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A rocket cuts through a solved Navier-Stokes flow, forcing the fluid to separate around its body and roll into a long turbulent wake. Using the D2Q9 lattice-Boltzmann method, the scene reveals vorticity, strain, Q-criterion vortex cores and wall shear.

Mathelirium

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26,718 просмотров • 13 дней назад •via X (Twitter)

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Flow Around AN Oscillating Airfoil Using Lattice Boltzmann Method (LBM)

Flow Around AN Oscillating Airfoil Using Lattice Boltzmann Method (LBM)

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A neural network can begin as a flat sheet and learn the shape of hidden data A self-organizing map turns learning into geometry. Each data point pulls one winning neuron toward it, but nearby neurons move too, and so the whole lattice bends without losing its neighborhood structure. The strange part is that the network is not given the roll shape. It discovers the shape through competition and local cooperation. Paper: Self-Organized Formation of Topologically Correct Feature Maps Authors: Teuvo Kohonen Year: 1982

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A Million-Dollar Storm Mathematics Still Cannot Tame. Turbulence matters because it is the default behavior of real fluids once motion becomes strong enough, e.g. air over wings, blood through vessels, weather in the atmosphere, water in oceans, fuel in engines, and flow in pipes and turbines. We can write down the Navier-Stokes equations for all of this, but in 3D one of the deepest open questions is still whether smooth solutions always stay smooth, or can break down in finite time. That is crucial because it asks whether the basic equations of fluid motion remain mathematically under control forever, or can form a true singularity where the theory itself breaks. Solve that and you got yourself a million dollars

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The Hidden Flow Inside Schrödinger’s Equation Once you define ρ = |ψ|² and differentiate it, Schrödinger equation rearranges into a continuity law, ∂ρ/∂t + ∇·j = 0, with j = (1/m)Im(ψ*∇ψ). Which means that probability is not just sitting there, it flows. Write ψ = r e^(iθ), and the current becomes j = (ρ/m)∇θ. So, the phase gradient is the steering field. When the phase winds by 2πn around a loop, the circulation is quantized, and the cores appear where ρ collapses so the phase can go undefined. In the animation, the ribbons trace that current, the color field shows phase, and the curls in the streamlines mark quantized vortex defects.

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A shear-front crosses the frabric and Spacetime remembers. If you want the Python script to play with...subscribe and I will share.

A shear-front crosses the frabric and Spacetime remembers. If you want the Python script to play with...subscribe and I will share.

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🙋‍♀️China has achieved its first-ever controlled recovery of a rocket booster! On the maiden flight of Long March-10B, the rocket successfully placed its payload into orbit, and its first stage returned and was captured by a net system on a seaborne platform.

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China has achieved its first-ever controlled recovery of a rocket booster, a breakthrough for the country's reusable space tech. On the maiden flight of Long March-10B, the rocket successfully placed its payload into orbit, and its first stage returned and was captured by a net system on a seaborne platform.

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Reporter: You said there would be no pause and now there’s a pause Trump: You have to have flexibility. I could say here’s a wall and I’m going to go through it and you can’t go through the wall. Sometimes you have to be able to go under the wall or around the wall or over the wall.

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