Science: "Science is organized knowledge. Wisdom is organized life."

[joecct]

Seeing supersonic sound waves

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[Kepler]

I want to see the research grant.

 

[Kepler]

This looks fun.

The new proof broadly consists of three steps: derive the macroscopic theory from the mesoscopic one; derive the mesoscopic theory from the microscopic one; and then stitch them together in a single derivation of the macroscopic laws all the way from the microscopic ones.

The first step was previously understood, and even Hilbert himself contributed to it. Deriving the mesoscopic from the microscopic, on the other hand, has been much more mathematically challenging. Remember, the mesoscopic setting is about the collective behavior of vast numbers of particles. So Deng, Hani and Ma looked at what happens to Newton’s equations as the number of individual particles colliding and ricocheting grows to infinity and their size shrinks to zero. They proved that when you stretch Newton’s equations to these extremes, the statistical behavior of the system—or the likely behavior of a “typical” particle in the fluid—converges to the solution of the Boltzmann equation.

There is a link to the Deng et al. paper and good luck. A sample:

The purpose of this work is twofold. First we extend the derivation of Boltzmann’s equation in [26] to the periodic setting Td (d = 2,3). Second, we connect this kinetic limit to the hydrodynamic limit in the abovecited works, to obtain a full derivation of the fluid equations starting from Newton’s laws on the particle system, thereby completing Hilbert’s original program. We summarize the main theorems as follows: • Theorem 1: Derivation of the Boltzmann equation on Td (d = 2,3). Starting from a Newtonian hard-sphere particle system on the torus Td (d = 2,3) formed of N particles of diameter ε undergoing elastic collisions, and in the Boltzmann-Grad limit Nεd−1 = α, we derive the Boltzmann equation (1.1) as the effective equation for the one-particle density function of the particle system. • Theorem 2: Derivation of the incompressible Navier-Stokes-Fourier system from Newton’s laws. Starting from the same Newtonian hard-sphere particle system on the torus Td (d = 2,3) close to global equilibrium, and in an iterated limit where first N → ∞, ε → 0 with α = Nεd−1 f ixed and then α → ∞ separately (there are also other variants, see Theorem 2), we derive the incompressible Navier-Stokes-Fourier system as the effective equation for the macroscopic density and velocity of the particle system. • Theorem 3: Derivation of the compressible Euler equation from Newton’s laws. Starting from the same Newtonian hard-sphere particle system on the torus Td (d = 2,3), and in an iterated limit where first N → ∞, ε → 0 with α = Nεd−1 fixed and then α → ∞ separately (there are also other variants, see Theorem 3), we derive the compressible Euler equation as the effective equation for the macroscopic density, velocity, and temperature of the particle system.

 

[Deutsche Gopher Fan]

This is jarring

https://www.reddit.com/r/Damnthatsinteresting/s/3X3GWcS17y

 

[Slap Shot]

This is jarring

https://www.reddit.com/r/Damnthatsinteresting/s/3X3GWcS17y

My BIL was stuck in that region for a day before he and his family could return to Yangon. Pretty scary stuff.

 

[Kepler]

Seeing a window turn into a wall of liquid and then solid again is not something I will forget.

A good quake is as perspective-altering as a good trip.

 

[Jimjamesak]

Seeing a window turn into a wall of liquid and then solid again is not something I will forget.

A good quake is as perspective-altering as a good trip.

Massive steel beams shaking like cooked spaghetti. You're not wrong.

 

[Kepler]

Massive steel beams shaking like cooked spaghetti. You're not wrong.

Yikes. That's new for me.

 

[Jimjamesak]

Yikes. That's new for me.

Not a particularly pleasant experience.

My mother lived through 1964. She doesn’t talk about it very often.

 

[Kepler]

Not a particularly pleasant experience.

My mother lived through 1964. She doesn’t talk about it very often.

Was she affected by the tsunami?

 

[Jimjamesak]

Was she affected by the tsunami?

No she was in Anchorage and Anchorage didn’t get hit by the tsunami.

She did see the ground move like a wave through, among other things.

I will say, from experience, the aftershocks are by far the worst part. It’s like being shot, then, when you’re resting at the hospital, someone comes along every hour or two and fires a small bb at you.