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fluid dynamics

A ring of bubbles in blue water.
fluid dynamics

Mathematicians Coax Fluid Equations Into Nonphysical Solutions

By Leila Sloman
May 2, 2022
Read Later

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

Simulated water particles swirl in an upward vortex.
mathematical physics

Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations

By Jordana Cepelewicz
April 12, 2022
Read Later

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near.

Fluorescent purple liquid splashes.
fluid dynamics

An Injection of Chaos Solves Decades-Old Fluid Mystery

By Adam Mann
January 4, 2022
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In the 1960s, drillers noticed that certain fluids would firm up if they flowed too fast. Researchers have finally explained why.

A GIF of ice melting in a glass of water
mathematical physics

Mathematicians Prove Melting Ice Stays Smooth

By Mordechai Rorvig
October 6, 2021
Read Later

After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.

A GIF showing increasingly more twists being added to the curves on a sphere.
geometry

Mathematicians Identify Threshold at Which Shapes Give Way

By Mordechai Rorvig
June 3, 2021
Read Later

A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.

An animation showing chaotic swirls of purple coalesce into a single line
Abstractions blog

New Quantum Algorithms Finally Crack Nonlinear Equations

By Max G. Levy
January 5, 2021
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Two teams found different ways for quantum computers to process nonlinear systems by first disguising them as linear ones.

Mathematician Lauren Williams standing in front of a whiteboard that has mathematics written on it.
combinatorics

A Mathematician’s Unanticipated Journey Through the Physical World

By Kevin Hartnett
December 16, 2020
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Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

fluid vortices
fluid dynamics

An Unexpected Twist Lights Up the Secrets of Turbulence

By David H. Freedman
September 3, 2020
Read Later

Having solved a central mystery about the “twirliness” of tornadoes and other types of vortices, William Irvine has set his sights on turbulence, the white whale of classical physics.

Multimedia

The Map of Mathematics

By Kevin Hartnett
February 13, 2020
Read Later

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.


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