Nondimensional Nightmares

Non dimensionalization has been the heart of Fluid Mechanics / Heat Transfer for more than a century. Elegant generalizations have been made by Fluid Mechanists, ranging from Osborne Reynolds, Prandtl, Nusselt to Stefan. Non dimensionalization has been man's most elegant attempt at trying to grasp one of Nature's most confunding yet awe inspiring phenomena: the behaviour of fluids.

Non dimesnionalization is a trademark of any Fluid Mechanics text book: rather than talk of velocity, diameter and viscosity seperately, their cumulative effect is described by a simple parameter. The Reynolds Number. Similarly, the Nusselt and the Biot Numbers. These numbers have been tested by experiment and by theory. They play an incredible role in today's experimental work: humongous dams can be simulated in the laboratory for dynamic similitude; aircraft wings can be brought to minute airfoil dimensions, again with dynamic similitude.

But, of course, Non Dimensionalization comes with a price. No doubt, you do generalize if you non-dimensionalize properly. But everybody isn't Einstien. There are those who - think of an effect - say radiation in a pipe. They realize that Radiation would play a significant role in improving the heat transfer within a pipe at high temperatures. Say 3000K. Now, if you show me a pipe that can carry water at 3000K - then I will show you the abominable snowman playing chess.

Of course, our man (the 3000K guy) decides to do some "numerical" modeling. He writes a finite difference code, solves the problem, optimizes it (perhaps optimizes the flow rate of water?). He is also aware that "3000K" will get him rejected from any peer reviewed Journal. So, he does what Reynolds did: Non - dimensionalizes. He divides it by the speed of sound multipled by something else, divided by the surface area of the duct .... you get the drift. The utter irrelevance hides behind the cloak of "non-dimensionalization".

And viola: he has a Non Dimensional Number! He calls it G or something - the "Radiation Parameter" - and assigns it a deceptively low value of 0.002. He never mentions the 3000K in the paper. He mentions the 0.002 instead. No peer rejects this: all the reviewers think this is marvelous new work. This gets accepted and published.

And years later, some unsuspecting PhD student like me spends a lot of money in printing out this verbosity, reads the utter bilge, gets fiercely upset and blogs his discontent. The frustrated PhD student also vows to mention typical values of various dimensional parameters if non-dimensional results are ever presented in his publications.

He should have gone to India

Michael Jackson would have been safer in India than in Bahrain. Bahrain is an Islamic country, and might sentence him to death if the accusations that he molested children are essentially proved to be true.

Had he gone to India, then the decrepit judicial system of the country would have:

1. Set the date of judgement in 2050 or something, by which time he would be dead

2. Acqutted him (beacuse of insufficient evidence, when in reality he would have bribed some politician to bribe some judge to get his acquittal).

3. He would have been imprisoned for a while before being let out on bail ... but since nothing would ever have the chance of being proven against him, his dignity (whatever is left of it) would have been salvaged.

The Indian judicial system is nice on paper - but there is no way of really testing it out. Getting justice in one's lifetime has become impossible in this country. A method for the speedy disposal of improtant cases is the need of the hour. For development is impossible without a robust justice system.

You can kill in India and not expect to be tried for a long time. You can be arrested for no reason at all and not be presented in a court for almost forever. The only way out is to befriend the politicians and see if they can "pressure" the judges to let you out easily.

On the Hilarity of Curvaceous Caricatures: A Spectral Approach

ABSTRACT
It has been noted that certain cartoon series such as Tom and Jerry (Quimby Era) [1], Mickey Mouse [2] ,Bugs Bunny [3] and Count Duckula [4] are more likely to produce chuckles from the average non-philistine spectator than Tom and Jerry (Jones Era) [5] - and anything else on either Nickelodeon or Cartoon Network today. In this work, a frequency domain methodology to arrive at a correlation between the funniness (the probability to produce a chuckle) and the spectral densities at higher frequencies has been described. Quantitative results have been withheld, since this information is very sensitive and might lead to the development of funny cartoons by countries within the axis of evil. It is undesirable to have happy enimies, for happiness results in a lifted morale.

INTRODUCTION

The spectrum has been around ever since that day when Fourier dreamed up his series and transform. The fourier transform is widely used in a discretized from in software such as Winamp to show the frequency content of an unstationary music (mp3) signal and also in critical space applications. (I'm sure it is used somewhere in space, right). Two dimensional fourier transforms are used by Net Nanny (possibly) to block po rnographic images - and they have also been used in the JPEG format of pictures, making possible the entire internet.

The spectrum has been exploited in movies such as G hostbusters and Ghost and numerous Indian movies too, which employ scenes of the supernatural. Turbulent flows show a cascading behavior in the spectral domain, something that seemed to be lost behind the noise in the time domain.

Cartoons have been around for a long time, and are universally accepted as examples of man on the pinnacle of his naughty creativity; right from the first Tom and Jerrys to the lump of mucus that graces the screen in those Mucinex commericals. Characters such as Dr. Von Goosewing and Daffy Duck send the average human into peals of laughter. Yet modern cartoons (the entire gamut of shows that cartoon network has to offer now, for one!) are unlikely to make anyone with an IQ exceeding that of a crushed pea laugh. South Park is more likely to make people Vomit than laugh, though the Simpsons has its funny times every now and then.

Common sense would tell us that it is just creativity that is lacking. But we beg to differ. Be believe that there are sinister forces afoot here. We postulate that the curvature of the edges of the cartoon is indicative of the funniness - the straighest edge resulting in a drag. We use a frequency domain method to estimate the harmonic content within an edge: the lower the harmonic content, the funnier the cartoon. We expect a straight line between funniness and power at higher frequencies.

RESULTS

Censored. Only harmless pictures allowed.

Goosewing, Dr Von: Deliriously Mindbogglingly funny. Observe curves.

Cat, Tom: Chuck Jones Era. Observe sharper nose. Distinctly unfunny.

Federal Law forbids further discussion.


Conclusion

Cartoons with sharper edges tend to be way more boring than rounder cartoons.

Refrences

1 .... 10 : Google.com: googling referenced term suffices.


Warning

It is strongly recommended that this study be taken with a pinch of salt and be quoted exclusively to quoters' risk. Author shall not be liable for any hurt egos.

Kicked out by the great firewall?

I think I might have solved the riddle that has been plaguing me for a very long time. Why do very few people read my blog? And why do fewer people comment on it?

I think the answer lies in my using the terms "Tinamen Square" in a few of my posts earlier. This would, in all probability, have resulted in my blog being kicked out by the Great Firewall of China, therefore, reducing my "market" by roughly 45 millon users.

No wonder, there's been scarce activity on the comments section of my blog of late. However, I, the optimist that I am, would like to look at the silver lining. The fact that my blog is probably blocked in China essentially means that it has been read by a few of the 30,000 odd Chinese censors. It is a gratifying feeling, since they would have had to delve real deep into this blog to catch the sensitive parts! So, I do know that a few people have read a lot of the 89 posts that precede this.

But then again, the pessimistic side contends that this could have been done by a computer. And alas, that is more realistic.

A Farmer's Plight

When I was younger, many years ago
Could seldom finish my food, I would throw.
straight Into the dustbin
When Mum wasn't looking.

When Mum would find out,
she would be displeased and shout
"You're so lucky, you have food,
other Indian children have to chew on wood!"

Such a poignant picture she would paint,
That I would feed guilty and faint.
I felt responsible for the poor being poor,
I decided to shun this wastage forever.

Kissan was a farmer I never did know.
And he now is no more.
He had taken his own life,
He had slit his neck with a knife.

It had rained well that year,
And when rain was not needed, the sky was clear.
There was not an insect, no pest
Kissan had a wonderful harvest.

He thought he was going to be rich,
but life can be such a bitch.
Everyone grew lots of food -
He would have earned more in a flood!

No one wasted food, you see-
We were careful, you and me.
We did not buy more from the farm,
The lack of demand caused the farm alarm.

And when everyone was careful with food,
Purchase no one would.
Kissan could not repay is debt,
He decided to face the bullet.

How can such a noble deed,
make an innocent man to death bleed?

Shooting and Killing

Once upon a time one small boy
Stepped on the foot of a big fat man
The man then fell on his knee
And suffered momentary agony.

Angered by the gall of the boy,
The man swore he would destroy
The boy and his family,
And he did so mercilessly.

He took a gun and shot them all,
In cold blood he saw them fall.
The fat man wanted the world to know
Don't mess with me, or your blood will flow.

The fat man then made many a gun,
He would give to some, and others he would shun.
And when other people tried to make them on their own,
The fat man would talk foul and frown.

And often, he would talk of dangers of the gun,
Scare the living daylights of everyone.
Others should not have the gun, he would say,
They might accidentally blow people away.

Foolproof Cryptography based on Navier-Stokes?

Here's the outline of an encryption algorithm that has no hope of being cracked.

Suppose you got a tank of water and some dye. When the water's all steady and stagnant, introduce your message in the water - scribble it in english using GRE words using a dye in the water. And then, shake the tank. Remember how you shake the tank, of course. Shake it like crazy. Make it turbulent. Let the dye mix up.

And at a precise instant, note the concentration of the dye at every point in space, the pressure at every point in space, the velocity at every point in space - and send that information as your "encoded" message.

In the "cipher", describe the geometry too ... essentially, describle all the final conditions and the problem. Cracking the code would essentially mean solving (DNSing) the time - reversed N/S ( the same as the original equation, with a negative viscosity instead!That makes it unphysical, for this spontaneously destroys entropy in an adiabatic system).

Basically the only people who will be able to "decipher" this information will be people who have access to an excellent DNS code and a Deep Thought (of the H2G2 fame) calibre computer. Such encryption shall lead to a DNS race between governments of the world - in the spirit of the current Nuclear Arms race. Larger chunks of national budgets will be awarded to DNS.

In the unlikely evemt that these efforts should culminate in a "crack", fret not. Use GRE words in the original message; it shall stay un-understood, though deciphered!

Inequities 2: Karim and Yusuf

In the town of Mumbai lived Karim
Abject poverty he lived in.
He drove a taxi for a life,
With the cab he fed his son and wife.

He struggled fifteen hours a day,
- for he needed every inch of this pay.
School isn't cheap, you know
English medium especially so.

They lived in a slum in town,
In a place rented, not their own.
It had a leaky roof,
And a landlord who was aloof.

Of Karim Yusuf had been a friend,
But their friendship came to a premature end,
WhenYusuf flew to a place far away,
namely the US of A.

Yusuf worked as a cabbie in New York,
Only 9 to 5 he needed to work!
He would get enough to eat and drink,
and a nice deposit in the bank.

He managed to buy an American House,
Just with his 9 to 5 income.
He married and American girl,
His was an American world.

And in pride, Yusuf would oft exclaim
" Why is America so rich?It's quite plain
It's just toil and hard work,
Karim is poor because he's a lazy Indian jerk!"

Free Speech and all that crap

(This is regarding the insensitive cartoons of Prophet Mohammed)

I believe there's nothing more dangerous than a blind believer in "principles". European media, especially the ones who have published those pictures after the original outrage - you're a bunch of bull-headed morons.

It sounds very nice when you say you "believe" in free speech. You are sure you are right about this, and believe that everyone should "respect" this right. So, you go and insult something that others hold very close to their heart. Free speech, after all.

If you're allowed to hold blind convictions, hold that "free speech" is the most important thing in the world, then you would be a hypocrite to condemn any reaction that follows.

This naive arrogance on the part of the European Media has caused hurt and aggravated the Islamic world. If the Europeans cannot respect the sentiments of the people in the Islamic world, the Islamic world will not respect the sentiments of the Europeans. Anarchy will prevail; and that is something the world can do without.

Principles and religion have been the downfall of man. Pragmatism and tolerance should replace principle. Since there are immensely many ways to look at a fact, having confidence in one's assessment of the same shows a kind of arrogance that proves almost fatal when negotiating with another culture - a culture that is largely different from the one one is accustomed to.

How the second law has been violated

All my life, I've been trying to come up with instances that "defy" the statistical reality that is the second law of Thermodynamics. I believe that my search has finally come to an end.

Most people would probably have heard of the Maxwell Daemon - the "door" that allows only the "faster" (and therefore hotter) molecules from a cold area to a hot area, and "slower" molecules from a hot area to a cold area, therefore, creating a machine that defies the second law. People have puzzled over this for a very long time - and some conclude that it is impossible to construct such a daemon. Its existence, like that of the Lochness Monster, Yeti and Bigfoot is suspect.

But America has a Maxwell Daemon of its own. The INS. America is a rich land: lots of water, food and beer for all; lots of cows and pigs to kill and eat; lots of cars to drive; lots of petroleum (oil) to burn. Countries like India, on the other hand, are not so lucky - lots of people starve to death, lots of people cannot have a full meal, lots of people live in utter poverty in slums.

But India does have lots of good brains. Lots of IIT and IIM graduates. Lots of equally skilled people from other colleges - right from Bihar to Kerala. And these guys, inevitably, after gaining some education of sorts, start dreaming the American dream. The INS allows them through willingly ("America should not lose its competitive edge"), but does not allow the beggar and the "unskilled" worker. And the denouement is the following: the Per Capita Income of Indian Americans is 1.5 times the American average - the people from one of the poorest countries in the world are the richest ethnic group in America.

There's lots of Indians in the Silicon Valley. Almost all universities in the USA (even MIT, Stanford, Princeton and the like) have a sizable proportion of Indian professors and students. Often the biggest Academic names are Indians. Lots of big companies have Indians on their payrolls. Hardly what you would expect from one of the poorest nations in the world.

But Zurek (2003) would say "Hey, the INS is doing some sort of work, right? So it isn't really a violation". But I would rationalize by saying that human beings aren't molecules. Especially me. I'm fat.

REFERENCES

W. Zurek, Maxwell'’s demon, Szilard'’s engine and quantum measurements, arXiv:quant-ph/0301076 (2003)