nonlinear dynamics – Quanta Magazine

New Proof Shows That ‘Expander’ Graphs Synchronize

Leila Sloman — Mon, 24 Jul 2023 14:36:23 +0000

Six years ago, Afonso Bandeira and Shuyang Ling were attempting to come up with a better way to discern clusters in enormous data sets when they stumbled into a surreal world. Ling realized that the equations they’d come up with were, unexpectedly, a perfect match for a mathematical model of spontaneous synchronization. Spontaneous synchronization is a phenomenon in which oscillators...

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What Causes Giant Rogue Waves?

Steven Strogatz — Wed, 14 Jun 2023 18:36:20 +0000

Sailors have spun yarns for centuries about gigantic rogue waves that could suddenly come out of nowhere to capsize the ships of unwary mariners. Scientists didn’t believe them because the stories seemed at odds with everything else known about waves. Then cameras and other instruments began to capture undeniable proof of the existence of rogue waves. Ton van den Bremer, an expert in fluid...

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New Proof Finds the ‘Ultimate Instability’ in a Solar System Model

Jordana Cepelewicz — Tue, 16 May 2023 14:05:08 +0000

In 2009, a pair of astronomers at the Paris Observatory announced a startling discovery. After building a detailed computational model of our solar system, they ran thousands of numerical simulations, projecting the motions of the planets billions of years into the future. In most of those simulations — which varied Mercury’s starting point over a range of just under 1 meter — everything proceeded...

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Hidden Chaos Found to Lurk in Ecosystems

Joanna Thompson — Wed, 27 Jul 2022 13:29:09 +0000

Physical scientists seem to find the phenomenon of chaos everywhere: in the orbits of planets, in weather systems, in a river’s swirling eddies. For nearly three decades, ecologists considered chaos in the living world to be surprisingly rare by comparison. A new analysis, however, reveals that chaos is far more prevalent in ecosystems than researchers thought. Tanya Rogers was looking back...

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New Quantum Algorithms Finally Crack Nonlinear Equations

Max G. Levy — Tue, 05 Jan 2021 16:45:27 +0000

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what mathematicians call linear differential equations. But in nonlinear systems, interactions can affect themselves: When air streams past a jet’s wings, the air flow alters molecular interactions...

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