With automated proof-checkers, a problem can be broken up into small chunks, solved bit-by-bit, then reassembled with confidence that every piece is correct. For some, this heralds a new area in ...

In this article, we investigate damped elastic inclusion systems characterized by nonconvex-valued perturbations, the summation of dual multivalued mappings, and history-dependent operators. By ...

In this work, a finite volume formulation developed for two-dimensional models is extended to deal with axisymmetric models of heat conduction applications. This formulation uses a vertex centered ...

The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the ...

Predicting how complex stochastic systems respond to small external perturbations is central in physics, climate science, and engineering. We combine the generalized fluctuation–dissipation theorem ...

The concept of FDT is rooted in analysis of response relations appearing in systems subject to stimuli and driven away from equilibrium. In a linear response regime, close to equilibrium, use of ...

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 ...

Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade ...