Loading video...

Video Failed to Load

There was a problem loading this video. This could be due to a temporary network issue or the video might be unavailable.

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

38,804 subscribers

26,718 views • 1 month ago •via X (Twitter)

Anya Rossi• Live Now

Private livecam show

0 Comments

No comments available

Comments from the original post will appear here

Related Videos

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

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

Mathelirium

13,981 views • 8 months ago

Cognition founder and 3x Olympiad gold medalist Scott Wu on the Navier-Stokes solution: "It's actually insane...guys, we just solved Navier-Stokes with AI. That is absurd. And I don't think it's going to stop." "All of this stuff is just going to get done. It's hard to put into words if you're not familiar with the scale of it. But Navier-Stokes is a very fundamental problem about fluid dynamics and such. It's been around forever, basically. And lots of people have sunk lots and lots of time into it." "The fact that this can even just be done in like a week — it's insane."

Cognition founder and 3x Olympiad gold medalist Scott Wu on the Navier-Stokes solution: "It's actually insane...guys, we just solved Navier-Stokes with AI. That is absurd. And I don't think it's going to stop." "All of this stuff is just going to get done. It's hard to put into words if you're not familiar with the scale of it. But Navier-Stokes is a very fundamental problem about fluid dynamics and such. It's been around forever, basically. And lots of people have sunk lots and lots of time into it." "The fact that this can even just be done in like a week — it's insane."

TBPN

103,154 views • 12 days ago

Submarine moving beneath sea ice sends pressure through the water and bends the frozen ceiling above it. The Mathematics of fluid-flow, elasticity and flexural-gravity bring this scene to life.

Submarine moving beneath sea ice sends pressure through the water and bends the frozen ceiling above it. The Mathematics of fluid-flow, elasticity and flexural-gravity bring this scene to life.

Mathelirium

48,793 views • 12 days ago

I am not joking. This is a Navier-Stocks simulation with a DGX simplified geometry. What this solution means and how it is achieved? (the following part is for CFD lovers) D3Q19 lattice-Boltzmann, incompressible Navier-Stokes in the low-Mach limit, BGK collision with a Smagorinsky subgrid closure, full-way bounce-back on the voxelised chassis, plus a passive thermal scalar. 94×140×55 at 3 mm, 12000 steps, converged to residual 0.0013.

I am not joking. This is a Navier-Stocks simulation with a DGX simplified geometry. What this solution means and how it is achieved? (the following part is for CFD lovers) D3Q19 lattice-Boltzmann, incompressible Navier-Stokes in the low-Mach limit, BGK collision with a Smagorinsky subgrid closure, full-way bounce-back on the voxelised chassis, plus a passive thermal scalar. 94×140×55 at 3 mm, 12000 steps, converged to residual 0.0013.

Marco Franzon

32,073 views • 1 month ago

$This scene asks a stranger question : What happens if the material has negative refractive index? As the electron moves through the metamaterial slab, the emitted radiation no longer follows the familiar Cherenkov geometry (see below). The energy flow forms a backward-directed cone, extending opposite to the electron's motion. Method used: Finite Element Method with Poynting style energy-flow tracers.$

This scene asks a stranger question : What happens if the material has negative refractive index? As the electron moves through the metamaterial slab, the emitted radiation no longer follows the familiar Cherenkov geometry (see below). The energy flow forms a backward-directed cone, extending opposite to the electron's motion. Method used: Finite Element Method with Poynting style energy-flow tracers.

Mathelirium

13,390 views • 24 days ago

Will OpenAI and Anthropic ever crack this one? Behind this beautiful turbulence cascade lies a Millennium Prize Problem: For the 3D Navier-Stokes equations, nobody has proved whether every smooth flow remains smooth forever or whether a singularity can form in finite time.

Will OpenAI and Anthropic ever crack this one? Behind this beautiful turbulence cascade lies a Millennium Prize Problem: For the 3D Navier-Stokes equations, nobody has proved whether every smooth flow remains smooth forever or whether a singularity can form in finite time.

Mathelirium

15,438 views • 1 month ago

The Navier-Stoles equations resolve how the flow divides around this 2D silhouette of the B-2 Spirit bomber.

The Navier-Stoles equations resolve how the flow divides around this 2D silhouette of the B-2 Spirit bomber.

Mathelirium

38,006 views • 11 days ago

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

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

Mathelirium

130,244 views • 4 months ago

Have You Ever Heard of Molecular Communication Systems? Instead of using radio waves or light, molecular communications send information carefully through released chemical particles. A transmitter emits molecules into a medium, the channel reshapes that signal through diffusion, flow, and randomness. The receiver reads the message from the molecules that arrive and bind. It is communication theory at microscopic scale, where physics, probability and biology all become part of the channel. Some applications you may know: Targeted drug delivery inside the body, microscopic health monitoring with nanosensors, and lab-on-a-chip.

Have You Ever Heard of Molecular Communication Systems? Instead of using radio waves or light, molecular communications send information carefully through released chemical particles. A transmitter emits molecules into a medium, the channel reshapes that signal through diffusion, flow, and randomness. The receiver reads the message from the molecules that arrive and bind. It is communication theory at microscopic scale, where physics, probability and biology all become part of the channel. Some applications you may know: Targeted drug delivery inside the body, microscopic health monitoring with nanosensors, and lab-on-a-chip.

Mathelirium

19,452 views • 6 months ago

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.

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.

Mathelirium

26,511 views • 5 months ago

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

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

Mathelirium

30,056 views • 5 months ago

Control Systems is the closest thing engineering has to magic! You get to measure what physics is doing right now, then fight back fast enough that the outcome looks impossible. Episode 3 In this scene a tall rocket falls toward a moving barge and lands using only a throttle knob and gimballed engine. We make it unfair on purpose by using crosswind gusts to shove the vehicle. The barge drifts and gently tilts so the target keeps sliding. Actuator lag and hard limits clamp the gimbal and throttle. A slosh-like internal wobble kicks in late and tries to phase-lag the controller into oscillations. You see the controller ride all these.

Control Systems is the closest thing engineering has to magic! You get to measure what physics is doing right now, then fight back fast enough that the outcome looks impossible. Episode 3 In this scene a tall rocket falls toward a moving barge and lands using only a throttle knob and gimballed engine. We make it unfair on purpose by using crosswind gusts to shove the vehicle. The barge drifts and gently tilts so the target keeps sliding. Actuator lag and hard limits clamp the gimbal and throttle. A slosh-like internal wobble kicks in late and tries to phase-lag the controller into oscillations. You see the controller ride all these.

Mathelirium

22,696 views • 6 months ago

Spacetime That Remembers A localized shear-front propagates across a deformable spacetime fabric. While the front passes, the fabric undergoes transient slip and shear. After it passes, a saturating memory field permanently modifies the weave, producing a non-reversible displacement. Particle constellations attached to the fabric settle into persistently shifted positions, making the post-front state measurably different from the pre-front state by visual inspection alone.

Spacetime That Remembers A localized shear-front propagates across a deformable spacetime fabric. While the front passes, the fabric undergoes transient slip and shear. After it passes, a saturating memory field permanently modifies the weave, producing a non-reversible displacement. Particle constellations attached to the fabric settle into persistently shifted positions, making the post-front state measurably different from the pre-front state by visual inspection alone.

Mathelirium

58,496 views • 7 months ago

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.

Mathelirium

17,146 views • 6 months ago

Fun video of using a barge and floating transfer to get a Vulcan rocket around the Wilson Lock while its down for repairs

Fun video of using a barge and floating transfer to get a Vulcan rocket around the Wilson Lock while its down for repairs

Tory Bruno

24,217 views • 1 year ago

The hose goes down into the horses stomach. The horse has colic. A blockage/twist somewhere along the track stopping flow. He's pumping water into the stomach and down the track to try and unblock. He's using the siphoning method

The hose goes down into the horses stomach. The horse has colic. A blockage/twist somewhere along the track stopping flow. He's pumping water into the stomach and down the track to try and unblock. He's using the siphoning method

XXLBM ☝️

376,243 views • 7 days ago

What Happens When a Black Hole Does More Than Fall? In General Relativity, a rotating Black Hole is described by the Kerr Metric. Its spin does something strange to spacetime... it drags the geometry around with it. The horizon sits at r₊ = M + √(M² - a²) but outside it there is another surface, the Ergosphere, r_E(θ) = M + √(M² - a²cos²θ) Inside that region, Spacetime is being swept around so strongly that remaining still is no longer possible. Every particle, every light thread, every local observer is forced to rotate with the geometry. For this scene, the C-metric acceleration remains alive in the background and the Black Hole still moves through the fabric, pulled along an axial defect. But the main event is Kerr frame dragging. The fabric twists. The Ergosphere breathes. Light paths shear into spirals. Particles that try to cross the region get carried around before falling inward. #GeneralRelativity #BlackHole #KerrMetric #FrameDragging #Ergosphere #Spacetime #EinsteinEquations #Astrophysics #Physics

What Happens When a Black Hole Does More Than Fall? In General Relativity, a rotating Black Hole is described by the Kerr Metric. Its spin does something strange to spacetime... it drags the geometry around with it. The horizon sits at r₊ = M + √(M² - a²) but outside it there is another surface, the Ergosphere, r_E(θ) = M + √(M² - a²cos²θ) Inside that region, Spacetime is being swept around so strongly that remaining still is no longer possible. Every particle, every light thread, every local observer is forced to rotate with the geometry. For this scene, the C-metric acceleration remains alive in the background and the Black Hole still moves through the fabric, pulled along an axial defect. But the main event is Kerr frame dragging. The fabric twists. The Ergosphere breathes. Light paths shear into spirals. Particles that try to cross the region get carried around before falling inward. #GeneralRelativity #BlackHole #KerrMetric #FrameDragging #Ergosphere #Spacetime #EinsteinEquations #Astrophysics #Physics

Mathelirium

27,112 views • 2 months ago

Why String Theory Won't Die The string theory idea refuses to die because it's one of the few frameworks that forces a quantum object and spacetime geometry into the same picture. In the render, a closed string isn’t just a loop doing pretty vibrations. Its internal phase pattern is a quantum degree of freedom, shown as color. At the same time, its motion stirs ripples in the surrounding metric, shown as the fabric below. One object, two roles. A wave-like state living on the string, and a curvature-like response spreading through the background. You can literally watch quantum stuff and gravity stuff talk to each other in the same scene. #StringTheory #Physics #QuantumMechanics #GeneralRelativity #MathematicalPhysics #SciComm

Why String Theory Won't Die The string theory idea refuses to die because it's one of the few frameworks that forces a quantum object and spacetime geometry into the same picture. In the render, a closed string isn’t just a loop doing pretty vibrations. Its internal phase pattern is a quantum degree of freedom, shown as color. At the same time, its motion stirs ripples in the surrounding metric, shown as the fabric below. One object, two roles. A wave-like state living on the string, and a curvature-like response spreading through the background. You can literally watch quantum stuff and gravity stuff talk to each other in the same scene. #StringTheory #Physics #QuantumMechanics #GeneralRelativity #MathematicalPhysics #SciComm

Mathelirium

13,657 views • 7 months ago