit), and the method of weighted residuals. Sure, the first is an algebraic system and the second one involves differential equations. (Even if the ansatz is algebraic (a polynomial), before getting to the residuals, you still have to differentiate it, thereby changing the nature of the game.) The algebraic vs the infinitesimal is a big difference, and it is there. Yet, the idea of a residual (and setting it to zero) is common.

Then, I recalled that it was basically the same guy who had thought of both of these ideas, at least in their seed form: C. F. Gauss. (Ok, off-hand, I think that the least squares had already been used by someone else, before Gauss, but Gauss reinvented it independently, anyway. (Turns out, that earlier guy was Legendre [^])). The fact that the same mind had invented both the techniques helped gain more confidence in this idea of treating something like the least squares as an analog of the MWR.

In this conference, I got a chance to sound out this idea to two senior professors of mathematics: Prof. Kaloni of University of Windsor, and Prof. Rathish Kumar of IIT Kanpur. Specifically, I asked them if someone had already worked out something following, say, a function spaces-based approach.

Here, I was trying very hard to recall my earlier general reading decades ago concerning topological interpretation of the differentiation operation and all, and its recent mention by Prof. Tim Poston in a brief communication that I had with him. (It was a point which I had not at all understood at all.) Now at this conference, while talking in the hallways and all, I was trying to recollect those words. But somehow, in the hustle and bustle of the conference and the very short time available for those lounge/hall discussions, I could not recall any of such words. So, I tossed the first word I could catch hold of: function spaces.

Prof. Kaloni thought that someone must have worked on it already. In contrast, Prof. Rathish Kumar raised an entirely different point: where is convergence on the algebraic side of it, he asked. According to him, MWR was not limited to just getting to the residual and setting its domain integral to zero. The essence of MWR also had to include the idea of convergence—of a (possibly infinite) sequence of steps, of a systematic process of reducing the discretization error. In contrast, on the algebraic side of it, he observed, it’s just a one-time affair: you just take the fit, and that’s it. There is nothing more to be done; there is no second step; there is no sequence; the idea of convergence doesn’t apply.

In the busy-ness of such sideways discussions, there was no time to explain that I could get (i.e. I already was thinking of) an algebraic system that can still involve the ideas of convergence. In fact, I thought about it and got at an example right on the fly. But I was sure I couldn’t have explained it in the right words—the idea just flashed right during the conversation. So, not to waste his time, I asked him what would he think of it if I could get such a system (a multi-step, converging but algebraic system), and try to establish an analog with the differential equations-involving MWR. He then said that perhaps such a thing has not been done before, and that it would be nice to have a connection like that formally worked out. [I will repeat this part in a separate post, also at iMechanica, but in the meanwhile, if you know that someone has already worked out something along these lines, please drop me a line; thanks in advance.]

So there. The stupid/evil primary intended readership, these discussions, per your government-funded and government-enforced “logic,” had nothing to do with mechanical engineering. After all, both the professors were from the department of mathematics. So, you the stupid/evil primary intended readership (consisting of folks like G. K. Kharate, A. A. Ghatol, D. W. Pande, G. B. Pant, their friends, etc.), you all sit cozy and quiet and keep on drawing your respective 6th-pay commission-enhanced salaries, allowances, refunds, etc. Keep faithfully doing that, you stupids/idiots/evils.

[I remain jobless; the “A Song I Like” section is once again being dropped.]

[E&OE]