Phase-field method is a density-based computational method at the mesoscale for modeling
and predicting the temporal microstructure and property evolution during materials …

Mesoscale simulations of blood flow, where the red blood cells are described as deformable
closed shells with a membrane characterized by bending rigidity and stretching elasticity …

In this paper, we study efficient numerical schemes of the classical phase field elastic
bending energy model that has been widely used to describe the shape deformation of …

For the time-fractional phase-field models, the corresponding energy dissipation law has not
been well studied on both the continuous and the discrete levels. In this work, we address …

In this paper, we develop a series of linear, unconditionally energy stable numerical
schemes for solving the classical phase field crystal model. The temporal discretizations are …

This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

In this paper, we consider the numerical solution of a binary fluid–surfactant phase field
model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg–Landau …

In this paper, we study the three-dimensional deformation of a vesicle membrane under the
elastic bending energy, with prescribed bulk volume and surface area. Both static and …

This paper reviews methods and applications of the phase field technique, one of the fastest
growing areas in computational materials science. The phase field method is used as a …

We extend our recent phase-field [T. Biben and C. Misbah, Phys. Rev. E 67, 031908 (2003)]
approach to 3D vesicle dynamics. Unlike the boundary-integral formulations, based on the …