How Emmy Noether's theorem uses the Lagrangian to provide a formula for calculating the quantity of symmetries in a ...

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 ...

Structural complexity of patterns, systems, and processes is a very basic and intuitively clear concept in human’s perception of reality that is very difficult to describe quantitatively. A demand in ...

Computational contact mechanics seeks for numerical solutions to contact area, pressure, deformation, and stresses, as well as flash temperature, in response to the interaction of two bodies. The ...

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) — ...