71–80 of 124 posts
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Aye either they have upturned a theory as august as general relativity or they’ve thrown the baby out with the bath water somewhere.
Based on my fairly layman understanding it could be as simple as the "weak solutions" not being as useful as they were thought to be.
Using this approach, Buckmaster and Vicol prove that these very weak solutions to the Navier-Stokes equations are nonunique. They demonstrate, for example, that if you start with a completely calm fluid, like a glass of water sitting still by your bedside, two scenarios are possible. The first scenario is the obvious one: The water starts still and remains still forever. The second is fantastical but mathematically p…
This makes senses to me. If you run a simulation at too low a resolution you run into ambiguity. By refining the grid you can resolve that ambiguity. Turbulent flow is chaotic, so this makes perfect sense to me. What this may lead to is a method of determining criteria for adaptive grid refinement. But I thought that already existed, so maybe just an improvement over what's out there.
I'm struggling to understand the significance of this, at least as the N-S equations are used in the real world. Many years ago, I interned with the Navy writing fortran code for fluid dynamics simulations on submarine hulls, and IIRC there were flow dynamics we observed consistently in the real world (e.g. oscillating vortices) that were fundamentally inconsistent with the results coming from our N-S calculations (w…
It brings to mind how people say "Bumble bee's defy the laws of physics to fly".
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Well general relativity breaks down at very small scales, and imparts the need for quantum mechanics ...
If you are really interested, somebody has bothered to make a special-relativity & quantum-indeterminacy compatible formulation of Navier-Stokes suitable for calculating shockwaves in extremely dense mediums such as the neutronium neutron stars are thought to be made of (where the speed of sound is comparable to the speed of light in a vacuum, hence the relativity, and the matter is degenerate and in states of superp…
I'm struggling to understand the significance of this, at least as the N-S equations are used in the real world. Many years ago, I interned with the Navy writing fortran code for fluid dynamics simulations on submarine hulls, and IIRC there were flow dynamics we observed consistently in the real world (e.g. oscillating vortices) that were fundamentally inconsistent with the results coming from our N-S calculations (w…
What I got from the article is that there's a possibility of a chaotic result: it may not be possible to get computed results which are arbitrarily close to the real-world results. I was reminded a bit of the famous Lorenz system (originally for weather prediction, IIRC), which turns out to be chaotic under some conditions.
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Ha... I guess I can be a bit terse. Just think of the “turbulence” in navier-stokes as valuation fluctuations. Without the realworld dampening effects of regulation, slow tranactions, and managed markets — volatility along the lines of the infinite incongruities posed in the article are possible. ( note: Im not referring to a pendactic ‘infinite’ wrt a blockchain).
Ah OK I get it now. I’m an applied mathematician and a macroeconomist that studied turbulence in financial markets and crashes thereof. I can assure you that the dynamics are pretty distinct. In economics wealth is not a conserved quantity whereas in physics energy and momentum are.