Researchers identify a hidden instability pattern in simple ocean wave models

Learn how natural systems exhibit characteristics of chaos theory

In biology, some mathematical models of ecosystem populations and heart irregularities show strong sensitivity to initial conditions, which scientists can simulate to determine quantitative tipping points at which these systems become unstable. Within the social sciences, crowd behavior and the virality of social media posts have shown how human behavior fits within the framework of chaos theory.

When experiencing turbulence, fluid elements undergo stretching and folding

Simulations show patches of fluid particles, such as splashes of milk, bend under turbulent flow, creating curvature that grows linearly then exponentially. This accelerated deformation enhances folding and mixing faster than other methods, such as stirring or beating.

Hurricane conditions are created in a University of Miami wind-wave tank

The SUrge-STructure-Atmosphere INteraction Wind Wave Laboratory contains a 38,000-gallon wave pool connected to a wind tunnel that can generate air currents of up to 155 mph. SUSTAIN allows scientists to study how the atmosphere interacts with the ocean in extreme weather.

The Navier-Stokes equations are fundamentally accurate but unsolved in 3D

The equations model fluids and have been shown to have solutions for all systems in two dimensions. Averaging and approximations let the equations be used in climate models, aerodynamics, and medicine, though their use in some systems produces nonsensical answers.

As of 2025, wave power projects remain in early research and testing phases

Waves can become a steady source of renewable energy because they do not pause like wind and solar power do. However, funding gaps and the effects of storms, salt exposure, and biofouling—mussels and other sea creatures attaching to wave machines—have presented challenges in scaling the technology beyond testing sites.

Symmetric patterns of magnetic stripes seen on either side of mid-ocean ridges

The symmetry provides evidence of seafloor spreading, where new oceanic crust is created at mid-ocean ridges, which pushes older ocean crust away on either side. Matching the pattern to magnetized material in rocks on Earth’s surface provided a timeline of ocean floor recycling.

How a competition honoring a king's birthday uncovered history's first chaotic system

A committee established a contest for King Oscar II's 60th birthday, featuring four unsolved problems in mathematics, including one on proving the stability of a system of more than two objects held together by gravity. Focusing on three celestial objects, Henri Poincaré won the prize for his proof, which he later learned was incorrect and, upon correcting it, instead proved these systems to be unstable.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

Sharp wave ripples in the brain tag experiences for long-term memory storage

These ripples were known to quickly replay neuronal sequences during sleep for consolidation. While awake, they help the brain prioritize memories to remember, and their disruption can impair memory formation.

See an anamorphic illusion of a massive crashing wave in South Korea

An enormous aquarium with perpetually crashing waves has popped up amidst an urban landscape in South Korea, but don’t expect to hear the water sloshing around if you walk by. Designed by District, the elevated tank is actually a massive anamorphic illusion. The digital media company created the pub

The story of two female programmers running the simulations behind chaos theory's discovery

Margaret Hamilton and Ellen Fetter worked on MIT's 800-pound Royal McBee LGP-30 computer, which was fed binary code on paper tape to perform computations. Among the computations performed were those involving equations describing the motion of gas in a circulating fluid for Edward Lorenz, widely considered the father of chaos theory.

Studying 'sonic' black holes

If a fish screams as it falls down a cascading waterfall accelerating to ridiculous speeds, will his fish friends above hear him scream? This analogy, odd as it is, has become an essential tool in the astrophysicists kit for learning how enigmatic black holes operate. Lab experiments mirroring the so-called sonic black hole have achieved insights for their cosmic counterparts. Read how it works in this brief piece.

The lifecycle of a financial bubble often follows a predictable pattern

Economist Hyman Minsky originated what became a five-stage model of an economic bubble: a new “displacement,” a rapid boom, euphoric speculation, early profit-taking by insiders, and finally panic selling. From Japan’s 1980s real-estate surge to the 2008 crash, the pattern repeats across eras and assets.

View the quantum mechanical depiction of electrons as waves around the atomic nucleus

Unlike Bohr's fixed paths, the quantum model describes electrons as exhibiting behavior resembling standing waves—waves that have fixed points at the end while vibrating, like a plucked guitar string. Rather than determining their exact positions, only the probabilities of electrons being in a specific region can be determined.

In 1974, a pair of neutron stars provided the first evidence of gravitational waves

Observations of a pulsar—a rapidly rotating neutron star that emits light—revealed it to be part of a system of two stars that orbited one another in a shrinking orbit, indicating gradual energy loss. Calculations showed that the changing orbit was consistent with gravitational waves predicted to carry energy away from such a system.

Ancient sunken plates may influence mantle convection and surface motion

Research suggests sunken tectonic plates can collide, assemble, and break apart to form structures called large low-velocity provinces. LLVPs can significantly enrich rising magma plumes with elements commonly seen on Earth’s surface.

How math whizzes exploit sportsbooks

Chris Dirkus is a professional sports bettor who approaches the hobby as a math problem, not from a fan's perspective. He focuses on mispriced odds in popular games where many fans are betting for high liquidity. He's one of a rare segment of sports bettors exploiting slow models and human mistakes.

The weakening of dark energy suggests a dynamic universe with evolving forces

The discovery, which came from analyzing extensive data from a major cosmological survey, challenges the assumed constancy of dark energy in modern physics. Understanding dark energy's behavior is crucial for predicting the universe's long-term evolution.

Why the ratios of helium isotopes are analyzed to investigate ocean circulation

Volcanic activity on the seafloor produces high ratios of helium-3 to helium-4, which can be tracked in ocean samples more easily than other elements because helium is nonreactive. Water from deep ocean currents can also be distinguished from air-exposed surface water sources by comparing these ratios, since atmospheric helium ratios are much lower.

The four types of seismic waves are categorized as body or surface waves

Primary (P) and secondary (S) waves are compression and shear waves, respectively, and travel through Earth’s interior, though secondary waves only move through solids. These waves’ energy is converted into rolling Rayleigh or horizontal Love waves at the surface.

Light waves can interfere and cancel each other out

When light waves travel past one another, their peaks and valleys combine, just as overlapping ripples in water can combine to form a larger ripple. When the peak of a light wave meets the valley of another of the same wavelength and brightness, the waves combine to produce no light.

The most bizarre numbers in the universe

Even for math-y types, some numbers are incomprehensible. This article dives into several kinds of numbers more complicated than even irrational numbers with endless decimals like "pi" or Euler's number: Noncomputable numbers. Read the bizarre...

Waves off the coast of Nazaré, Portugal, can reach over 100 feet and are caused by the area's deep underwater canyon geography

The fast Fourier transform breaks down wave signals into discrete components

The algorithm was initially discovered by German mathematician Carl Friedrich Gauss in 1805, but his notes were not found until after his death. Today, FFTs form the basis for most compression software in media and are essential to technologies such as radar, sonar, and telecommunications.

The magic angle to skip a spinning stone is 20 degrees

The traditional shoreside activity—reputedly practiced by luminaries Shakespeare and Homer—can be broken down into its bare physics, from hydrodynamics and momentum to gravity.

How the moon creates tides

Anyone who has visited large bodies of water virtually anywhere on Earth notices low and high tides occur at regular intervals, a process primarily driven by the moon’s gravitational pull. This explainer details how the motion of the Earth and Moon interact to create tides.

Deep sea fish rely on a molecular strengthener to prevent being crushed

Trimethylamine N-oxide (TMAO) stabilizes hydrogen bonds and prevents water and proteins within organisms from being misshapen under immense pressure. Compounds called piezolytes protect cellular membranes from being crushed in regions like the Mariana Trench, where pressures are 1,100 times greater than surface atmospheric pressure.

Fish populations in the Great Barrier Reef have increased after installing waterproof speakers on the ocean floor that played recordings of sounds from healthy coral reefs.

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

All rainbows are 'raincircles' caused by water droplets separating white sunlight into a spectrum of colors, but Earth's surface blocks the bottom half of the circle from our line of sight.

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

How Amazon operates a 'flywheel' business model, a self-reinforcing cycle that drives continuous growth

Pure water does not conduct electricity because this flow of energy requires the movement of charged particles, and water is a neutral molecule.

While the sun's gravity keeps the planets in orbit, their gravity also pulls on the sun, causing it and everything else in the solar system to orbit around a mutual balance point called the barycenter—the true center of the solar system.

Hedge funds, the private investment firms that trade a wide swath of financial assets, make money by imposing steep fees on investors and from the fund's investment performance.

While El Niño moves warm Pacific Ocean waters east along the equator, La Niña moves them west, shifting where rainfall will become more common for months.

Volcanoes 'die' when their supply of magma runs out, if they are shifted away from their underlying magma reservoir, or if they get clogged by collapsing or their magma cooling back into rock.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Scientists can determine Earth's past climate conditions by analyzing air trapped in microscopic bubbles within ice cores—columns of compressed snow layers that build up over hundreds of thousands of years.

To reduce wrinkles in clothing, research recommends gentle wash cycles with more water and tumble drying with smaller loads and longer times.

Stanford built a Google Maps for the Roman Empire, revealing how much it cost to travel in the ancient world

Some renewable energy sources may weaken the resiliency of electric grids by removing outage buffers provided by coal- and natural gas-fired plants, which provide the system with more time to find a new power source if a plant goes down.

US consumers collectively owe more than $1T to credit card companies—almost as much as they owe in auto loans.

SpongeBob exemplifies Aristotle's philosophy for living well because he understands that happiness doesn't come from external factors like money, recognition, or power.

Gerrymandering works through two techniques: cracking opposing voters across districts to dilute their power, and packing them into a few to waste their votes in lopsided majorities.

In 2009, the nation was gripped by the story of a missing young boy who was believed to be floating over Colorado in a homemade balloon, until it was revealed that he was at home the whole time.

The 1987 Nintendo video game 'Stadium Events' isn't known for being particularly fun, but its scarcity has made it a highly sought-after item that has sold for up to $35K at auction.

The Mona Lisa's celebrity status and repeated restorations have obscured what made the painting so revolutionary for its time

Brian Wilson wrote the Beach Boys' 'Don't Worry Baby' for the Ronettes, but the legendary girl group rejected it.

Hookworm infection, though risky, may help fight certain autoimmune conditions by tamping down the immune system's inflammatory response.