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 ...

Stochastic fluid dynamics extends classical fluid mechanics by incorporating randomness and uncertainty directly into the governing equations. This approach utilises stochastic differential equations ...

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 ...

Scientific progress is not usually straightforward. Researchers pursue and abandon lines of inquiry. Results languish. Theories take decades to cohere. But sometimes the accumulation of scientific ...

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 ...

Mathematicians have suspected for years that under specific circumstances, the Euler equations fail. But they've been unable to identify an exact scenario in which this failure occurs. Until now. The ...

Tests of a proposed friction-factor equation have shown it to be accurate for calculating pressure loss in turbulent flow for a pipeline transporting a non-Newtonian fluid, such as most crude oils and ...