A mathematical problem that had remained unsolved for more than 10 years in the physics of complex systems has finally been ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

The study of reaction–diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of ...

Yet recent direct observations in systems without a large separation of timescales — for example, the diffusion of colloids on phospholipid fluid tubules and in biofilament networks 4, 5 (Fig. 1a) — ...