Boltzmann Equation Solved, the New Way

xt writes "The Boltzmann equation is old news. What's news is that the 140-year-old equation has been solved, using mathematical techniques from the fields of partial differential equations and harmonic analysis, some as new as five years old. This solution provides a new understanding of the effects due to grazing collisions, when neighboring molecules just glance off one another rather than collide head on. We may not understand the theory, but we'll sure love the applications!"

Re:Meaning of "Solved"

[deadline]

I think most people have the wrong idea about the "Butterfly Effect." IIRC, the weather scientists were talking about the precision with which they would need to know air movement to make longer term predictions. i.e. the longer the forecast the more digits of precision are needed in your measurement. They were referring to the level of precision and not to butterflies causing a tornado or other such nonsense. Unfortunately, the media like to report it otherwise.

Re:That's quite interesting

[Warlord88]

A gas can often be treated as a compressible fluid in CFD,

A gas is a compressible fluid.

there are a great many open source PDE solvers

The most general solvers are the most handicapped. Even the ridiculously costly commercial solvers (Ansys, Fluent, etc.) solve a limited number of problems. I was working on a project that attempted to numerically simulate the effect of electromagnetic waves on the brain. Obviously, you need to solve the Maxwell's equations in horrible medium that is your brain. That's when I realized how woefully indadequate the commercial solvers (that claim to simulate the problem) are.

Ideal gas is not chaotic, weather is

[syousef]

What they really proved, at long last, is that gaseous systems are stable for small perturbations.

In layman's terms: the Butterfly Effect is bogus. It takes a very large perturbation to convert a stable portion of atmosphere into a storm, and the flutter of a butterfly's wings is not significant to tipping the balance.

Um since when was weather on this planet equivalent to an ideal gas? An ideal gas is not a chaotic system. So the Boltzmann equation has nothing to do with the butterfly effect. You're talking out of your arsehole, and slashdot is collectively too ignorant to call you for it, hence you've been modded informative. Fucking sad.