相关论文: Existence results for diffuse interface models des…
A fully discrete semi-convex-splitting finite-element scheme with stabilization for a Cahn-Hilliard cross-diffusion system is analyzed. The system consists of parabolic fourth-order equations for the volume fraction of the fiber phase and…
We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…
If the Electroweak Symmetry Breaking Sector turns out to be strongly interacting, the actively investigated effective theory for longitudinal gauge bosons plus Higgs can be efficiently extended to cover the regime of saturation of unitarity…
We consider a fluid-structure interaction problem in the Eulerian, phase-field formulation. The problem is described using the Navier--Stokes equations for a viscous, incompressible fluid, coupled with the incompressible hyperelasticity…
The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we…
We give a complete and rigorous derivation of the mechanical energy for twisted 2D bilayer heterostructures without any approximation beyond the existence of an empirical many-body site energy. Our results apply to both the continuous and…
This paper is devoted to the numerical study of droplet impact on solid substrates in presence of surfactants. We formulate the problem in an energetically variational framework and introduce an incompressible Cahn-Hilliard-Navier-Stokes…
The formation of codimension-one interfaces for multi-well gradient-driven problems is well-known and established in the scalar case, where the equation is often referred to as the Allen-Cahn equation. The proofs rely for a large on a…
This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is introduced and studied. The model describes some mechanisms…
We develop a novel finite element method for a phase field model of nematic liquid crystal droplets. The continuous model considers a free energy comprised of three components: the Ericksen's energy for liquid crystals, the Cahn-Hilliard…
We study the well-posedness of a modified degenerate Cahn-Hilliard type model for surface diffusion. With degenerate phase-dependent diffusion mobility and additional stabilizing function, this model is able to give the correct sharp…
We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…
We focus on the derivation and analysis of a model for multi-component phase separation occurring on biological membranes, inspired by observations of lipid raft formation. The model integrates local membrane composition with local membrane…
We consider phase-field models with and without lateral flow for the numerical simulation of lateral phase separation and coarsening in lipid membranes. For the numerical solution of these models, we apply an unfitted finite element method…
We prove existence of weak solutions and weak-strong uniqueness for a mathematical model which couples the evolution of a phase-parameter $\varphi$ satisfying a Cahn-Hilliard type relation with the one of an additional variable $\sigma$…
We present and analyze an unconditionally energy stable and convergent finite difference scheme for the Functionalized Cahn-Hilliard equation. One key difficulty associated with the energy stability is based on the fact that one nonlinear…
We consider coarsening dynamics associated with a Burgers--Cahn--Hilliard system modeling a two-phase flow in one space dimension. Our emphasis is on the effect that coupling between the phase and fluid dynamics has on coarsening rates, and…
We present an adaptive simulation framework for binary-fluid flows, based on the Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard (AGG NSCH) diffuse-interface model. The adaptive-refinement procedure is guided by a two-level hierarchical…
We prove the existence of weak solutions to a viscoelastic phase separation problem in two space dimensions. The mathematical model consists of a Cahn-Hilliard-type equation for two-phase flows and the Peterlin-Navier-Stokes equations for…
We propose and investigate a model for lipid raft formation and dynamics in biological membranes. The model describes the lipid composition of the membrane and an interaction with cholesterol. To account for cholesterol exchange between…