Recent decades have witnessed a bloom in research at the interface of complex geometry and nonlinear partial differential equations. This interdisciplinary field explores the deep and intricate ...

Complex Hessian equations extend the classical framework of the complex Monge–Ampère equation by involving the m-th elementary symmetric function of the eigenvalues of the complex Hessian. This ...

In theory, almost any aspect of the physical world can be modeled and analyzed mathematically. In practice though, performing the mathematical manipulations required to perform an analysis can rapidly ...

The team has improved the capabilities of physics-informed neural networks (PINNs), a type of artificial intelligence that incorporates physical laws into the learning process. Researchers from the ...

This chaotic-looking "double pendulum" follows a large number of rules that govern its motion. Researchers have trained AI to take data from its movements to uncover simple equations that successfully ...

(Nanowerk Spotlight) As our digital devices handle increasingly complex computations, scientists have looked to physics for inspiration on new computing paradigms. Rather than shuttling electrical ...

A team of engineers has proven that their analog computing device, called a memristor, can complete complex, scientific computing tasks while bypassing the limitations of digital computing. A team of ...