Navier-Stokes equations – Quanta Magazine

Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations

Jordana Cepelewicz — Wed, 16 Nov 2022 15:40:45 +0000

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the weather, design better airplanes, and characterize how blood flows through the circulatory system. These equations are deceptively simple when written in the right mathematical language. However...

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Mathematicians Coax Fluid Equations Into Nonphysical Solutions

Leila Sloman — Mon, 02 May 2022 13:45:49 +0000

For nearly two centuries, all kinds of researchers interested in how fluids flow have turned to the Navier-Stokes equations. But mathematicians still harbor basic questions about them. Foremost among them: How well do the equations adhere to reality? A new paper set to appear in the Annals of Mathematics has chipped away at that question, proving that a once-promising class of solutions can...

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Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations

Jordana Cepelewicz — Tue, 12 Apr 2022 15:36:17 +0000

For more than 250 years, mathematicians have been trying to “blow up” some of the most important equations in physics: those that describe how fluids flow. If they succeed, then they will have discovered a scenario in which those equations break down — a vortex that spins infinitely fast, perhaps, or a current that abruptly stops and starts, or a particle that whips past its neighbors infinitely...

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The Uselessness of Useful Knowledge

Robbert Dijkgraaf — Wed, 20 Oct 2021 14:15:32 +0000

Is artificial intelligence the new alchemy? That is, are the powerful algorithms that control so much of our lives — from internet searches to social media feeds — the modern equivalent of turning lead into gold? Moreover: Would that be such a bad thing? According to the prominent AI researcher Ali Rahimi and others, today’s fashionable neural networks and deep learning techniques are based on a...

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Mathematicians Identify Threshold at Which Shapes Give Way

Mordechai Rorvig — Thu, 03 Jun 2021 13:49:34 +0000

In the 1950s, four decades before he won a Nobel Prize for his contributions to game theory and his story inspired the book and film “A Beautiful Mind,” the mathematician John Nash proved one of the most remarkable results in all of geometry. Among other features, it implied that you could crumple a sphere down to a ball of any size without ever creasing it. He made this possible by inventing a...

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