Two novel and efficient modified techniques based on recently developed stabilized
invariant energy quadratization (IEQ) approach to deal with nonlinear terms in gradient flows …

The effect of ultrasonication on the solidification microstructure of recycled Al-alloys is
investigated using custom Al–2Si–2Mg–1.2 Fe–xMn alloys (x= 0.5 and 1%, in wt.%) through …

Comparing with the classical local gradient flow and phase field models, the nonlocal
models such as nonlocal Cahn–Hilliard equations equipped with nonlocal diffusion operator …

The phase-field crystal equation is a sixth-order nonlinear parabolic equation and have
received increasing attention in the study of the microstructural evolution of two-phase …

We develop efficient energy stable numerical methods for solving isotropic and strongly
anisotropic Cahn–Hilliard systems with the Willmore regularization. The scheme, which …

Al-Si alloys processed by laser rapid solidification yield eutectic microstructures with
ultrafine and interconnected fibers. Such fibrous structures have long been thought to bear …

Three-dimensional phase-field simulations are performed to follow the formation of facets at
the surface of a silicon crystal in contact with its melt. We focus on the anisotropies of both …

Here we use phase field to model and simulate “hopper” crystals, so named because of their
underlying cubic structure but with a hopper-like depression on each of the six faces. Over …

The growth of faceted crystals occurs often in nature and industry, involving often the
presence of flow. The growth of faceted crystals is the result of interface kinetics and …

In this paper, we introduce a high-precision Hermite neural network solver which employs
Hermite interpolation technique to construct high-order explicit approximation schemes for …