4 ms·

I never thought about this before reading the article but now it seems pretty obvious to me that both descriptions can not yield the same results under all circ

by danbruc 11y ago

I never thought about this before reading the article but now it seems pretty obvious to me that both descriptions can not yield the same results under all circumstances. The Navier–Stokes equations are based on quantities like density and flow velocity which are only really meaningful if you have sufficiently many particles to average about. In consequence I am hardly surprised that one gets disagreeing results under extreme conditions like very low densities.

semi-extrinsic 11y ago
I'm also quite surprised that this article tries to spin it as very novel. We've known this for literally a hundred years. Moreover, there's no mention of the pioneers in the field - Chapman, Engskog, Burnett, Knudsen, etc - much to my dismay. The recommendation is for major revisions including a detailed literature review. </grumpy-reviewer-mode>
- tanderson92 11y ago
  I was also dismayed when they referred to KdV (Korteweg de Vries) theory as a "relatively unheralded" theory. KdV theory is an incredibly well known and thoroughly studied area of Mathematics.
  - vanderZwan 11y ago
    Well, those two statements aren't necessarily mutually exclusive, because it can still be relatively unheralded. But only because every physicist knows of Navier-Stokes.
darkmighty 11y ago
I think it's not that obvious. For example, Maxwell's equations represent essentially a complete description of classical electrodynamics. Even though in most formulations it involves densities, it will work fine for point-like charges where the density is singular but integrable. Of course, when QM comes in the theory expands to quantum electrodynamics (QED), but Maxwell's equations match very well (exactly for linear media?) the quantum mechanical predictions when you average the probabilities. It sounds reasonable to expect a fluid theory that explains well macroscopic phenomena, even if the fluid really is granular, where we could hope the approximation would hold on average or something like that. But apparently it turns out that N-S doesn't model important qualitatively distinct phenomena.

by danbruc 11y ago

semi-extrinsic 11y ago

I'm also quite surprised that this article tries to spin it as very novel. We've known this for literally a hundred years. Moreover, there's no mention of the pioneers in the field - Chapman, Engskog, Burnett, Knudsen, etc - much to my dismay. The recommendation is for major revisions including a detailed literature review. </grumpy-reviewer-mode>

tanderson92 11y ago
I was also dismayed when they referred to KdV (Korteweg de Vries) theory as a "relatively unheralded" theory. KdV theory is an incredibly well known and thoroughly studied area of Mathematics.
- vanderZwan 11y ago
  Well, those two statements aren't necessarily mutually exclusive, because it can still be relatively unheralded. But only because every physicist knows of Navier-Stokes.

darkmighty 11y ago

I think it's not that obvious. For example, Maxwell's equations represent essentially a complete description of classical electrodynamics. Even though in most formulations it involves densities, it will work fine for point-like charges where the density is singular but integrable. Of course, when QM comes in the theory expands to quantum electrodynamics (QED), but Maxwell's equations match very well (exactly for linear media?) the quantum mechanical predictions when you average the probabilities. It sounds reasonable to expect a fluid theory that explains well macroscopic phenomena, even if the fluid really is granular, where we could hope the approximation would hold on average or something like that. But apparently it turns out that N-S doesn't model important qualitatively distinct phenomena.