# A flip, but not a flop…

“Why is it that when you look in the mirror, the left and right directions appear flipped, but not the up and down?”

Do not read further until you have honestly tried answering that question!

The question was asked at the Physics StackExchange.

As often is the case, using only text is not at all good when it comes to explaining physics [^]; adding figures does help [^]. And then, animations are even better at it than having just “dead” (static) figures. Going further, interactive graphics, which let the user participate in manipulating the presentation of information, of course beats those mere animations. Better than that, if possible, is an actual demonstration in real life, accompanied by an explanation using simple words.

…As far as the above question is concerned, the Physics Girl [^] does a fairly good job [^].

The best mode of teaching-learning, of course, is an actual and immediate interaction with a person, who in turn might use (and allow you to use) any and all of the above options!

And that’s the reason why, regardless of how much technology progresses, the actual person-to-person type of teaching will never go out of business.

A Video I Liked:

A Thought Leader’ gives a talk that will inspire your thoughts: [^]

# Shaken, because of a stir

We have demonstrably been shaken here on earth, because of a stir in the cosmos.

The measured peak strain was $10^{-21}$ [^].

For comparison: In our college lab, we typically measure strains of magnitude like $10^{-3}$ or at the most $10^{-4}$. (Google search on “yield strain of mild steel” does not throw up any directly relevant page, but it does tell you that the yield strength of mild steel is 450 MPa, and all mechanical (civil/metallurgical/aero/etc.) engineers know that Young’s modulus for mild steel is 210 GPa. … You get the idea. …)

Einstein got it wrong twice, but at least eventually, he did correct himself.

But other physicists (and popular science writers, and blog-writers), even after getting a full century to think over the issue, still continue to commit blunders. They continue using terms like “distortions of spacetime.” As if, space and time themselves repeatedly “bent” (or, to use a euphemism, got “distorted”) together, to convey the force through “vacuum.”

It’s not a waving of the “spacetime” through a vaccum, stupid! It’s just the splashing of the aether!!

The Indian credit is, at the most, 1.3%.

If it could be taken as 3.7%, then the number of India’s science Nobels would also have to increase dramatically. Har Gobind Singh Khorana, for instance, would have to be included. The IAS-/MPSC-/scientist-bureaucrats “serving” during my childhood-days had made sure to include Khorana’s name in our school-time science text-books, even though Khorana had been born only in (the latter-day) Pakistan, and even if he himself had publicly given up on both Pakistan and India—which, even as children, we knew! Further, from whatever I recall of me and all my classmates (from two different schools), we the (then) children (and, later, teen-agers) were neither inspired nor discouraged even just a tiny bit by either Khorana’s mention or his only too willing renunciation of the Indian citizenship. The whole thing seemed too remote to us. …

Overall, Khorana’s back-ground would be a matter of pride etc. only to those bureaucrats and possibly Delhi intellectuals (and also to politicians, of course, but to a far lesser extent than is routinely supposed). Not to others.

Something similar seems to be happening now. (Something very similar did happen with the moon orbiter; check out the page 1 headlines in the government gazettes like Times of India and Indian Express.)

Conclusion: Some nut-heads continue to run the show from Delhi even today—even under the BJP.

Anyway, the reason I said “at most” 1.3 % is because, even though I lack a knowledge of the field, I do know that there’s a difference between 1976, and, say, 1987. This fact by itself sets a natural upper bound on the strength of the Indian contribution.

BTW, I don’t want to take anything away from Prof. Dhurandhar (and from what I have informally gathered here in Pune, he is a respectable professor doing some good work), but reading through the media reports (about how he was discouraged 30 years ago, and how he has now been vindicated today etc.) made me wonder: Did Dhurandhar go without a job for years because of his intellectual convictions—the way I have been made to go, before, during and after my PhD?

As far as I am concerned, the matter ends there.

At least it should—I mean, this post should end right here. But, OK, let me make an exception, and note a bit about one more point.

The experimental result has thrown the Nobel bookies out of business for this year—at least to a great part.

It is certain that Kip Thorne will get the 2016 Physics Nobel. There is no uncertainty on that count.

It is also nearly as certain that he will only co-win the prize—there will be others to share the credit (and obviously deservingly so). The only question remaining is, will it be just one more person or will it be two more (Nobel rules allow only max 3, I suppose), what will be their prize proportions, and who those other person(s) will be (apart from Thorne). So, as far as the bettors and the bookies are concerned, they are not entirely out of the pleasure and the business, yet.

Anyway, my point here was twofold: (i) The 2016 Physics Nobel will not be given for any other discovery, and (ii) Kip Thorne will be one of the (richly deserving) recipients.

[E&OE]

/

# Yo—4: The 2014 Physics Nobel

The physics Nobel for this year has gone to Isamu Akasaki, Hiroshi Amano and Shuji Nakamura, for the invention of the blue LED. Check out the official Nobel prize page to see the huge cost savings the invention implies [^]. Very, very, very well deserved!

Congratulations to all the winners.

Their invention has already begun transforming our lives, and, definitely, much more is slated to come. Just to name two: (i) flexible LEDs, (ii) lost-cost designer walls smartly emitting diffuse light (so that the light (in the sense lamp) is not different from the wall, the wall itself is light)… The possibilities are just astounding… For instance, think how it might affect (i) buildings architecture and interior designing, (ii) lighting inside tunnels/underground transportation…. You couldn’t wish for more…

Or, may be, you could! (Hey, this is science and this is life… There is always scope for more!) … If you ask me to single out just one thing, as far as these light- and energy-related matters go, I would choose: cost-effective (i.e. scalable and high energy-density) artificial photo-synthesis. … But then, that is strictly for another day.

As of today, do pause to note here that the realization of the blue LED also took something like three decades! Enormous achievement, that!!

Congratulations to the winners, once again!

* * * * *   * * * * *   * * * * *

A Song I Like:
(Hindi) “pyaar baanTate chalo…”
Singer: Kishore Kumar
Music: Laxmikant Pyarelal
[BTW, if some of you don’t like some part of the lyrics, or of the video, then that can be OK by me, I can understand. Just don’t let it spoil this song itself for you, though. [And, also avoid the cynical temptation to associate this song with the money-distribution that does often go on, at the time of elections.] Instead, just take this song as a song, and appreciate that joyous sense which it carries, the sense of innocence and benevolence which comes so abundantly overflowing from it.]

[E&OE]

# 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 a`T’ 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.

* * * * *   * * * * *   * * * * *

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

[E&OE]

/