In this video, we explain the capstan equation and how friction affects a rope or string wrapped around a surface. You’ll learn where the equation comes from, what each term means, and how it’s ...

GPT-5.2 Pro delivers a Lean-verified proof of Erdős Problem 397, marking a shift from pattern-matching AI to autonomous ...

Gas and dust flowing from stars can, under the right conditions, clash with a star's surroundings and create a shock wave.

A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, ...

Solve two Atwood machine problems step by step, including the effects of friction and an inclined plane. Learn how to set up free-body diagrams, apply Newton’s laws, and avoid common mistakes in ...

In this paper, the equation for the gravity wave spectra in mean atmosphere is analytically solved without linearization by the Adomian decomposition method. As a consequence, the nonlinear nature of ...

Abstract: Wave equation-based traveltime inversion is a method that uses traveltime information to obtain the low-wavenumber components of subsurface velocity models. This helps create a reliable ...

Magnetic materials are used to make MRI machines, hard drives, wireless chargers, and phone speakers. It takes a lot of expensive research and development to create new materials. “And there’s no ...

Right now, quantum computers are small and error-prone compared to where they’ll likely be in a few years. Even within those limitations, however, there have been regular claims that the hardware can ...

This paper is devoted to numerically solving the Burgers’ equation in unbounded region, which describes the nonlinear wave propagation and diffusion effect. How to numerically and efficiently solve ...

A new boundary-value technique is proposed for the treatment of initial-boundary-value problems for linear and mildly non-linear wave equations. Several illustrative examples are offered to ...