The phase field method for geometric moving interfaces and their numerical approximations
This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …
surface evolution and related geometric nonlinear partial differential equations (PDEs) …
Modeling membrane curvature generation due to membrane–protein interactions
H Alimohamadi, P Rangamani - Biomolecules, 2018 - mdpi.com
To alter and adjust the shape of the plasma membrane, cells harness various mechanisms
of curvature generation. Many of these curvature generation mechanisms rely on the …
of curvature generation. Many of these curvature generation mechanisms rely on the …
Efficient linear schemes with unconditional energy stability for the phase field elastic bending energy model
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 …
bending energy model that has been widely used to describe the shape deformation of …
Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model
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 …
be efficiently handled with the scalar auxiliary variable (SAV) approach, and we develop the …
Numerical approximations of the Navier–Stokes equation coupled with volume-conserved multi-phase-field vesicles system: fully-decoupled, linear, unconditionally …
X Yang - Computer Methods in Applied Mechanics and …, 2021 - Elsevier
We consider the numerical approximation of the flow-coupled multi-phase-field elastic
bending energy model of lipid vesicles. Based on the classical model with approximate …
bending energy model of lipid vesicles. Based on the classical model with approximate …
Numerical analysis of second order, fully discrete energy stable schemes for phase field models of two-phase incompressible flows
In this paper, we propose several second order in time, fully discrete, linear and nonlinear
numerical schemes for solving the phase field model of two-phase incompressible flows, in …
numerical schemes for solving the phase field model of two-phase incompressible flows, in …
A novel fully-decoupled, second-order time-accurate, unconditionally energy stable scheme for a flow-coupled volume-conserved phase-field elastic bending energy …
X Yang - Journal of Computational Physics, 2021 - Elsevier
Different from the classical phase-field elastic bending model of lipid vesicles that uses a
penalty term to conserve volume approximately, in this paper, a new model with accurate …
penalty term to conserve volume approximately, in this paper, a new model with accurate …
A numerical method for the quasi-incompressible Cahn–Hilliard–Navier–Stokes equations for variable density flows with a discrete energy law
In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes
equation with fluid–fluid interface when the fluids have different densities [48]. Under minor …
equation with fluid–fluid interface when the fluids have different densities [48]. Under minor …
Computational approaches to substrate-based cell motility
F Ziebert, IS Aranson - npj Computational Materials, 2016 - nature.com
Substrate-based crawling motility of eukaryotic cells is essential for many biological
functions, both in developing and mature organisms. Motility dysfunctions are involved in …
functions, both in developing and mature organisms. Motility dysfunctions are involved in …
Efficient and stable exponential time differencing Runge–Kutta methods for phase field elastic bending energy models
The Willmore flow formulated by phase field dynamics based on the elastic bending energy
model has been widely used to describe the shape transformation of biological lipid …
model has been widely used to describe the shape transformation of biological lipid …