Even while enjoying my writer’s block, I still won’t disappoint you. … My browsing has yielded some material, and I am going to share it with you.

It all began with googling for some notes on CFD. One thing led to another, and soon enough, I was at this page [^] maintained by Prof. Praveen Chandrashekhar of TIFR Bangalore.

Do go through the aforementioned link; highly recommended. It tells you about the nature of my trade [CFD]…

As that page notes, this article had first appeared in the AIAA Student Journal. Looking at the particulars of the anachronisms, I wanted to know the precise date of the writing. Googling on the title of the article led me to a PDF document which was hidden under a “webpage-old” sub-directory, for the web pages for the ME608 course offered by Prof. Jayathi Murthy at Purdue [^]. At the bottom of this PDF document is a note that the AIAA article had appeared in the Summer of 1985. … Hmm…. Sounds right.

If you enjoy your writer’s block [the way I do], one sure way to continue having it intact is to continue googling. You are guaranteed never to come out it. I mean to say, at least as far as I know, there is no equivalent of Godwin’s law [^] on the browsing side.

Anyway, so, what I next googled on was: “wind tunnels.” I was expecting to see the Wright brothers as the inventors of the idea. Well, I was proved wrong. The history section on the Wiki page [^] mentions Benjamin Robins and his “whirling arm” apparatus to determine drag. The reference for this fact goes to a book bearing the title “Mathematical Tracts of the late Benjamin Robins, Esq,” published, I gathered, in 1761. The description of the reference adds the sub-title (or the chapter title): “An account of the experiments, relating to the resistance of the air, exhibited at different times before the Royal Society, in the year 1746.” [The emphasis in the italics is mine, of course! [Couldn’t you have just guessed it?]]

Since I didn’t know anything about the “whirling arm,” and since the Wiki article didn’t explain it either, a continuation of googling was entirely in order. [The other reason was what I’ve told you already: I was enjoying my writer’s block, and didn’t want it to go away—not so soon, anyway.] The fallout of the search was one k-12 level page maintained by NASA [^]. Typical of the government-run NASA, there was no diagram to illustrate the text. … So I quickly closed the tab, came back to the next entries in the search results, and landed on this blog post [^] by “Gina.” The name of the blog was “Fluids in motion.”

… Interesting…. You know, I knew about, you know, “Fuck Yeah Fluid Dynamics” [^] (which is a major time- and bandwidth-sink) but not about “Fluids in motion.” So I had to browse the new blog, too. [As to the FYFD, I only today discovered the origin of the peculiar name; it is given in the Science mag story here [^].]

Anyway, coming back to Gina’s blog, I then clicked on the “fluids” category, and landed here [^]… Turns out that Gina’s is a less demanding on the bandwidth, as compared to FYFD. [… I happen to have nearly exhausted my monthly data limit of 10 GB, and the monthly renewal is on the 5th June. …. Sigh!…]

Anyway, so here I was, at Gina’s blog, and the first post in the “fluids” category was on “murmuration of starlings,” [^]. There was a link to a video… Video… Video? … Intermediate Conclusion: Writer’s blocks are costly. … Soon after, a quiet temptation thought: I must get to know what the phrase “murmuration of starlings” means. … A weighing in of the options, and the final conclusion: what the hell! [what else], I will buy an extra 1 or 2 GB add-on pack, but I gotta see that video. [Writer’s block, I told you, is enjoyable.] … Anyway, go, watch that video. It’s awesome. Also, Gina’s book “Modeling Ships and Space Craft.” It too seems to be awesome: [^] and [^].

The only way to avoid further spending on the bandwidth was to get out of my writer’s block. Somehow.

So, I browsed a bit on the term [^], and took the links on the first page of this search. To my dismay, I found that not even a single piece was helpful to me, because none was relevant to my situation: every piece of advice there was obviously written only after assuming that you are not enjoying your writer’s block. But what if you do? …

Anyway, I had to avoid any further expenditure on the bandwidth—my expenditure—and so, I had to get out of my writer’s block.

So, I wrote something—this post!

[Blogging will continue to remain sparse. … Humor apart, I am in the middle of writing some C++ code, and it is enjoyable but demanding on my time. I will remain busy with this code until at least the middle of June. So, expect the next post only around that time.]

[May be one more editing pass tomorrow… Done.]

[E&OE]

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# Whassup? “Making room…”

Honestly, for the past quite a few days, I’ve been summarily in that (Marathi) “sun-saan” mood. … Yes, in that mood, and for quite a few days…. Continuously at a stretch, in fact.

Sometime during the initial phase of this mood, somewhere at just the sub-surface level, I did idly think of trying my hand at writing blog posts, just so as to come out of it. Then, exactly at that same sub-surface level, with exactly that same shade of that idle nothing-ness in which I was engulfed, I also saw these thoughts pass me by. …

… It never happens. … I mean, at least with me, it never so happens that I can bring myself to writing something, anything, even just a blog post, when I am trapped in that mood of not wanting to do anything in particular. … I actually end up doing nothing in such times.

No, you can’t call it the writer’s block; it would be too narrow a description. The point is, when it happens, it is “everyone’s and everything’s block.” I mean, at such times, I can’t do even just plain arm-chair thinking. …

Thinking is an active verb, not passive. And, the gloom-some passivity is such that I don’t find myself even thinking about the gloom-some things, even if these go on registering with me. You know, things like the HDD crash, the continuing jobless-ness, etc.

… But, no, nothing happens when I am in that mood. N o t h i n g.

[No, at such times, I am not day-dreaming, even. Not even just hibernating. And, I certainly am not even in that meditative frame either. [I know meditation. I have done it, too.]]

So, all in all, I am being extraordinarily accurate when I say: nothing happens.

This time round, the mood lasted for a few days. Until this morning.

No, no one else had any role to play in my coming out of it. None. None whosoever. I myself did. Rather, I just passively observed myself coming out of it, and then, actually having come out of it. Right this morning. Just a few hours ago.

Yes, before that, I did watch some TV these past few days. But, no, not even retards (or American psychologists) could possibly level the accusation that watching TV lets one “come out” of such moods. Certainly not, when it is me. TV is incapable of affecting me too much, one way or the other. I am being honest here. That’s actually how my bodily constitution is made up like. TV does not affect me too much, for the better or for the worse. It always remains just plain boring, in a mild sort of a way. That’s all.

Anyway, that’s about all I can write about the recent experience, by me, and of that mood.

Now, what is it that I did to come out of… Wrong! Invalid line of thought!!

So, what is it that I did after I came out of it?

I did some search on something and browsed a few URLs. What in particular? I will jot it down right in this post, but before that, allow me a moment to explain the title of this post.

Those among the English-speaking peoples who are fortunate enough to be playing cricket, there is a peculiar circumstance that used to happen in the one-day 50 overs cricket matches, about 20—30 years ago. The circumstance would occur once a match progressed to the late 30s in the overs.

… In terms of overs, the game from about the late teens to the late 30s could easily go replicating my mood above. But, somehow, either the bowlers or the batsmen or both would come out of it, sometimes even in a virtual snap of sorts, though it would happen mostly only gradually, once they arrived in the late 30s in the overs. May be, perhaps, as a result of the spin and the medium-pace bowlers being taken off and the fast bowlers being brought back in, for their second (and last) spell.

Then. Suddenly. Zzzoooooom. A good-length ball, left alone by the batsman (almost as a matter of habit); it safely lands in the gloves of the fumbling wicket-keeper, who should have been prepared but is still taken by a bit of a surprise. Zzzooooom. A second ball, now on the off-stump, swinging ever so slightly out the off-stump. Oh yes! There still is some swing left in this wicket! The batsman does something like waving his bat at it, fumbles, but is lucky enough to survive. Then, a very fast-paced short-length ball, in fact a bouncer! The batsman ducks. The wicket-keeper stretches all the way back, but manages to catch it. Finally, the batsman is found adjusting his gear, esp. his helmet. Yet another good-length delivery, somewhat slower in pace, slightly outside the off-stump, again with just so slight an outswing. Well-collected by the wicket-keeper. No changes in the fielding. And then, finally, comes The Ball. This time, it’s a furiously paced one, right on the leg—yorker! Within a split-second, stepping aside on the front-foot…

The cricket-knowing people [whether English-speaking or otherwise] could easily complete the last sentence above.

Among the commonly available options, the one I like to imagine here is this: Dancing down the wicket, leaving all the stumps in the open, the batsman makes room for himself, and hits at the ball hard, with his full strength. The ball connects with the meat of the bat, and the next instant, it is seen racing past the extra-cover boundary. No, you have not been able to catch how or where the ball went, really speaking. All that your visual field has in the meanwhile registered is the whitish figure of that fielder in the covers first rising up in a contorted fashion in the air, with both his hands wildly outstretched out and up, and just when that slim figure of that talented fielder begins—almost as if unbelievably by now—to go down, you instinctively strive to look past beyond him. And then, you see it. The ball has taken the first harsh bounce past the fielder, not caring a whit for the grass, and it is now racing… no, in fact it already has gone past the boundary line, for a four… [To me, such a four is more appealing than an artful but wily hook off a leg-side delivery for a sixer. The latter somehow appears almost meekish, as compared to this brawnishly—even if not very artfully—executed cover drive. That is, when such a cover drive is an answer to a yorker. Even if the yield to the side is only 4, not 6.]

Well, I left watching cricket roughly in the mid-1990s. When someone says “cricket” or “cricketers,” about the only match that I somewhat remember (after a 5–10 second gap or more), or the “last” complete match I probably saw, was the one in which both Rahul Dravid and Sourabh Ganguly were either brand new, or at the most only 2–3 matches old. I haven’t watched much cricket after that. May be two or three matches (in full), and some more matches, some half-way through or so. None of these matches, I remember any more. And, I am completely certain that (except for some irritating times when I am only gone to a restaurant for a drink and some good food, and yet, cricket finds a way to pounce on me off a big glaring screen) I have not watched any cricket over the past 10+ years. Whether India was playing Pakistan or not. Whether Sachin Tendulkar was in form or not. … You get the idea.

But still, some visuals and phrases have remain etched in the memory. One of them is: “Making room for himself.”

If the going has not been so good, and yet, it has also not been very particularly bad either, if you have been in that greyish or slumberish sort of a mood of not wanting to do anything, or in an even worse mood: in that (Marathi) “sun-saan” mood, then: Once you find yourself having come out of it, the first thing you gotta do, IMO, is: Make room for yourself.

So, I did. Right this morning. (A few hours ago.)

I re-realized that one application of CFD is in the computer graphics and games programming field. (I had well-realized this point in the past, of course, but all the downloaded materials and sources had gone in that HDD crash.)

So, this morning, I spent some time browsing the ‘net for CFD simulations for computer graphics. … Interesting!

I need to add “Fluids simulation for computer graphics” as one of my active research interests, while updating my resume.

Should I conduct a course on Fluids Simulation for the CS folks, esp. for those working in the IT industry in Pune or Mumbai? Would someone be interested? Drop me a line. I am all ears. And, I am serious. (I will even simplify the maths while presenting the topics, and I will also supply some elementary codes. The students must, however, bring both their laptops and minds to the class.))

Let me know—before I possibly slip back once again into that yawnish/slumberish/worse—(Marathi) “sun-saan” (i.e. in English, roughly, tomb-silent) kind of a mood…

* * * * *   * * * * *   * * * * *

A Song I Like:

(Hindi) “jeenaa ye koi jeenaa to nahin”
Singer: Shailendra Singh
Music: Bappi Lahiri
Lyrics: Gulshan Bawra

[Yes, IMO, here, it’s Shailendra Singh’s version that easily outdoes Lata’s. [But then, honestly, isn’t the tune here better suited to a male voice?]… And, yes, IMO, here (as also on many other under-appreciated occasions), this “RD Clone” has managed to actually deliver on the goods! When I was in college, the intellectuals back then had this tendency to smirk at even just a passing mention of Bappi Lahiri’s name. But, even back then, I would think that he didn’t deserve it—even if he indeed was, for much part, an RD (and many others) Clone. Yes, I would also air this opinion of mine, back then. Anyway, this is certainly one of his best songs; see if you like it, too.

[An editing touch is sure due; may or may not get effected. Done. Expect more posts of a similarly long-winding and pointless nature, at least in the near future.]

[E&OE]

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# The most economic particles model of a[n utterly] fake fluid—part 1

Real fluids are viscous.

Newton was the first to formulate a law of viscosity; his law forms an essential part of the engineering fluid mechanics even today.

The way the concept of viscosity is usually presented to undergraduates is in reference to a fluid moving over a horizontal solid surface, e.g., water flowing over a flat river-bed. The river-bed itself is, of course, stationary. The students are then asked to imagine a laminar flow in which the horizontal layers of fluid go slipping past each other with different velocities. The viscous forces between the fluid layers tend to retard their relative motion. Now, under the assumption that the layer adjacent to the stationary solid surface has zero velocity, and that the flow is laminar, a simple parabolic profile is obtained for the velocity profile. The velocity progressively increases from 0 at the solid surface to some finite mainstream value as you go up and away from the horizontal solid surface. Newton’s law is then introduced via the equation:

$\tau \propto \dfrac{dU}{dy}$

where $\tau$ is the shear stress between the fluid layers slipping past each other, and $\frac{dU}{dy}$ is the velocity gradient along the vertical direction. The constant of proportionality is viscosity, $\mu$:

$\mu \equiv \dfrac{\tau}{\left(\dfrac{dU}{dy}\right)}$

This picture of layers of fluids slipping past with progressively greater velocities, as in a deck of card given a gentle horizontal push, is easy to visualize; it helps people visualize what otherwise is not available to direct perception.

That’s quite fine, but then, as it happens, sometimes, concrete pictures also tend to over-concretize the abstract ideas. The above mentioned picture of viscosity is one of these.

You see, the trouble is, people tend to associate viscosity to be operative only in this shear mode. They can’t readily appreciate the fact that viscous forces also arise in the normal direction. The reason is, they can’t as easily imagine velocity gradients along the flow direction. No engineering (or physics) text-book ever shows a diagram illustrating the action of viscosity along the direction of the flow.

One reason for that, in turn, is that while in solids stress depends on the extent of deformation, in fluids, it depends on the rate of deformation. Indeed the extent of possible deformation, in fluids, is theoretically undefined (or infinite, if you wish). A fluid will continually go on changing its shape so long as a shear stress is applied to it… It’s easily possible to pour water from a tap onto a tilted plate, and then, from that plate onto the bottom of a kitchen sink, without any additional stress coming into picture as the water continuously goes on deforming in the act of pouring. The fact that water has already suffered deformation while being poured from the tap to the plate, does not hinder the additional deformation that it further suffers while falling off from the plate. And, all this deformation, inasmuch as it involves a change of the initial shape, involves only shear. And, as to the stress, when it comes to fluids, the extent of deformation does not matter; the rate of deformation—or the velocity gradient—does. Stress in fluids is related to the velocity gradient, not to the deformation gradient (as in solids).

Another, related, reason for the difficulty in visualizing viscosity appearing in the normal direction is that, in our usual imagination, we can’t visualize fluids being gripped from its ends and pulled apart, the way solids (e.g. rubber band) can be. The trouble is not in the stretching part of it; the trouble is in the “being held” part of it: you can’t grab of a piece of a fluid in exactly the same way as you can, say, a bite of food. There is no bite of water, only a gulp of it. But the practical impossibility of holding fast onto an end of a fluid also carries over when it comes to imagining fluids being stretched purely along the normal direction, i.e., without involving shear.

Of course, as far as exerting a normal force to a fluid is concerned, people have no difficulty imagining that. You can always exert a compressive normal force on a fluid, by applying a pressure. But then, that is only a compressive force, and, a static situation. You don’t have to have spatially varying velocities to arrive at the concept of pressure—indeed, you don’t make any reference to the very idea of velocity, in that concept. Pressure refers to static forces.

Now, when people try to visualize velocity gradients in the normal direction, they unwittingly tend to take the visualization on the lines parallel to the viscosity-defining picture. So, they take, say, a 10 m/s velocity vector at origin, an 8 m/s velocity vector at the point x = 1, a 6 m/s vector at x = 2, and so on. Soon, they end up imagining having a zero magnitude velocity vector.

But this is a poorly imagined situation because it can never be realized in one-dimension—quantitatively, it violates the mass conservation principle, i.e. the continuity equation (at least for the incompressible 1D flow without sources/sinks, it does).

Now, when pushed further, people do end up imagining an L’ kind of bend in a pipe (or a fluid bifurcating at aT’ joint), i.e., taking velocity vectors to be just x-components of a 2D/3D velocity field.

But, speaking in general terms, at least in my observation, people still can’t easily imagine viscosity being defined in reference to velocity gradients along the direction of the flow. Many engineers in fact express a definite surprise at such a definition of viscosity. The only picture ever presented to them refers to the shear deformation, and given the peculiar nature of fluids, velocity gradients in the normal direction (i.e. along the flow) are not as easy to visualize unless you are willing to break continuity.

Recently when Prof. Suo wrote an iMechanica post about viscosity (in reference to a course he is currently teaching at Harvard), the above-mentioned observations came rushing to my mind, and that’s how I had a bit of discussion with him on this topic, here [^].

As mentioned in that discussion, to help people visualize the normal viscosity, I then thought of introducing a particles model of fluid, specifically, the Lennard-Jones (LJ) fluid [^]. It also goes well with my research interests concerning the particles approaches to fluids.

But then, of course, I have been too busy just doing the class-room teaching this semester, and find absolutely no time to pursue anything other than that—class-room teaching, or preparation for the same, or follow-up activities concerning the same (e.g. designing assignments, unit tests, etc.). But no time at all is left for research, blogging, or why, even just building a few software toys at home. (As a matter of fact, I find myself hard-pressed to find time even for just grading of unit-test answer-books.)

Therefore, writing some quick-n-simple illustrative software (actually, completing writing this software—something which I had began last summer) was out of the question. Still, I wanted to steal some time, to think about this question.

I therefore decided to drastically simplify the matters. I would work on the problem, but only to the extent that I can work on it off my head (i.e. without using even paper and pencil, let alone a computer or a software)—that’s what I decided.

So, instead of taking the $(1/r)^{12} - (1/r)^6$ potential, I began wondering what if I take a simple $1/r$ attractive potential (as in Newtonian gravity). After all, most every one knows about the inverse-square law, and so, it would be easier for people to make the conceptual connections if a fluid could be built also out of the plain inverse-distance potential.

So, the question was: (Q1) if I take a few particles with (only attractive) gravitational interactions among them—would they create a fluid out of them, just the way the LJ potential does? And if the answer is yes, then would these particles also create a solid out of them, too, just the way the LJ potential does?

Before you rush into an affirmative answer, realize here that the LJ potential carries both attractive and repulsive terms, whereas the gravitational interaction is always only attractive.

But, still, suppose such a hypothetical fluid is possible, then, (Q2) what would distinguish this hypothetical fluid from its corresponding solid? How precisely would the phase transition between the solid and fluid occur? For instance, how would the fluid consisting of only gravity-interacting particles, melt or solidify?

And, (Q3) what is the minimum number of such particles that must be present before they can create a solid? a fluid? a liquid? a gas?

Of course, answering these questions is not a big deal (neither is thinking up these questions). The point is, I had some fun thinking along these lines, in whatever time I could still find.

However, since this post is already more than a thousand words-long, let me stop here, and ask you to think about the above mentioned questions. In my next post, I will give my answers to them. In the meanwhile, think about it, have fun, and if you think you have got an answer that you could share with me, feel free to drop a comment or an email.

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A Song I Like:
(Marathi) “waaT ithe swapnaatil sampali jaNu…”
Singer: Suman Kalyanpur
Music: Ashok Patki
Lyrics: Ashok Paranjape

[E&OE]

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