I mentioned last October at the end of a post that:

Penny Smith, a mathematician at Lehigh University, has posted a paper on the arXiv that purports to solve one of the Clay Foundation Millenium problems, the one about the Navier-Stokes Equation. The paper is here, and Christina Sormani has set up a web-page giving some background and exposition of Smith’s work.

There’s further work here.

Fluid dynamics theory works on nanoscale outside vacuum

A propane liquid nanobridge breaks up in a nitrogen gas environment. Credit: Georgia Tech/Uzi Landman

In 2000, Georgia Tech researchers showed that fluid dynamics theory could be modified to work on the nanoscale, albeit in a vacuum. Now, seven years later they’ve shown that it can be modified to work in the real world, too – that is, outside of a vacuum. The results appear in the February 9 issue of Physical Review Letters.

It’s well-known that small systems are influenced by randomness and noise more than large systems. Because of this, Georgia Tech physicist Uzi Landman reasoned that modifying the Navier-Stokes equations to include stochastic elements – that is give the probability that an event will occur – would allow them to accurately describe the behavior of liquids in the nanoscale regime.

Writing in the August 18, 2006, issue of PRL, Landman and post doctoral fellow Michael Moseler used computer simulation experiments to show that the stochastic Navier-Stokes formulation does work for fluid nanojets and nanobridges in a vacuum. The theoretical predictions of this early work have been confirmed experimentally by a team of European scientists (see the December 13, 2006, issue of Physical Review Letters). Now, Landman and graduate student Wei Kang have discovered that by further modifying the Moseler-Landman stochastic Navier-Stokes equations, they can accurately describe this behavior in a realistic non-vacuous environment.

To read the full article go here.

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