In his doctoral thesis, Michael Roop develops numerical methods that allow finding physically reliable approximate solutions ...

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

Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

Mathematics is the language that lets us describe the universe. Galileo Galilei was already convinced of that in the 16th century. But even everyday phenomena such as the melting of an ice cube in a ...

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...

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 ...