Vortices play a fundamental role in the physics of two-dimensional (2D) fluids across range length scales, from quantum superfluids to geophysical flows. Despite history dating back Helmholtz, point vortices 2D fluid continue pose interesting theoretical problems, owing their unusual statistical mechanics. Here we show that strongly interacting Helmholtz-Onsager vortex systems can form edge mod...

Machine learning is becoming an increasingly popular method for building mathematical models from observations of natural processes. Here, the central challenge to impart structure into model parameterization enforce physical relevance, yet retain a degree generality so that large variety dynamics can be learned. We introduce novel methodology, based on data-driven extension classical Onsager p...

In this note, necessary and sufficient conditions for the existence of an entropy structure certain classes cross-diffusion systems with diffusion matrix A ( u ) are given, based on results from factorization. The is important in analysis such equations since typically neither symmetric nor positive definite. particular, normal ellipticity all symmetry Onsager implies its definiteness hence str...