flow

In 1934 Jean Leray proved that the Navier–Stokes equations always have solutions "in a generalized sense". Whether a solution stays smooth or can break down into a singularity he could not tell, and nobody could for ninety years. In 2000 the Clay Institute made the question one of its seven Millennium Prize problems.

Water in a tank spins at nearly four revolutions per second, and, as if by magic, a column the size of a dinner table emerges. The vortex lives for dozens of rotations, even though everything around it churns and trembles. Where does such stability come from? The secret is that the vortex is not isolated.

In a Paris laboratory, light was made to flow around an obstacle the way water flows around a rock in a stream. But this water is special: it feels no friction.

Plasma is a gas in which electrons are stripped from atoms and roam freely. Sometimes, regions where electrons are almost absent spontaneously appear in such a gas; they are called holes. It is like a whirlpool forming in a stream, pulling everything around it in. But exactly how such a whirlpool is born has long remained a mystery.

Microwave plasma in a vortex is like a kitchen mixer that simultaneously heats and stirs the gas. In the reactor, the gas is swirled, and microwaves heat it to thousands of degrees, tearing carbon dioxide molecules apart. Scientists created a computer model of such a reactor to understand how pressure affects the process.

The early universe was less like a calm pond and more like a boiling cauldron. Matter flowed, collided, and swirled against the backdrop of rapid spatial expansion. To understand how stars and galaxies emerged from this hot soup, physicists build digital simulations. This new work is the third part in a series on lattice-based cosmological modeling. The first two focused on fields; this one deals with fluids.

The brain self-cleans its waste: cerebrospinal fluid flows through narrow channels surrounding arteries. The channel walls are soft and ripple with each pulse, and the tissue is porous like a sponge. Every heartbeat turns arteries into tiny pumps, driving fluid through the pores.

A person in a boat turns by shifting their body weight. An unmanned vessel uses the same trick: a sliding weight inside the hull does the steering. Its movement is controlled by a neural network, anticipating the chaos of waves and gusts of wind. The propeller pushes the boat forward, while the weight shifts balance — like moving from one foot to the other.

Quantum matter rarely treats us to the spectacle of self-motion. Where the classical world teems with starling murmurations, fish schools, and bustling bacteria, quantum thermodynamics long remained serene.

Imagine a packed dance floor where dancers glide without any friction — passing through each other without a touch. That's a superfluid. In a neutron star's crust, neutrons could behave this way, but a rigid lattice of ions gets in the way, like suddenly sticking the dance floor full of pillars.

Strike a bell, and it hums at a single pitch. But if you place a second clapper inside, and they ring without touching each other, the sound becomes more complex. That's roughly how the neutron star from the new study is built. It's not just a hot sphere: inside, two immiscible fluids can flow — for instance, superfluid neutrons and ordinary plasma.

In the first moments of the universe's existence, space was filled with hot plasma, where particles emerged and disappeared like bubbles in a boiling pot. The traces of these processes, stretched to gigantic sizes by expansion, are preserved in the cosmic microwave background — ancient light that has reached us across billions of years.

When water boils in a kettle, waves of steam ripple through the kitchen. A similar process happens in space, in plasma — gas so hot that electrons are stripped from atoms. Around black holes and neutron stars, this plasma isn't just hot: its particles zip around at nearly the speed of light.

In helium cooled to near absolute zero, the liquid stops rubbing against itself and begins to flow without any resistance.

A thin stream of water on a shower glass gathers into winding rivulets that quiver and shift before your eyes. Such a liquid film flowing down a vertical surface is a classic example of chaos in nature: it all flows downward, sure, but the surface lives its own unpredictable life.

In the macroscopic world we know, any motion inevitably decays: friction, a dissipative process that scatters energy, intervenes. But quantum reality has surprises in store.

The diffusion equation, a mathematical tool describing how particles spread out in space, has long painted a paradoxical picture: a disturbance, like ripples on Water, instantly engulfs the entire universe. This challenged the theory of relativity, which holds that nothing can move faster than light.

Bacteria in a drop of water jostle and swim: each on its own, but together they create patterns. With weak motion, the fluid churns like soup on a high flame: vortices collide, and the flow direction changes every second. This is called bacterial turbulence.

Water swirls into a ring, and that ring flies through the bulk without breaking apart. Such vortex rings, from smoke rings to underwater currents, follow laws that are hard to capture on paper. Usually, the flow is divided into millions of cubic cells, and each one is tracked.