Mathematicians Solve 140-Year-Old Boltzmann Equation

[n2doc]

May 13, 2010
(PhysOrg.com) -- Two University of Pennsylvania mathematicians have found solutions to a 140-year-old, 7-dimensional equation that were not known to exist for more than a century despite its widespread use in modeling the behavior of gases.

The study, part historical journey but mostly mathematical proof, was conducted by Philip T. Gressman and Robert M. Strain of Penn’s Department of Mathematics. The solution of the Boltzmann equation problem was published in the Proceedings of the National Academy of Sciences. Solutions of this equation, beyond current computational capabilities, describe the location of gas molecules probabilistically and predict the likelihood that a molecule will reside at any particular location and have a particular momentum at any given time in the future.

During the late 1860s and 1870s, physicists James Clerk Maxwell and Ludwig Boltzmann developed this equation to predict how gaseous material distributes itself in space and how it responds to changes in things like temperature, pressure or velocity.

The equation maintains a significant place in history because it modeled gaseous behavior well, and the predictions it led to were backed up by experimentation. Despite its notable leap of faith -- the assumption that gases are made of molecules, a theory yet to achieve public acceptance at the time — it was fully adopted. It provided important predictions, the most fundamental and intuitively natural of which was that gasses naturally settle to an equilibrium state when they are not subject to any sort of external influence. One of the most important physical insights of the equation is that even when a gas appears to be macroscopically at rest, there is a frenzy of molecular activity in the form of collisions. While these collisions cannot be observed, they account for gas temperature.

Gressman and Strain were intrigued by this mysterious equation that illustrated the behavior of the physical world, yet for which its discoverers could only find solutions for gasses in perfect equilibrium.

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http://www.physorg.com/news192967537.html

[Make7]

1. Why they gotta always be showin off there fancy book learnin?

But seriously, that's pretty amazing that Maxwell and Boltzmann developed such a complicated and accurate equation at that point in history. Pure genius.
 

[8 track mind]

8. Hey!!!

I have muh gawd, and muh bible. Don't be tellin me no commie pinko librawl math hogwarsh!

[postulater]

2. Does it help model the behaviour of BPs gas?

If so, then put them to work on it.

They might as well do something useful/practical/urgent.

[Ian David]

3. Finally, proof of the He Who Smelt It Dealt It Axiom. n/t

[iamtechus]

4. Really useful

Could be used to model the behavior of a phart in a whirlwind.

[jberryhill]

6. "an initial small disturbance in the gas is short-lived and quickly becomes unnoticeable"

This contradicts the Silent But Deadly Principle.

[JackintheGreen]

5. UPenn represent!

Holler!

:woohoo:

[cloudbase]

7. You Quakers

shouldn't be boastful, now!

[Lionel Mandrake]

9. They did no such thing.

They didn't SOLVE the Boltzmann Equation. What they did was to PROVE THE EXISTENCE OF SOLUTIONS in a particularly difficult case - the case of long-range interactions.

There is a big difference between finding a solution and proving the existence of a solution.

[Scuba]

10. Finally !