Proceedings of the National Academy of Sciences · 20 August 2026 · From issue 24

Stochastic theory for pattern formation and front propagation in transitional pipe turbulence

One math model explains three different turbulence patterns seen in pipe flow experiments.

Xueying Wang, Hong-Yan Shih et al.

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A tribute article honors botanist Peter Raven's decades of research and conservation leadership.
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A laser mapped four hiding spots for radioactive thorium atoms inside a crystal.
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One rice gene variant grows plants faster and produces more grain at once.
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