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

We review recent advances in multiscale modeling of the mechanics of healthy and
diseased red blood cells (RBCs), and blood flow in the microcirculation. We cover the …

The phase-field method has become an important and extremely versatile technique for
simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface …

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 …

Cell migration is a pervasive process in many biology systems and involves protrusive
forces generated by actin polymerization, myosin dependent contractile forces, and force …

We develop a computational model, based on the phase-field method, for cell
morphodynamics and apply it to fish keratocytes. Our model incorporates the membrane …

We consider in this paper gradient flows with disparate terms in the free energy that cannot
be efficiently handled with the scalar auxiliary variable (SAV) approach, and we develop the …

The hydrodynamic Q-tensor model has been used for studying flows of liquid crystals and
liquid crystal polymers. It can be derived from a variational approach together with the …

We present efficient, second-order accurate and adaptive finite-difference methods to solve
the regularized, strongly anisotropic Cahn–Hilliard equation in 2D and 3D. When the surface …

We develop a thermodynamically consistent phase-field model to simulate the dynamics of
multicomponent vesicles. The model accounts for bending stiffness, spontaneous curvature …