Saturday, September 6, 2008

Result may be interesting..

But the process made it possible will be fascinating..
(for me)

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Does these numbers mean anything to you? This are the heart of a product from my company. This is how result look like... most of the time. It is regarding an empirical model.. parameters. Think about the rigorous process made this possible..

Einstein's diffusivity... I don't know how many times and with how many people I told this.. but let me.. again here.....

If you go through the math of the derivation for diffusion coefficient, the heart is central limit theorem, which says mean of sum of random distributions will follow a Gaussian distribution.

Let me explain.. If you are trying to generate 10 random numbers with some random number generator which works at a mean 0, then the probability of getting the sum (of those 10 numbers) '0' is very high.. (which means you are at the center of bell of Gaussian). But for the same random numbers to get a sum.. of -1 is less compared to 0. (As we are using mean 0 random number generator)..

There is a more sophisticated and rigorous math to prove this.. anyways..
Imagine a situation.. where you have a large particle surrounded by small particles which are continuously bombarding the large one with random force whose mean you know.

At a given instant.. one particle may be hitting one way.. and the other will be hitting it in an another way.. and net force is the sum all the small (random) forces.. which we don't know at given time.. (as the nature of the force is random and not deterministic)

You can not really solve the time evolution easily.. BUT you can get the mean behavior of the big particle from our central limit theorem which says.. the mean force of sum of random distributions is a Gaussian.. which we know..

after that some math rigor follows...

What ever I discussed here is the RESULT. The process to connect an abstract mathematical concept to a physical thing is.... I can not really find appropriate words for this context, but beautiful should work!!

PS: The point I want to make is, I don't agree that we can share happiness... if it is so.. the other has to feel every minute and step that made my happiness possible which would be rare. You may merely see me being happy.. and get your own happiness which is different process altogether.

PPS: On a second thought, what the heck is this.....??
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