Formulation of discrete models for propagation problems

It is quite possible to formulate a discrete model in an apparently natural way which, upon computation, produces only garbage. This is especially true in propagation problems–that is, problems described by parabolic and hyperbolic equations. An excellent historical example is provided by Richardson’s pioneering paper¹, in which his suggested method for the conduction equation, describing the cooling of rod, was found to be completely unstable by O’Brien, Hyman and Kaplan². Another example concerns the transverse vibration of a beam. in 1936 Collatz³ proposed a ‘natural’ finite difference procedure for the beam equation , but fifteen years later⁴ the algorithm was found to be computationally unstable.

[1] Richardson L F, Trans. R. Soc., A210, 307, 1910.
[2] O’Brien G G, Hyman M A, and Kaplan S, J. Math. Phys., 29, 223, 1951.
[3] Collatz L, Z. angew. Math. Mech., 16, 239, 1936.
[4] Collatz L, Z. angew. Math. Mech., 31, 392, 1951.

– Numerical methods for partial differential equations, William F Ames (1969)

What it means to be a professor

On the eve of the passing away of Daya Krishna, a professor of philosophy at Rajasthan University, Pratap Bhanu Mehta reflects on what it means to be a professor (which, inevitably leads him to the decline of Indian University system):

Dayaji’s passing away is of more than local significance. The academic world he represented is one that is irrevocably lost, though arguably we need it even more. He conducted his professional life on an ideal we can scarcely imagine: the idea of a professoriate. This was founded on two assumptions. The first was that the primary purpose of a university is to cultivate the intellect and the life of the mind. If a university is made instrumental and subordinate to other purposes — social engineering, political goals or cultural pride — it loses its essential character.

This idea that universities can achieve the most when they are thought of as a non-instrumental space, challenging our consciousness to surpass itself, is almost completely extinct in modern India. Now our universities exist ostensibly for every purpose other than the cultivation of the intellect. This reflects a huge loss in our cultural sensibilities. One of the reasons why it is impossible to reinject romance into the idea of a university, and why university reform is so difficult, is that we cannot even conceive of what it is like to dedicate institutions for the cultivation of intellect in the true sense of that impoverished word.

The second assumption was that being a professor was a vocation in the true sense of the term, with its own inherent dignity, norms and autonomy. But this is both an institutional idea and an existential one. Institutionally it meant that the professoriate is a vocation that in the conduct of its professional obligations is answerable primarily to itself. It may aim to reach popular audiences, but it does not take its standards from them; it may speak to holders of power, but it does not let power define its agenda; it may aim at useful knowledge, but utility does not exhaust the value or significance of knowledge. Although we often talk about university autonomy, this discussion is limited to securing the autonomy of vice-chancellors from government. What we have lost is a sense of a self-governing and self-regulating professoriate that despite all its fractiousness is united by a commitment to cultivating the intellect, nothing less and nothing more.

Existentially, Dayaji could convince you that there are few things in life more pleasurable, and more important than a good seminar. Indeed, for him it was almost a democratic form of sociability: where each argument had its individuality, yet there was communication. There was difference but also the possibility of transformation; disagreement, but not sullied by strategic or personal considerations.

The decline in Rajasthan University, whose intellectual life Dayaji almost single-handedly kept alive for years, is also a measure of how a whole academic world has disappeared. For those who encountered Rajasthan University campus, he provided a glimpse of what being a professor meant: that odd combination of detached irony and passionate questioning that only a Socratic intellect can muster.

But creating a new and exciting academic milieu is not just about institutional reform; it is about recapturing a space for non-instrumental views of knowledge, about valuing an adventure of the mind without quite second-guessing what it will come up with. Dayaji would have been the first to acknowledge that the next generation will often be cleverer than last, but whether it can recreate a vibrant university life is still open to question. The best compliment to Dayaji is that he was a professor, in the truest sense of that impoverished word. With his passing, the last remnants of a professoriate in India are coming to an end.

Link via Arun Thiruvengadam at Law and other things. Take a look!

PS: Here is a book cover with a photograph of Prof. Krishna, I presume.

Electron microscopy of materials

Today I heard a wonderful lecture by Dr. Ulrich Dahmen, Director, National Center for Electron Microscopy on Electron microscopy as an observatory of the nanoworld.

Though the title carried the word “nano”, Dahmen did not confine himself to the nano-world alone; towards very early in his talk for example, he showed a video made by some summer students. The video began with a shot of the glowing green traffic light at the Cedar and Oxford intersection of the University of California, at Berkeley. Then the camera started zooming in by factors of ten to show the LEDs, their internal structure, the optical micrographs, scanning electron micrographs, and, finally transmission electron micrographs to show the atomic arrangement at the Angstrom scale. At the end, it zoomed back to the traffic light to indicate the structures at various levels (and how they build up to some everyday object like the traffic light).

Similarly, at the early stages of his lecture, Dahmen indicated how, in the entire twenty years of its service, the total volume that had been observed at the microscopy centre is one cubic centimetre. To put this number in perspective, Dahmen indicated that in some Aluminium alloys the total number of precipitates in one cubic centimetre is the same as the number of stars in a galaxy (of the order of 10¹⁵ , if I remember correct), and the electron microscope is capable of looking at each of these precipitates in greater detail.

Most of Dahmen’s talk revolved around some very interesting microscopic studies on Aluminium-Lead alloys. That embedded lead particles, if small enough in size, can get superheated to even 100 degrees is well known. I have also blogged in the past about vacancy mediated strain accommodation in these systems. However, I did not know about the Brownian motion of liquid lead inclusions (via step nucleation, I understand). The videos of these small lead particles executing random motion was very cool; you can find more information on these studies at this page. I also learnt about some magic shapes effects that occur in these systems due to elastic stress effects; here is the paper in PRL which gives the details of a theory that explains these magic shapes:

Pb Nanoprecipitates in Al: Magic-Shape Effects due to Elastic Strain

J. C. Hamilton, F. Léonard, E. Johnson, and U. Dahmen

Abstract:
We present a theory for size-dependent shapes of Pb nanoprecipitates in Al, introducing the concept of “magic shapes,” i.e., shapes having near-zero homogeneous elastic strains. Our quantitative atomistic calculations of edge energies show their effect on precipitate shape to be negligible, thus it appears that shapes must be due to the combined effect of strain and interface energies. By employing an algorithm for generating magic shapes, we replicate the experimental observations by selecting magic-shape precipitates with interfacial energies less than a cutoff value.

Dahmen also showed how the precipitates shapes of a single grain when it nucleates at the grain boundary have very different characters in the two grains owing to the differences in orientation, and how these differences in the precipitate-matrix interface leads to premelting of incoherent interfaces in these systems. This paper in Philosophical Magazine has some more details on such studies:

Observations of interface premelting at grain-boundary precipitates of Pb in Al

U. Dahmen; S. Hagège; F. Faudot; T. Radetic; E. Johnson

Abstract:
This work reports direct observations showing the effect of size and interface structure on premelting behaviour of nanoscale inclusions. Using in-situ transmission electron microscopy it was possible to observe premelting of individual Pb inclusions in Al, each bounded by two distinctly different topotaxial interfaces. Such particles were generated by precipitating single-crystal Pb inclusions a few tens of nanometres in size at grain boundaries in Al. At equilibrium these particles adopt compound shapes, made from two segments whose shape and interface structure is characteristic of their misorientation with the matrix crystal. Only one of these interfaces premelts. In close agreement with a simple model, the width of the liquid layer depends reversibly on undercooling and interface curvature, and hence on particle size. The observed behaviour confirms previous reports on interface-dependent melting. By observing the selective melting of different interfaces for the first time on individual particles, it was possible to rule out experimental uncertainties and to show unambiguously that inclusion melting depends strongly on interface structure.

Finally, Dahmen went on to describe the next generation transmission electron microscopes, known as TEAM — Transmission Electron Aberration-corrected Microscope, which are free of spherical and chromatic aberrations, and hence can achieve half-an-Angstrom resolution, which, Dahmen indicated, is, in a way, an answer to a challenge posed by Feynman nearly fifty years ago:

The electron microscope is not quite good enough, with the greatest care and effort, it can only resolve about 10 angstroms. I would like to try and impress upon you while I am talking about all of these things on a small scale, the importance of improving the electron microscope by a hundred times. It is not impossible; it is not against the laws of diffraction of the electron. The wave length of the electron in such a microscope is only 1/20 of an angstrom. So it should be possible to see the individual atoms. What good would it be to see individual atoms distinctly?

We have friends in other fields—in biology, for instance. We physicists often look at them and say, “You know the reason you fellows are making so little progress?” (Actually I don’t know any field where they are making more rapid progress than they are in biology today.) “You should use more mathematics, like we do.” They could answer us—but they’re polite, so I’ll answer for them: “What you should do in order for us to make more rapid progress is to make the electron microscope 100 times better.”

On the whole, it was a great talk — I enjoyed every minute, every micrograph and every movie of it. It is a pity that we do not record them and post them to YouTube!

Another critique of Sacks’ Musicophilia

Gerard McBurney in the NewStatesman (via A&L Daily) (The first few paragraphs of the online version seems to be a bit mangled):

… did prompt me to wonder why I find Sacks’s stories, however curious, disturbingly unsatisfactory. Perhaps it is that reading such loosely linked sequences of peculiar tales feels like going to a peep show or wandering in a zoo, an effect compounded by Sacks’s sweetly confidential prose style. It is hard to see what he wants us to take away from the whole rather than the parts. No doubt this is precisely why so many people find his books mesmerising.

A bigger problem is what he says about music. There are muddled references to particular pieces and technical matters, and an amateurish account of how Tchaikovsky composed as opposed to how Beethoven did, which do not inspire confidence. An intriguing mention of Ravel’s disastrous mental decline at the end of his life is undermined by a dinner party-like attempt to connect this to the repetitiveness of the composer’s Bolero that ignores both what the piece is and what the composer most interestingly said about it.

…

… Sacks, [...] makes reference to many kinds of music and rejoices in the high culture of his own musical upbringing. And yet there is little here to suggest recognition of different levels of complexity and different kinds of meaning. Music seems to have been reduced to a single flat plane of significance.

On the whole, however, the review is a bit positive about Sacks’ book; in any case, I have my copy from the library, and will start reading it soon; then, I will be able to make up my mind about the book by myself.

First rule of reviewing

Daniel Green tells us Updike’s first rule of reviewing:

Try to understand what the author wished to do, and do not blame him for not achieving what he did not attempt

and, amends it to read

Try to perceive what the author’s book has accomplished. Do not misperceive it as an artifact of the author’s “intent.” Judge it according to standards appropriate to the sort of thing it is, not to the sort of thing you’d like it to be.

Though meant for literary reviewing, I think it would be a good first rule for scientific reviewing too: I have seen more than one scientific paper or talk critiqued by saying “The author should have done this or that” instead of poking holes in what has already been done (since such involved criticism requires a better understanding and a sharper intellect than what it takes to say  “You should do that”). What is more, we do not even need Green’s amendment for scientific reviewing, since, we just need to know what the authors’ intentions are, if those intentions had been achieved by what they did, and, if not, what else needs to be done.

Hari Kunzru on art and freedom of expression

Art isn’t about promoting social cohesion, or cementing community relations. It’s about telling the truth as you see it, even if it annoys or offends some people. That’s called freedom of expression, and last time I checked we all thought it was quite a good idea.

Hari Kunzru in a letter to the Guardian; via (who else?) Jenny.

Case of the curious alloy

Mathew Peet writes about a curious paper he has found:

Looking through some literature recently I was surprised to find a paper on microalloying which had used both niobium and columbium, in different amounts. The paper has 5 authors and is published in Scripta Materialia Influence of short austenitising times on the fracture behaviour or a microalloyed automotive spring steel by Wise, Spice, Davidson, Heitmann and Krauss. Scripta Materialia, 44, 2001, 299-304.

As Peet notes, Niobium and Columbium are the same elements; however, Wikipedia tells that Columbium was also the suggested name for Americium; but, it cannot be that Americium is what has been added to the steel since it is radioactive. A search for the authors in Scripta does not return any errata, either. The alloy used in the study is a commercial spring steel called DuraSteel^TM, it seems. Here is another case, where, I would have loved to see the referee reports!

Which is the best primer on economics?

Economic principals has a recommendation:

The primer I have enjoyed most, the one I would recommend to a friend who wanted to learn how economists think about the world right now, is one that passed almost completely unnoticed into the stream, perhaps because it is so slight. But then, that is the point of Economics: A Very Short Introduction, by Partha Dasgupta, the Frank Ramsey Professor of Economics at Cambridge University. He boils down everything that’s ordinarily included in a thousand-page introductory text, and more, to 160 graceful but undersized pages.

Along the way, there is also a discussion of the other, more popular introductory economics books (and, their shortcomings), reasons as to why Partha Dasgupta is ideally suited for writing such an introduction, and how Dasgupta’s primer is the ideal one:

It’s good that people are reading economics primers, good too that a genre now exists apart from those lugubrious (but necessary) texts. Yet economics is so obviously incomplete, even in its own terms, as a way of understanding the world, that the less cocksure are its expositors in their pronouncements, the better. I wish more people would read Dasgupta’s book, and I wish that more economists would write variations on its theme. It is a model specimen.

Sounds interesting; take a look!

PS: The Very Short Introduction series is available in India too (and, if I remember correctly, is not very costly either). So, here is a volume which might be worth buying.

Update: Thanks to Swarup, here are a couple of samples from Dasgupta’s writing: Mathematics and economic reasoning (pdf) and Modern economics and its critics, 1 (pdf). Happy reading!

Digital collections on the web

Anthony Grafton in an online only piece at the New Yorker:

In this issue, Anthony Grafton writes about the libraries of the past, and what they tell us about the books of the future. Here Grafton points to some favorite archives and historical resources.

Might be a good place to start browsing online resources.

Walter Moers’ The city of dreaming books

I recently finished reading The city of dreaming books by Walter Moers. I understand that this is the third book (or fourth?) in the Zamonia series; however, this is my first in the series.

It is an interesting book, especially if you like reading books about books, as this reviewer at The Entropy Pump notes:

I love books, and a book like this pushes all the right buttons for me. Even if it hadn’t any plot, I probably would have still liked it. Just the descriptions of Buchhaim with its small and old streets full of second hand bookshops, with all its denizen whose only love is the written word, made me feel like discovering reading and books for the first time again. TCoDB is a written love letter for books, wrapped into an exhilarating adventure that never loses sight of entertaining the reader, yet always managing to be a little more than just an adventure.

One of the charms of the book is that it can be read at several levels as this review at Hasta la vista, Vista notes:

You can take The City of Dreaming Books in many ways; a fantasy for the not so young, a witty parody on the literary world and the sorts of people who inhabit it, a playful treatise on literary tricks and devices, an exercise in getting your readers to identify with an innocent but plucky dinosaur with authorial pretensions or just a deeply charming and enjoyable book to fall in love with. Moers is cartoonist as well as writer, and his distinctive illustrations help bring the quirky denizens of Bookholm to life.

Here is another recommendation from Eye on everything (though, unlike the reviewer, I did like the ending, and would not have minded if it was a bit shorter, to tell the truth; however, I do agree that I would have liked Yarnspinner a bit more pro-active, and a bit less annoying — but, probably, you can not expect any better than that from a dynosaur):

Like I’ve mentioned before over and over again, if you love books, and if you love reading, then I’m sure you’re gonna love this book. It’s a book that almost every avid reader will be able to relate to.

It’s funny, wildly imaginative, the characters are endearing (just love those Booklings), and almost anything and everything you can associate with books or reading is referenced or parodied here.

I noticed TCoDB at Barnes and Noble, and the book cover and title looked interesting (though, I could not understand how it ended up on the bargain priced book aisle). So, next time when I went to the library, and saw the book in the recent books section, I picked it up; and, I was not disappointed. So, you might want to give it a try too, if you like such fantasies. Have fun!