Fluid dynamics, a cornerstone of applied mathematics and engineering, investigates the behaviour of fluids in motion. Within this broad field, active scalar equations play a pivotal role by ...

The study of quantum dynamics in conjunction with nonlinear Schrödinger equations (NLS) sits at the confluence of mathematical physics, quantum mechanics and nonlinear analysis. This field ...

In the past few decades, the use of phase field-modeling equations for mathematical modeling has progressed. Phase separation has been studied extensively in thermodynamics and materials engineering, ...

Molecular dynamics simulation is a powerful and widely employed computational method that investigates the motion and interactions of molecules under different conditions, revealing the structure, ...

Mathematics is the language that lets us describe the universe. Galileo Galilei was already convinced of that in the 16th century. But even everyday phenomena such as the melting of an ice cube in a ...

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the ...