drag

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.

A hydrogen bubble on a platinum electrode behaves like a swimmer trying to surface, but every time it almost breaks free, something below grabs its legs. In the lab, high-speed cameras captured this behavior: a millimeter-sized bubble hangs near the surface, even though buoyancy pulls it upward with a force thousands of times stronger than surface tension can hold.

A crowd at the entrance to a narrow corridor behaves differently than in a spacious hall: some people get pressed against the walls, others are pushed forward. Roughly the same happens when an elongated particle finds itself in a fluid teeming with self-propelled dumbbells. Until now, it was unclear why such a particle moves faster along its long axis than across it, and how the crowd density affects its speed.

A raindrop slides on the wind and hits the ocean not straight down but at an angle. At that moment, its energy splits into two channels: one pushes the water forward along the flight path, the other presses it downward into the depths. Which channel proves stronger determines what happens at the surface: a quiet submergence, a fan of spray to one side, or a crown that shatters in all directions.

A raindrop falls on glass and flattens into a pancake. Add a bit of polymer to the water, and it becomes elastic, like jelly. You'd think such a jelly would spread differently.

Two pieces of sandpaper are pressed tightly together. As you start to slide them, they first catch on the rough spots, then suddenly slip. A fault in the Earth behaves much the same way during an earthquake. But there's a crucial detail: how far do you need to push the edges before the grip gives way? This distance is called the critical slip distance.

Water droplets shoot out of a nozzle one after another, like cyclists on a narrow track. The faster ones catch up with the slower ones and merge into larger drops. This simple mechanism is called ballistic aggregation, and until now it had only been observed on cosmic scales: this is how dust particles stick together to form planets.

Soil is not a solid sponge but a labyrinth of pores of various sizes. After rain, water does not fill them all at once: first the narrowest ones, then the wider ones. Physicists built a theory of this process based on a simple image — a set of communicating vessels.

In the conventional Heisenberg picture, spins at low temperatures are supposed to line up in a strict pattern. But there are crystals — like pyrochlore — where geometry has its own way. Each ion sits at a vertex of a tetrahedron, and the main interaction enforces a rule: two spins point inward, two outward.

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.

Cosmic rays do not travel in straight lines. Charged particles accelerated to enormous speeds loop through the Galaxy's magnetic field like dust motes in a gust of wind. It's usually assumed that they simply scatter along and across field lines.

At the heart of a warp drive lies Einstein's idea that massive bodies curve spacetime — the very stage on which all cosmic events unfold. Picture a bubble of such curved spacetime. Inside it, the ship floats without any G-forces, like a passenger in an airplane cabin who doesn't feel the headwind.

A hot liquid flows easily: molecules dart around, collide, and quickly find new spots. But cool it below its freezing point, and everything changes. Motion nearly freezes, and viscosity skyrockets. The key question isn't that particles are lazy, but where they can even go. The authors combined two established ideas.

A drop of thick shampoo falls into water and freezes into a strange rope. A liquid that both flows and springs back is called viscoelastic. In it, tiny particles under ultrasound behave quite differently than in water. Viscoelasticity is a material's ability to both spread like honey and return to shape like rubber.

Sugar dissolves in tea, and then with a single motion gathers back into the spoon. In an ordinary kitchen, you won't see that — viscosity and disorder get in the way. But in the world of ultra-slow motions, where inertia vanishes, such tricks become reality.

Inside every neuron, there's a long, thin channel, the axon, through which signals travel from the cell body to other cells. To keep this channel working, mitochondria constantly shuttle along it. These tiny organelles produce energy and move in both directions, like cars on a narrow road.

A ship gliding through water constantly rubs against it, like a palm against a rough surface. This friction eats fuel and slows progress. One way to reduce it is to blow air under the hull: water stops sticking to the hull, and drag drops. But air is finicky: sometimes it helps, sometimes it hurts.

A drop of water on a table usually sits still. But make the table slightly softer on one edge and stiffer on the other, and the drop will crawl toward the stiffer side. This phenomenon is called durotaxis: the liquid itself chooses where to flow, without pumps or electricity. This trick works because the surface under the drop is not uniform.

A tiny oil drop squeezes through a water channel narrower than itself. In pure water, it crawls along calmly, like a round bead. But add a little soap to the water, and the drop begins to bend, like a caterpillar.

The void can produce particles if a strong enough field is applied. Physicists call this the Dirac–Klein paradox. Previously, explaining it required the most complex calculations of quantum field theory. But we can make do with a visual image: a tightly stretched rubber band with a knot. The knot is a particle.

When you pull on a piece of metal, it changes shape and simultaneously becomes stronger. The secret lies in tiny defects in the crystal lattice called dislocations. They are like wrinkles in a rug: moving a wrinkle shifts the rug more easily than dragging the whole rug.

Deep inside Earth lies a solid iron core about the size of the Moon. It floats in liquid metal and sways slightly, like a pit in a peach when you shake the fruit. Such oscillations are called Slichter modes: the core shifts both along the planet's axis and perpendicular to it. Three forces act together to damp this motion.

Inside the kidneys, liver, and other organs, fluid flows through channels that squeeze and release like a hose underfoot. The walls of these channels are not rigid: they are porous, elastic, and soaked with moisture.

The James Webb Space Telescope is gazing more and more at exoplanets — worlds orbiting alien stars. Some of them are scorching rocky spheres, tidally locked with one side forever facing their star. There, rock melts into oceans of liquid lava. How does this lava move?

A flat sheet with slits in a flow of water or air behaves like self-adjusting blinds. The pressure opens the gaps, and each strip of material tilts, turning into a miniature wing. Thus, even a sheet placed perpendicular to the flow generates not only drag but also significant lateral lift.

A drop of oil in water, coated with soap molecules, behaves differently from a bare drop. Soap molecules are tiny rods: one end loves water, the other loves oil. In a quiescent fluid, they stand on the surface like a picket fence, lowering the surface tension — the force that pulls the drop into a sphere.

A raindrop falling to the ground strikes with a certain force. But what if the drop isn't round but elongated like a cigar or flattened like a pancake? It turns out that shape is everything: the impact force can vary by more than a factor of ten just because of how the drop looks at the moment of impact.

In most magnetic materials, a domain wall, the boundary between regions with different magnetization, moves in one direction under current, set by the current's direction. But in ferrimagnets near a special point where the angular momenta of two sublattices cancel each other, the behavior changes.

The Sun drives the water cycle, and rain returns it to the ground. But now, every drop is a tiny hammer striking the surface. Floating plastic particles (microplastics, mostly carbon) upon impact jump up like popcorn kernels on a hot skillet. But instead of popping, they get wrapped in a thin water film and turn into weightless beads.

A coin spinning on a table is a familiar sight. At first it rotates quickly, then it tilts, and its rattling becomes faster and faster. In the last seconds it seems to hover: the rotation slows, but the coin just won't finally lie flat. This final moment is a real puzzle for physicists.

Inside a magnet, there are regions where all the atomic magnets point in the same direction. Between such regions lies a narrow transition zone where the magnetization direction gradually rotates. This zone is called a domain wall. Previously, it was considered massless: give it a push, and it stops immediately.

A particle wanders through a medium scattered with obstacles. Sometimes it pushes them aside like a snowplow, and it was thought that this pushing is what eventually stops the motion. But in three-dimensional space, that mechanism doesn't work. It turns out that stopping arises from rare events: every so often, a particle randomly finds itself in a trap, and all exits close, as if doors slam shut.

Glass is a material with attitude. It seems fragile, but powerful invisible forces can live inside it. In chemically strengthened glass, the surface is compressed like a stretched rubber band, while the interior is stretched. When a fast object hits such glass, that rubber band snaps in many places at once. Scientists fired projectiles at glass and watched how it shattered.

A hawk soars over a field, its wings tracing an intricate dance. Each flap, each tilt is not random but a combination of simple motions that can be broken down into components. Collective behavior in the air may seem intuitive, but behind it lies strict mechanics. Scientists recorded the hawks' movements using cameras that track the position of every point on the wing and tail.

A pot of water heated from below is a simple example of turbulence. Hot fluid rises, cold fluid sinks, and the flow spontaneously breaks into rotating cells that look like horizontal rolls. In a new study, physicists took a wide rectangular container (ten times longer than its height) and tracked how many such rolls appear.

When two tectonic plates grind against each other, a layer of pulverized rock ends up between them, like sand between your palms. This layer, which geologists call fault gouge, behaves not like solid rock but like a thick paste: it can compact, dilate, and slide. Whether a fault ruptures in a devastating earthquake or creeps slowly and safely depends on its whims.

In a jar of oily liquid float millions of tiny magnetic grains: each about the size of a bacterium. Switch on a magnet, and the grains, like obedient little soldiers, line up into long threads. But why do they form threads rather than clumps? It turns out it's not just about magnetism.

A drop falls into a glass, and a tiny jet, a thin fountain, shoots up from the surface for an instant. Something similar happens with a bubble stuck to the wall of a tube when you yank the tube downward. Water around the bubble rushes in, and a jet fires from its top. The speed of this jet depends on the bubble's shape — how much it bulges, like an umbrella dome.

Inside every muscle is a team of rowers: myosin proteins that grab actin filaments, take a stroke, and let go. The fuel for the stroke is the ATP molecule. When the rowers work in sync, the muscle contracts and the body moves. For decades, two models existed: one explained why the boat moves slower with increasing load, the other — how the rowers move their arms.

A water droplet races across a taro leaf like a bead on a freshly waxed floor. But it doesn't just glide: it picks up electricity. Thirty years ago, scientists explained why lotus leaves stay dry: their surface is covered with microscopic bumps that trap air. Now it turns out that water on leaves has another, hidden power.