A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer. In 1900, the great mathematician David Hilbert presented a list of 23 unsolved ...

The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous features of the physical world: the flow of fluids. The equations, which date to the 1820s, are today used to ...

We continue our exploration of fluids and fluid dynamics. We continue our exploration of fluids and fluid dynamics. How do fluids act when they're in motion? How does pressure in different places ...

Physics-informed neural networks (PINNs) represent a burgeoning paradigm in computational science, whereby deep learning frameworks are augmented with explicit physical laws to solve both forward and ...

Now, artificial intelligence (AI) tools are providing powerful new ways to address long-standing problems in physics. “The ...

During its teenage and young adult years—what is now referred to as its “classical” period—physics made a lot of mistakes. In the old physics, mass and energy were separately conserved; particles’ ...

The irregular, swirling motion of fluids we call turbulence can be found everywhere, from stirring in a teacup to currents in the planetary atmosphere. This phenomenon is governed by the Navier-Stokes ...