4 ms·
The best commentary I have seen on the article comes from a coworker, who took the time to dissect why the conclusion from this article is not surprising: The
by MyHypatia 11y ago
The best commentary I have seen on the article comes from a coworker, who took the time to dissect why the conclusion from this article is not surprising:
The notion of a fluid is more generally related to the concept of a continuum which allows for the PDE description the Navier-Stokes equations offer. It is taken for granted that density or velocity are point-quantities in space, but there can be no such simplifying description in rarefied situations or more precisely when the Knudsen number is not small. Batchelor 1967 has a good discussion on this. In addition the notion of viscosity which relies on writing the deviatoric stress as proportional to the gradient in velocity relies on dropping the higher order terms in the velocity gradient Maclaurin series assuming they are small (which they usually are for very small Knudsen number).A Boltzmann-like description will always be more general because it is a pdf-based description which is really just fancy counting and doesn't have the Knudsen number limitation. Therefore calling the Navier-Stokes equations incomplete is a bit imprecise. It would be more accurate to say that the labels (fluid, material, continuum) are great simplifications which are incredibly useful when they apply.
- vanderZwan 11y ago> Therefore calling the Navier-Stokes equations incomplete is a bit imprecise. Oh, those sloppy mathematicians... ;) (for the non-physicists/mathematicians: a running gag between mathematicians and physicists is that the former accuse the latter of being sloppy, because the latter take a lot of mathematical liberties. Allegedly, in my old university there was a joint class between physics and mathematics (I never got that far to see for myself), and the professor would start the first lesson with "I brought barf bags for the mathematicians. You're going to need them." I even have a friend who switched from physics to maths because he claimed to be disgusted by the way physicists "proved" their "theorems". Luckily he mellowed out a bit after marrying an applied physicists - they even published a paper together.)
- MyHypatia 11y agoHaha, yea. From an engineering perspective... you can spend all day debating the philosophical implications of taking a derivative and have very interesting conversations, or you could just take the derivative because it's useful and go make things.
- semi-extrinsic 11y agoWe had a professor in quantum optics who would quip before doing certain things (e.g. zeta function regularization) that "the following derivation is unsuitable for people with a preexisting heart condition and mathematicians".