Unruled Notebook

Entries from July 2006

What is the Shape of the Earth

July 28, 2006 · 2 Comments

In the Principia (1687), Newton gave this argument:

The Earth is spinning about its axis perpendicular to the Equator.

(Recall Newton proved Kepler’s Laws of planetary motion in his Principia. Newton didn’t exactly use words like Equator, axis etc., but essentially said this. Anyway, the text we read in current reprints of Principia is the English translation of what he wrote in Latin; so no more nit picking in these lines please).
Suppose two wells are dug, one from the Polar surface and the other from the Equatorial surface, respectively, to the center of the Earth (see Figure) and filled with water. EarthPearShape

The weight of the water in these wells must be equal, otherwise, the ‘excess’ water will ‘splash’ out of the Earth.

The weight of water in each of these wells is equal to the mass of water times the effective acceleration. The effective acceleration is the gravitational acceleration (recall, Newton explained how gravity works in the Principia) minus the acceleration due to ‘centrifugal force’ (whoops!) brought about by the spinning of the Earth. This effective acceleration, due to the action of the centrifugal force, is slightly less in the Equatorial direction than in the polar direction, where the action of the centrifugal force is absent.

Since the weight of the water in these wells must be equal, to offset the decrease in the effective acceleration, there should be more mass of (incompressible) water in the equatorial well. This is possible only if the equatorial well is ‘longer’ than the polar one. So, the Earth, due to its spinning about an axis perpendicular to the Equator, should be an oblate spheroid, with a bulge in the equatorial direction and a flattening near the Poles!

A mere ‘thought experiment’. A remarkable feat of reasoning.

There is an interesting follow-up story attached to this gem of scientific thinking. This is reported by Subrahmanyam Chandrashekar while discussing star shapes.

When Newton proposed this argument in his Principia, there was Giovanni Domenico Cassini in France, who thought the other way. Cassini, with his measurement of the meridian arc within France, thought that the Earth is elongated at the Poles and shortened at the Equator. Being the first director of the Paris observatory, the discoverer of, among other astronomical things, the 4,700 mile gap between the A and B rings of Saturn, called the Cassini division, Cassini was a big-shot in France. So the fight for who is right continued even after the death of both of these giants.

An expedition, under the captaincy of Pierre Louis Maupertius, was launched in 1738 to the Arctic region to measure the radius of the Earth. The result showed that the polar radius of the Earth (6,363,806.283 m) is shorter than the equatorial one (6,397,300 m).

Newton was right!

It seems, upon hearing this result, Voltaire chided the group that went to the Arctic on why they needed to go to the Arctic to know something that Newton knew without looking out of his window.

Such rare genius shaped (Science on) this Earth, otherwise burdened mostly by myopic mortals.

Categories: Science Notes
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The Ivory Tower – 4

July 26, 2006 · Leave a Comment

And so, The Ivory Tower got off to a flying start, with smirks and perks, just like our friendship.

So much so that the guy with whom I started this magazine occupied my life at one point, almost all of the best part of my waking days.

That comes to about three hours per day, everyday, for six years. That’s a lot of occupation that I could charge him a hefty bill as rent.

Every evening, from our college to his home, from his home to mine and from mine to his and me back to mine, we walked a few kilometers (fewer miles for ABCDs), discussing animatedly. To the point that the challenge of predicting and evading the crowd in the dreaded crowded labyrinthine Main Guard Gate streets and in between our houses was lost on us while walking. We trundled and talked, scuttled and spoke about (t)it.

He is a pious theist who believes God created me, an atheist. So he takes me to temples. And I liked going with him. I anyway reasoned since I was an atheist, I should all the more go to temples since I anyway didn’t believe the God that was supposed to be there. We never agreed upon the other but that’s why we stayed together. And visited temples, whenever we get the chance, which is daily.

He is good in debating, almost polemical. While I commit all of the mistakes that you get pinched for at a JAM event (stutter, stammer, lisp etc.), he had impeccable vocabulary and excellent fluency in English, a language I never learnt formally and correctly. To my surprise, after two years into our friendship, he even scripted and enacted a humorous skit in his college in English. For my part, I used to collect all sorts of trivia and was good in quiz, another youthful fantasy that one time was silently putting the skids on my career. Anyways, during those five six years, we were almost the uncrowned “local kings” in our respective avocations.

He had benign eyes that were bespectacled into enlightened focus. I could get for myself only the spectacle part, with a Lennon inspired granny glasses that I pinched from somewhere. But I looked and behaved too showy and sarcastic and never genuine with these paraphernalia. Maybe I actually am phony or things deserved it.

But our friendship continued to grow, perhaps only out of these incongruities.

He is impeccable in his dress style and things suited him to the hilt. He could wear an informal half-hand shirt like a formal full-hand shirt. An ordinary pair of leather sandals looked golden covering his legs. I used to clad myself in khaki uniform that is compulsory for workshop in the engineering campus. Everybody hated it and I had five of them. I wore a pair of dirty canvas shoes on with “boot lickers beware, I taste bad” scribbled in bold.

At any time of the day, or night, or the time when he just wakes up from bed, he had a combed hair that covered a head that contained more principles than friends. I hastily had my brain and hair covered with a cap that said “Entropy, Stop Increasing!”

I should say he tolerated me in these things because he basically is very decent and civil and courteous and gentle and clumsy and honest and gracious and naïve and…so I thought.

While he was cynical and celibate and principled and pure, I flirted with almost everybody who was not my gender or mother. At one time I had more girl friends than friends who were girls. Much to the chagrin of my mother.

He was a mother’s boy. Every mother liked him and his guffaw of a laugh. I could smile. And I am too silent for the comfort of those mothers.

He had a flute that he never played and everybody including those mothers respected him for that. I had a guitar with which I never learnt to play ‘Let It Be’ correctly. And ‘when I found myself in times of trouble,’ it is because Mother of Mary was coming to me as I had tried playing with Mary.

Categories: Narration

Free Convection For Dummies

July 22, 2006 · 23 Comments

A fluid layer heated from below and relatively cooled from the top (say, water kept in a vessel heated on a stove) is a simple free convection system, which experiences a local force imbalance in a gravitational field resulting in the convection of the fluid. This convection or displacement of some portion of the fluid (water, in our vessel) from one local position to another (inside the vessel) is the result of the buoyancy of the heated layer and the magnitude of it depends on the temperature difference prevailing between the top and bottom portion of the fluid layer (vessel).The earliest description of (free) convection was written in the 1790s by Benjamin Thompson, Count Rumford, a description he used to account for the transfer of heat in an apple pie. The most significant and systematic experimental work was done by the Frenchman Henri Benard in the early 1900s. The results of these experiments, i.e., why there are convection currents in a heated fluid layer, by a theory put forth by John William Strutt, Lord Rayleigh. Some physicists have had the insight of originating a new field of study thereby making the first word(s) about it. But Lord Rayleigh, according to Subrahmanyam Chandrashekar, had said the last words of many subjects and sealed them once and for all. In one of his last articles, published in 1916, he attempted to explain what is now known as Rayleigh-Benard Convection. Though his explanation was superceded in later years, his work remains as the starting point for most of the modern theories of convection.

In what follows, we shall discuss qualitatively, how and why there is convection motion in a fluid heated differentially. For doing this, a simplified fluid, as against a real one, is considered in the two dimensional model. A thin layer of the fluid is confined fully between two semi-infinite flat plates so that there is no gap (free surface) between the plates and the sandwiched fluid. By semi-infinite we mean plates of definite thickness vertically and long, infinite length horizontally and by a thin layer we mean that the horizontal dimension (length, in Figure 1) of the fluid layer is very large when compared to that of the vertical. These requirements ensure minimal interference of the side boundaries (walls etc.) in the convection.

We can now subject the thin layer of the fluid to a controlled experiment where the fluid is heated from the bottom in such a way that the temperature of the bottom portion of the fluid remains uniform (spatial invariance) and steady (temporal invariance). A similar cooling condition is imposed at the top portion so that the temperature gradient across the height is uniform. This means that the graph between Temperature and Time is a straight line as shown in Figure 1. In the language of calculus this means the change in temperature with respect to height or time is a non-zero constant.

Further, by simplified fluid we mean the fluid is assumed to be incompressible (why?) with its density being the only property that is changing with respect to the change in temperature (what other property could change w.r.t. to T?), while the fluid experiences uniform gravitational force on the entire volume (when can the fluid experience non-uniform gravitational influence?).

Now we shall construct a model in which a packet of the above fluid is considered with a random dimension. The displacement of this packet above or below from its present position is controlled by forces whose nature is yet to be seen but are nevertheless responsible for convection. The packet considered can be of any size and shape but the displacement must be small. The initial displacement of the packet need not be due to any imbalance in the forces we are studying but a random displacement from the mean position – which will eventually occur if we wait long enough – is sufficient. To further understand how convection would result in this simplified model, we need to be familiar with buoyancy, viscosity, surface tension and thermal diffusivity of fluids.

Let us begin with buoyancy and proceed to explain free convection motion and used the other concepts as and when required to refine our understanding.

We all have heard of buoyancy in our school stories and how it made Archimedes run naked shouting Eureka!, to explain his method involving buoyancy force differences to find the silver impurities in the royal crown of the King of Heron supposedly made of pure gold. This kind of buoyancy force in a fluid arising without heating is due to the pressure difference across the fluid packet, which when balanced by the weight force of the packet, ensures static equilibrium.

However when heated, the fluid packet considered in Figure 2 has lesser density at the bottom relative to the surrounding which makes it raise up, when the gravitational force is acting downwards. This is because of the increase in the buoyancy force which disrupts the static equilibrium. Suppose in the fluid packet in Figure 2, if water is filled and allowed to get immersed to a certain depth as shown, it will stay in the position inside the trough maintaining its static equilibrium. This is because the weight of the packet is balanced by the upward reaction force, by the water in the trough, called the buoyancy force.

The static pressure in the water trough increases as we go down because the weight of the water layer above each point also contributes to the net force experienced by that point. So this static pressure is greater on the bottom side of the packet than the upper. This balance in forces can get affected by the actual weight of the fluid in the packet and the pressure difference across the packet. For a heavier packet the weight force increases causing the packet to sink to a different height where the upward buoyancy force equals the weight force to make the packet float. So heavier, more massive, objects of identical volume hence with higher density, sink when compared to lighter objects.

Now consider the same fluid packet at the bottom of the trough in Figure 2 with the heat supplied to it from below, as shown. This packet considered has a higher temperature and so has lesser density (density, in general, decreases with increase in temperature for fluids) when compared to the average density of the entire layer. This means, the fluid packet of certain mass ‘dm’ expands as it is heated. A similar packet at the top side of the domain in Figure 2 will have relatively higher density due to its lesser temperature. Hence this packet, also of mass ‘dm’, is cooler and occupies lesser volume than the hotter one in the bottom. As long as the fluid packets remain in their respective position they are surrounded by fluid of identical average density and so maintain their static equilibrium with the surrounding. Suppose now due to some random fluctuation a very small displacement is given to the bottom fluid packet in the upward direction. This will result in an imbalance in the forces acting on the packet.

The fluid packet which is originally of lesser density than the surrounding average density due to its higher temperature now is pushed up into a region of higher density (and lower temperature). This creates a positive buoyancy as explained earlier, which causes the packet to raise. The raise will be sustained till the density of the fluid packet while raising equals that of the surrounding. At this point it will simply float as the static equilibrium is restored. The upward force is proportional to the density difference and volume of the packet. As the fluid packet raises through regions of relatively colder fluid whose average density progressively increases due to the lack of additional heat, it results in an increased density gradient between the packet and the surrounding, which accelerates the raise.

On similar analysis the downward push of a packet of colder fluid in Figure 2 makes it enter a region of lesser average density resulting in the `heaviness’ of the packet thus propelling it down. It would sink getting its initial disturbance enhanced. Both of these motions are simultaneous and continuous. The ‘hole’ left by the hotter fluid packet as it raises up is (and has to be) filled by fluid from somewhere else in the domain of Figure 2. In principle, this is done by the colder fluid packet that is propelled down from the top. Essentially, the differential heating results in the hotter and colder fluid packets exchanging places in the domain of Figure 2. Thus the whole of the fluid layer is eventually overturned resulting in a continuous circulation of the fluid between the hot and cold ends. This circulation should prevail as long as the temperature gradient could be maintained by the heating, thus maintaining the local buoyancy force imbalance.

A graphic representation of the convection flow in such a simplified experiment is shown in the animation below.

It would seem from the above explanation that (free) convection will be observed in a fluid region whenever there is a temperature gradient, however small it may be. But such sensitive dependence of the initiation of the flow on the temperature gradient is not observed in actual circumstances. There is a critical value of some variable, beyond which only convection flow results. Remember, we are yet to use the other concepts like viscosity and thermal diffusivity.

And this is where Lord Rayleigh showed his wit. And it merits another note.

Categories: Fluid Sciences · Lecture Notes · Science Notes · Thermal Sciences
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Ramesh Mahadevan is back as Mahadevan Ramesh

July 15, 2006 · 6 Comments

Lend me your ears Joacim Martillos, Virendra Vermins and “test message” Respondurangans:

Ramesh Mahadevan has reverse-migrated. As Mahadevan Ramesh.

Observe the names. How much more “reverse-migrated” can one get from the USA, to be actually back in Chennai? Back in the aftermath of my successful Nobel prize whining Ph. D. in a Dull Ass of a city, I was introduced to his writings in the internet by one of his Ohio-state colleagues, my then future boss. One of the reasons I joined that company was because of that introduction.

Since then, Ramesh, is my internet writing hero of humorous asides and serious besides. He is the inspiration that made me believe (deluded?) that I could as well write essays with no point whatsoever, but could escape the wrath of the readers with style and narration alone. So much is my self-belief that I continue to infest a blog, almost full of such writings. Some of my writings on Carnatic music in Tamil and English are inspired by his excellent four part introduction to indian music. Words from one of his essays

Take a lot of data in life, do a lot of analysis. But don’t write a final report any time soon. The day you do that, you know you are hopelessly old.

summed up many things in life for me. It taught me further on how to observe anybody or anything, and later analyze it in writing or discussion without having to be judge mental.

I believe his humorous stories are nevertheless only a front, sort of a social mask, that belies an active intellect and excellent individual with high thinking. I don’t need to cite his writings on Hindu Muslim riots and his reasons for moving back

…..The reasons for my reverse migration are part-selfish and a tiny bit altruistic – essentially to pursue what I consider my passions…..Most of my thinking is rooted in making India stronger in the face of stiff (and these days, unfettered, WTO brand) Globalization. This, I envision, will involve (1) educating the people about it and lobbying our lawmakers and influential people to better-present India’s case and concerns in world forums such as WTO; protest, if necessary against unfair world trade practices. (2) to combat cultural imperialistic implications so that we do not lose our essential Indian-ness. (3) to make sure our youths have the necessary skill-sets to be globally competitive; to make sure our economic engines, such as the BPO operations, run smoothly for a long time and the positive results trickle down to the poor and (4) to stop the Manufacturing jobs going out of India to other Asian countries such as China – by teaching and inculcating modern Manufacturing methods in India. How am I going to work on my ‘passion’? I have no clue. But I am making tentative attempts.

for reiterating my belief.

So, after having read about his return to chennai, as Abi would agree, in joy I did yell, then swell and then ruminating upon his writings, rested in a spell. The reason my outstretched hand hesitated and withdrew later from calling upon him in person, although he invites it by providing his number in his blog. For, I have never met him in person and my relationship with him is only through his writings, a bubble that I would cherish to keep in shape.

Ramesh promises to write more and as a premonitory, has even written for one last time perhaps, on the topic of coming back to India for the ABCDs – the Aminjakarai born, nevertheless confused desis.

Therein he has pondered on 10 points to consider while making the move. The 11th one that in his modesty he forgot to mention, could now be,

11) You could actually meet in person the legendary IIT-K alumnus, Ohio-State silverus, Carnegie goldus, Soc.Culture.Indian blasphemous, rest of us delirious, father of all internet desi humour, mother of all internet desi rumour, the man who has traveled all the 50 and odd states of the USA (including perhaps Iraq), the one and only Mahadevan Ramesh, a.k.a. circa pre-blog-era, Ramesh Mahadevan…

…in flesh and blood and in a dhoti.

Categories: Micro Muse
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Survey Sins of the Times

July 10, 2006 · 16 Comments

It is that time of the year again, where the anxious gullible is fed with enough printed material soaked in vague statistics based on “national poll” surveys that either conclude sometimes correctly with wrong reasons or conclude wrongly with correct reasons or is plain inconclusive and correctly so, because of the method of the survey.

One such survey has already been given the treatment by Prof. Madhukar Shukla of XLRI in his blog alternate perspective. What follows is not as hilarious as that one, but only a sober set of mundane doubts that I have.

I came to know of Science of the Times, the recent Outlook magazine survey for top 100 engineering colleges and top 25 medical colleges through a post in the nanopolitan, a blog by Dr. Abinandhan from IISc. By reading the cover story and the methodology of survey, one can form one’s opinion without having to read this post any further for my opinion.

From the methodology one could learn that

Cfore conducted the study in two phases. In the first, a pilot survey was conducted among students, faculty members and industry representatives to finalize the main parameters. Based on this, it identified five factors�intellectual capital, infrastructure and facilities, pedagogic systems and processes, industry interface and placements.

What is “intellectual capital” in the above survey method? How is it objectively defined and quantified for this survey to rank a particular institute?

If it is the “knowledge content” of the faculty of that institute, which could be measured by how many of them hold Ph. D. degrees, then as faculties of most of these engineering institutes would agree, a Ph. D. is not necessary for teaching the UG courses. I myself have been a faculty in one such engineering institute for three years, before my Ph. D. degree, but with reasonable success – I know this because my increments were based then on my teacher evaluation. So, how are institutions that actually have good UG faculty without Ph. D.s treated in this survey?

Next, let us say the “infrastructure and facilities” are measured by some standardized scale. One institute can prescribe a good syllabus for the UG program and may lack the infrastructure (lab equipment and machines, computers, classrooms with proper teaching aids etc.) to successfully impart the syllabus to the students. So it may not get a high rank in this category. Fair enough. But there are institutions that deliberately reduce the syllabus. For instance, a specific experiment may be supplemented with another simpler one or altogether cancelled to suit the (non)available infrastructure and (lack of) facilities. But on paper, this would mean that the infrastructure of that institute is “adequate” to teach the “prescribed” syllabus. How is this factored into this survey?

If “pedagogic systems and processes” include syllabus content and how it is taught (hopefully), how are these things quantified objectively?

The success of an institution lies solely with its output, in this case, UG degree holders educated in engineering. If the UG graduates are “successful” then the institute is successful. The only glitch is how to define success for the UG graduates. One measure is to find out whether they get a job after they graduate (or even before they do). In this context, I think the “placements” section is the only place where the actual worth of an institute is being measured. But this depends on various factors including past performance of an institute, the relevance of a particular UG program for that year’s job market, the job market itself for that year, etc. How are these factored into the survey?

Proceeding with the methodology of the survey we further learn that

In the second phase, a semi-structured questionnaire was designed and given to senior faculty members in various institutes who had more than ten years of teaching experience in different states.

Firstly, what is special about this “senior faculty” population? Has any statistics been done on how many of those “senior faculty” consulted, actually have taught UG program courses for “more than 10 years”? On the other hand, why not the opinions of “junior” faculty, who actually teach most of the UG programs in most of these institutes need not be considered?

Secondly, what about institutions with no “senior faculty” as defined by this survey, but are still producing UG graduates with reasonable “success” (they get jobs)?

Thirdly, what is “semi-structured questionnaire”? Does this mean the other remaining “semi” is “unstructured”? Why not simply make it known to the public, what the questions asked in this questionnaire are? If it is too detailed, it can be put in the internet.

Further, the methodology suggests

The respondents were asked to give weightages to different parameters and evaluate the institutes that they were aware of on a ten-point scale. The rating that the respondents gave to their own institutes was not considered.

“The respondents were asked to…..evaluate the institutes that they were aware of…” (bold-font mine)

Wait a minute: Does this mean if some institutes are not heard of or eluded the memory of the “senior faculties” at the time of the survey, they didn’t make it into the survey board at all? This is, a wee bit (only a wee bit, I assure you), confusing for me.

If I am the “senior faculty”, and since the rating that I give for my institute is not considered anyway, I could as well consciously put down any “rival institute” I chose to, by not having them in my top 10 at least. Before jumping at me that I am claiming all “senior faculty” are liars, just answer my implied question about the survey of how it avoids “human fudge factors” in an objective analysis.

Proceeding with this argument, if I were not from the IITs, I might just choose the IITs as top institutes rather than the non-IITs, since, I can safely assume that everyone else in my situation will do the same. It is no surprise then, that the IITs top the list.

The hierarchy amongst them (IITs) in the top list could as well be explained by the random perturbation in the opinions of the consulted senior faculties among the IITs itself, as the “senior faculty” from most of the rest of the institutes are going to anyway point IITs as the best in India (and so essentially doesn’t contribute to the survey to determine the top 10 at least). This argument could be proved if the survey is taken again exactly with the same population. Chances are high that there could be a redistribution in the first five, but all of them will again be IITs.

Finally, the methodology states

In all, 208 faculty members participated in the survey. The sum total of average rating score that each institute got against different parameters was used to rank the institutes. Only the engineering colleges that offered under-graduate programmes and that were evaluated by at least 10 senior faculty members got into the final list.

The cover story itself points out “there are 1,346 engineering colleges approved by the All India Council for Technical Education”. If one were to consider only 10 “senior faculty” in each of these institutes, their total population is 13460, out of which 208 is about 1.5 percentage (if it is only 1 “senior faculty” per engineering college then 208 is about 15.5 percentage and my question still is valid). What scientific statistical method is employed to pick 208 as the representative “statistically significant” group to conduct this survey?

If a magazine in a few pages cannot do a survey with all of these details in place, then why should one believe the results of the survey alone?

On the other hand, perhaps all of these questions are taken care of by the Cfore group, which conducted the survey. May be they or Outlook magazine can release the appropriate data and details in the internet so that credibility is given to their commendable efforts to provide the public with useful information and silence nit pickers and nosy parkers with some semblance of common sense.

As I am in a profession where as an academic exercise my very existence is sometimes suspected, I am unable to watch the nebulous clouds of reason serenade past my youthful and immature hot-head. Hence, I made the above post with questions about the method of survey (and only that). If most of them have been or will be answered by Cfore or Outlook, no, need not be to my satisfaction, but to the satisfaction of any objective standard, I can start rejoicing.

After all, the survey reports my department to be the top in India (and I believe in that, with or without this survey).

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Categories: Academics
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