Transitions are to be found throughout the natural world. The laws of nature are usually
represented by differential equations, which can be regarded as dynamical systems—both …

Our Earth's atmosphere and oceans are rotating geophysical fluids that are two important
components of the planet's climate system. The atmosphere and the oceans are extremely …

The process of phase separation of binary systems is described by the Cahn-Hilliard
equation. The main objective of this article is to give a classification on the dynamic phase …

Geophysical flows comprise a broad range of spatial and temporal scales, from planetary-to
meso-scale and microscopic turbulence regimes. The relation of scales and flow …

We study the stability and dynamic transition of a rotating electrically conducting fluid layer in
the presence of an external magnetic field based on the Boussinesq approximation. By …

Partial differential equations are fundamental tools in mathematics, science, and
engineering. For instance, electrodynamics is governed by the Maxwell equations, the two …

The current article focuses on the examination of nonlinear instability and dynamic
transitions in a double-diffusive rotating couple-stress fluid layer. The analysis was based on …

In this article, we study the dynamic transition of the Rayleigh–Bénard convection with
internal heating and varying gravity. We show that this problem can only undergo a …

In this article, we initiate a program of research to study dynamic phase transitions in
nonlinear sciences. The main objective of this article is two-fold. First, we introduce some …

This article presents a phenomenological dynamic phase transition theory—modeling and
analysis—for liquid helium-4. First we derive a time-dependent Ginzburg–Landau model for …