# Causality. And a bit miscellaneous.

0. I’ve been too busy in my day-job to write anything at any one of my blogs, but recently, a couple of things happened.

1. I wrote what I think is a “to read” (if not a “must read”) comment, concerning the important issue of causality, at Roger Schlafly’s blog; see here [^]. Here’s the copy-paste of the same:

1. There is a very widespread view among laymen, and unfortunately among philosophers too, that causality requires a passage of time. As just one example: In the domino effect, the fall of one domino leads to the fall of another domino only after an elapse of time.

In fact, all their examples wherever causality is operative, are of the following kind:

“If something happens then something else happens (necessarily).”

Now, they interpret the word `then’ to involve a passage of time. (Then, they also go on to worry about physics equations, time symmetry, etc., but in my view all these are too advanced considerations; they are not fundamental or even very germane at the deepest philosophical level.)

2. However, it is possible to show other examples involving causality, too. These are of the following kind:

“When something happens, something else (necessarily) happens.”

Here is an example of this latter kind, one from classical mechanics. When a bat strikes a ball, two things happen at the same time: the ball deforms (undergoes a change of shape and size) and it “experiences” (i.e. undergoes) an impulse. The deformation of the ball and the impulse it experiences are causally related.

Sure, the causality here is blatantly operative in a symmetric way: you can think of the deformation as causing the impulse, or of the impulse as causing the deformation. Yet, just because the causality is symmetric here does not mean that there is no causality in such cases. And, here, the causality operates entirely without the dimension of time in any way entering into the basic analysis.

Here is another example, now from QM: When a quantum particle is measured at a point of space, its wavefunction collapses. Here, you can say that the measurement operation causes the wavefunction collapse, and you can also say that the wavefunction collapse causes (a definite) measurement. Treatments on QM are full of causal statements of both kinds.

3. There is another view, concerning causality, which is very common among laymen and philosophers, viz. that causality necessarily requires at least two separate objects. It is an erroneous view, and I have dealt with it recently in a miniseries of posts on my blog; see https://ajitjadhav.wordpress.com/2017/05/12/relating-the-one-with-the-many/.

4. Notice, the statement “when(ever) something happens, something else (always and/or necessarily) happens” is a very broad statement. It requires no special knowledge of physics. Statements of this kind fall in the province of philosophy.

If a layman is unable to think of a statement like this by way of an example of causality, it’s OK. But when professional philosophers share this ignorance too, it’s a shame.

5. Just in passing, noteworthy is Ayn Rand’s view of causality: http://aynrandlexicon.com/lexicon/causality.html. This view was basic to my development of the points in the miniseries of posts mentioned above. … May be I should convert the miniseries into a paper and send it to a foundations/philosophy journal. … What do you think? (My question is serious.)

Thanks for highlighting the issue though; it’s very deeply interesting.

Best,

–Ajit

3. The other thing is that the other day (the late evening of the day before yesterday, to be precise), while entering a shop, I tripped over its ill-conceived steps, and suffered a fall. Got a hairline crack in one of my toes, and also a somewhat injured knee. So, had to take off from “everything” not only on Sunday but also today. Spent today mostly sleeping relaxing, trying to recover from those couple of injuries.

This late evening, I naturally found myself recalling this song—and that’s where this post ends.

4. OK. I must add a bit. I’ve been lagging on the paper-writing front, but, don’t worry; I’ve already begun re-writing (in my pocket notebook, as usual, while awaiting my turn in the hospital’s waiting lounge) my forth-coming paper on stress and strain, right today.

OK, see you folks, bye for now, and take care of yourselves…

A Song I Like:

(Hindi) “zameen se hamen aasmaan par…”
Singer: Asha Bhosale and Mohammad Rafi
Lyrics: Rajinder Krishan

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

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

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

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

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

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

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

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

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

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

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

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

Accordingly, I am ceasing blogging for now.

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

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

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

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

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

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

And, oh, just one more thing…

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

Which Song Do You Like?

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

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

# 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]

/

# Blogging some crap…

I had taken a vow not to blog very frequently any more—certainly not any more at least right this month, in April.

But then, I am known to break my own rules.

Still, guess I really am coming to a point where quite a few threads on which I wanted to blog are, somehow, sort of coming to an end, and fresh topics are still too fresh to write anything about.

So, the only things to blog about would be crap. Thus the title of this post.

Anyway, here is an update of my interests, and the reason why it actually is, and also would be, difficult for me to blog very regularly in the near future of months, may be even a year or so. [I am being serious.]

1. About micro-level water resources engineering:

Recently, I blogged a lot about it. Now, I think I have more or less completed my preliminary studies, and pursuing anything further would take a definitely targeted and detailed research—something that only can be pursued once I have a master’s or PhD student to guide. Which will only happen once I have a job. Which will only happen in July (when the next academic term of the University of Mumbai begins).

There is only one idea that I might mention for now.

I have installed QGIS, and worked through the relevant exercises to familiarize myself with it. Ujaval Gandhi’s tutorials are absolutely great in this respect.

The idea I can blog about right away is this. As I mentioned earlier, DEM maps with 5 m resolution are impossible to find. I asked my father to see if he had any detailed map at sub-talukaa level. He gave me an old official map from GSI; it is on a 1:50000 scale, with contours at 20 m. Pretty detailed, but still, since we are looking for check-dams of heights up to 10 m, not so helpful. So, I thought of interpolating contours, and the best way to do it would be through some automatic algorithms. The map anyway has to be digitized first.

That means, scan it at a high enough resolution, and then perform a raster to vector conversion so that DEM heightfields could be viewed in QGIS.

The trouble is, the contour lines are too faint. That means, automatic image processing to extract the existing contours would be of limited help. So, I thought of an idea: why not lay a tracing paper on top, and trace out only the contours using black pen, and then, separately scan it? It was this idea that was already mentioned in an official Marathi document by the irrigation department.

Of course, they didn’t mean to go further and do the raster-to-vector conversion and all.  I would want to adapt/create algorithms that could simulate rainfall run-offs after high intensity sporadic rains, possibly leading also to flooding. I also wanted to build algorithms that would allow estimates of volumes of water in a check dam before and after evaporation and seepage. (Seepage calculations would be done, as a first step, after homogenizing the local geology; the local geology could enter the computations at a more advanced stage of the research.) A PhD student at IIT Bombay has done some work in this direction, and I wanted to independently probe these issues. I could always use raster algorithms, but since the size of the map would be huge, I thought that the vector format would be more efficient for some of these algorithms. Thus, I had to pursue the raster-to-vector conversion.

So I did some search in this respect, and found some papers and even open source software. For instance, Peter Selinger’s POTrace, and the further off-shoots from it.

I then realized that since the contour lines in the scanned image (whether original or traced) wouldn’t be just one-pixel wide, I would have to run some kind of a line thinning algorithm.

Suitable ready made solutions are absent and building one from the scratch would be too time consuming—it can possibly be a good topic for a master’s project in the CS/Mech departments, in the computer graphics field. Here is one idea I saw implemented somewhere. To fix our imagination, launch MS Paint (or GIMP on Ubuntu), and manually draw a curve in a thick brush, or type a letter in a huge font like 48 points or so, and save the BMP file. Our objective is to make a single pixel-thick line drawing out of this thick diagram. The CS folks apparently call it the centerlining algorithm. The idea I saw implemented was something like this: (i) Do edge detection to get single pixel wide boundaries. The “filled” letter in the BMP file would now become “hollow;” it would have only the outlines that are single pixel wide. (ii) Do raster-to-vector conversion, say using POTrace, on this hollow letter. You would thus have a polygon representation for the letter. (iii) Run a meshing software (e.g. Jonathan Schewchuk’s Triangle, or something in the CGAL library) to fill the interior parts of this hollow polygon with a single layer of triangles. (iv) Find the centroids of all these triangles, and connect them together. This will get us the line running through the central portions of each arm of the letter diagram. Keep this line and delete the triangles. What you have now got is a single pixel-wide vector representation of what once was a thick letter—or a contour line in the scanned image.

Sine this algorithm seemed too complicated, I thought whether it won’t be possible to simply apply a suitable diffusion algorithm to simply erode away the thickness of the line. For instance, think that the thick-walled letter is initially made uniformly cold, and then it is placed in uniformly heated surroundings. Since the heat enters from boundaries, the outer portions become hotter than the interior. As the temperature goes on increasing, imagine the thick line to begin to melt. As soon as a pixel melts, check whether there is any solid pixel still left in its neighbourhood or not. If yes, remove the molten pixel from the thick line. In the end, you would get a raster representation one pixel thick. You can easily convert it to the vector representation. This is a simplified version of the algorithm I had implemented for my paper on the melting snowman, with that check for neighbouring solid pixels now being thrown in.

Pursuing either would be too much work for the time being; I could either offload it to a student for his project, or work on it at a later date.

Thus ended my present thinking line on the micro-level water-resources engineering.

2. Quantum mechanics:

You knew that I was fooling you when I had noted in my post dated the first of April this year, that:

“in the course of attempting to build a computer simulation, I have now come to notice a certain set of factors which indicate that there is a scope to formulate a rigorous theorem to the effect that it will always be logically impossible to remove all the mysteries of quantum mechanics.”

Guess people know me too well—none fell for it.

Well, though I haven’t quite built a simulation, I have been toying with certain ideas about simulating quantum phenomena using what seems to be a new fluid dynamical model. (I think I had mentioned about using CFD to do QM, on my blog here a little while ago).

I pursued this idea, and found that it indeed should reproduce all the supposed weirdities of QM. But then I also found that this model looks a bit too contrived for my own liking. It’s just not simple enough. So, I have to think more about it, before allocating any specific or concrete research activities about it.

That is another dead-end, as far as blogging is concerned.

However, in the meanwhile, if you must have something interesting related to QM, check out David Hestenes’ work. Pretty good, if you ask me.

OK. Physicists, go away.

3. Homeopathy:

I had ideas about computational modelling for the homeopathic effect. By homeopathy, I mean: the hypothesis that water is capable of storing an “imprint” or “memory” of a foreign substance via structuring of its dipole molecules.

I have blogged about this topic before. I had ideas of doing some molecular dynamics kind of modelling. However, I now realize that given the current computational power, any MD modelling would be for far too short time periods. I am not sure how useful that would be, if some good scheme (say a variational scheme) for coarse-graining or coupling coarse-grained simulation with the fine-grained MD simulation isn’t available.

Anyway, I didn’t have much time available to look into these aspects. And so, there goes another line of research; I don’t have much to do blogging about it.

4. CFD:

This is one more line of research/work for me. Indeed, as far as my professional (academic research) activities go, this one is probably the most important line.

Here, too, there isn’t much left to blog about, even if I have been pursuing some definite work about it.

I would like to model some rheological flows as they occur in ceramics processing, starting with ceramic injection moulding. A friend of mine at IIT Bombay has been working in this area, and I should have easy access to the available experimental data. The phenomenon, of course, is much too complex; I doubt whether an institute with relatively modest means like an IIT could possibly conduct experimentation to all the required level of accuracy or sophistication. Accurate instrumentation means money. In India, money is always much more limited, as compared to, say, in the USA—the place where neither money nor dumbness is ever in short supply.

But the problem is very interesting to a computational engineer like me. Here goes a brief description, suitably simplified (but hopefully not too dumbed down (even if I do have American readers on this blog)).

Take a little bit of wax in a small pot, melt it, and mix some fine sand into it. The paste should have the consistency of a toothpaste (the limestone version, not the gel version). Just like you pinch on the toothpaste tube and pops out the paste—technically this is called an extrusion process—similarly, you have a cylinder and ram arrangement that holds this (molten wax+sand) paste and injects it into a mould cavity. The mould is metallic; aluminium alloys are often used in research because making a precision die in aluminium is less expensive. The hot molten wax+ceramic paste is pushed into the mould cavity under pressure, and fills it. Since the mould is cold, it takes out the heat from the paste, and so the paste solidifies. You then open the mould, take out the part, and sinter it. During sintering, the wax melts and evaporates, and then the sand (ceramic) gets bound together by various sintering mechanism. Materials engineers focus on the entire process from a processing viewpoint. As a computational engineer, my focus is only up to the point that the paste solidifies. So many interesting things happen up to that point that it already makes my plate too full. Here is an indication.

The paste is a rheological material. Its flow is non-Newtonian. (There sinks in his chair your friendly computational fluid dynamicist—his typical software cannot handle non-Newtonian fluids.) If you want to know, this wax+sand paste shows a shear-thinning behaviour (which is in contrast to the shear-thickening behaviour shown by, say, corn syrup).

Further, the flow of the paste involves moving boundaries, with pronounced surface effects, as well as coalescence or merging of boundaries when streams progressing on different arms of the cavity eventually come together during the filling process. (Imagine the simplest mould cavity in the shape of an O-ring. The paste is introduced from one side, say from the dash placed on the left hand side of the cavity, as shown here: “-O”. First, after entering the cavity, the paste has to diverge into the upper and lower arms, and as the cavity filling progresses, the two arms then come together on the rightmost parts of the “O” cavity.)

Modelling moving boundaries is a challenge. No textbook on CFD would even hint at how to handle it right, because all of them are based on rocket science (i.e. the aerodynamics research that NASA and others did from fifties onwards). It’s a curious fact that aeroplanes always fly in air. They never fly at the boundary of air and vacuum. So, an aeronautical engineer never has to worry about a moving fluid boundary problem. Naval engineers have a completely different approach; they have to model a fluid flow that is only near a surface—they can afford to ignore what happens to the fluid that lies any deeper than a few characteristic lengths of their ships. Handling both moving boundaries and interiors of fluids at the same time with sufficient accuracy, therefore, is a pretty good challenge. Ask any people doing CFD research in casting simulation.

But simulation of the flow of the molten iron in gravity sand-casting is, relatively, a less complex problem. Do dimensional analysis and verify that molten iron has the same fluid dynamical characteristics as that of the plain water. In other words, you can always look at how water flows inside a cavity, and the flow pattern would remain exactly the same also for molten iron, even if the metal is so heavy. Implication, surface tension effects are OK to handle for the flow of molten iron. Also, pressures are negligibly small in gravity casting.

But rheological paste being too thick, and it flowing under pressure, handling the surface tensions effect right should be even bigger a challenge. Especially at those points where multiple streams join together, under pressure.

Then, there is also heat transfer. You can’t get away doing only momentum equations; you have to couple in the energy equations too. And, the heat transfer obviously isn’t steady-state; it’s necessarily transient—the whole process of cavity filling and paste solidification gets over within a few seconds, sometimes within even a fraction of a second.

And then, there is this phase change from the liquid state to the solid state too. Yet another complication for the computational engineer.

Why should he address the problem in the first place?

If the die design isn’t right, the two arms of the fluid paste lose heat and become sluggish, even part solidify at the boundary, before joining together. The whole idea behind doing computational modelling is to help the die designer improve his design, by allowing him to try out many different die designs and their variations on a computer, before throwing money into making an actual die. Trying out die designs on computer takes time and money too, but the expense would be relatively much much smaller as compared to actually making a die and trying it. Precision machining is too expensive, and taking a manufacturing trial takes too much time—it blocks an entire engineering team and a production machine into just trials.

So, the idea is that the computational engineer could help by telling in advance whether, given a die design and process parameters, defects like cold-joins are likely to occur.

The trouble is, the computational modelling techniques happen to be at their weakest exactly at those spots where important defects like cold-joins are most likely. These are the places where all the armies of the devil come together: non-Newtonian fluid with temperature dependent properties, moving and coalescing boundaries, transient heat transfer, phase change, variable surface tension and wall friction, pressure and rapidity (transience would be too mild a word) of the overall process.

So, that’s what the problem to model itself looks like.

Obviously, ready made software aren’t yet sophisticated enough. The best available are those that do some ad-hoc tweaking to the existing software for the plastic injection moulding. But the material and process parameters differ, and it shows in the results. And, that way, validation of these tweaks still is an on-going activity in the research community.

Obviously, more research is needed! [I told you the reason: Economics!]

Given the granular nature of the material, and the rapidity of the process, some people thought that SPH (smoothed particle hydrodynamics) should be suitable. They have tried, but I don’t know the extent of the sophistication thus far.

Some people have also tried finite-differences based approaches, with some success. But FDM has its limitations—fluxes aren’t conserved, and in a complex process like this, it would be next to impossible to tell whether a predicted result is a feature of the physical process or an artefact of the numerical modelling.

FVM should do better because it conserves fluxes better. But the existing FVM software is too complex to try out the required material and process specific variations. Try introducing just one change to a material model in OpenFOAM, and simulating the entire filling process with it. Forget it. First, try just mould filling with coupled heat transfer. Forget it. First, try just mould filling with OpenFOAM. Forget it. First, try just debug-stepping through a steady-state simulation. Forget it. First, try just compiling it from the sources, successfully.

I did!

Hence, the natural thing to do is to first write some simple FVM code, initially only in 2D, and then go on adding the process-specific complications to it.

Now this is something about I have got going, but by its nature, it also is something about you can’t blog a lot. It will be at least a few months or so before even a preliminary version 0.1 code would become available, at which point some blogging could be done about it—and, hopefully, also some bragging.

Thus, in the meanwhile, that line of thought, too comes to an end, as far as blogging is concerned.

Thus, I don’t (and won’t) have much to blog about, even if I remain (and plan to remain) busy (to very busy).

So allow me to blog only sparsely in the coming weeks and months. Guess I could bring in the comments I made at other blogs once in a while to keep this blog somehow going, but that’s about it.

In short, nothing new. And so, it all is (and is going to be) crap.

More of it, later—much later, may be a few weeks later or so. I will blog, but much more infrequently, that’s the takeaway point.

* * * * *   * * * * *   * * * * *

(Marathi) “madhu maagashee maajhyaa sakhyaa pari…”
Lyrics: B. R. Tambe
Singer: Lata Mangeshkar
Music: Vasant Prabhu

[I just finished writing the first cut; an editing pass or two is still due.]

[E&OE]